U.S.  ENVIRONMENTAL.PROTECTION AGENCY

                    Region IX Laboratory

                     620 Central Avenue

                 Alameda, California  94501

       SELECTED FIELD AND LABORATORY BIOLOGY METHODS

                      Table of Contents


  I.   Sample Collection

 II.   Sample Collection Forms

III.   Algal Bioassays

      A.   Laboratory Bioassay Directions

      B.   Cell Mass Measurement

      C.   Measuring Dry Weight

      D.   Measuring Algal Chlorophyll

      E.   Maintaining Algal Cultures in the Laboratory

 IV.   Statistical Procedures

  V.   Fish Bioassays

 VI.   Use of Random Numbers

VII.   Appendix

          Tables of Useful Data
Prepared by Milton G. Tunzi, Ph.D., EPA Laboratory
620 Central Avenue, Alameda, California 94501
(Comments and corrections would be appreciated)
First Edition October 1973
Second Edition February 1974

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Page Intentionally Blank

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                                                        11758
            U.S. ENVIRONMENTAL PROTECTION AGENCY

                    Region IX Laboratory

                     620 Central Avenue

                 Alameda, California  94501

        SELECTED FIELD AMD LABORATORY BIOLOGY METHODS

                      Table of Contents


  I.  Sample Collection

 II.  Sample Collection Forms

III.  Algal Bioassays

      A.  Laboratory Bioassay Directions

      B.  Cell Mass Measurement

      C.  Measuring Dry Weight

      D.  Measuring Algal Chlorophyll

      E.  Maintaining Algal Cultures in the Laboratory

 IV.  Statistical Procedures

  V.  Fish Bioassays

 VI.  Use of Random Numbers

VII.  Appendix

          Tables of Useful Data
Prepared by Milton G. Tunzi,  Ph.D.,  EPA Laboratory
620 Central Avenue, Alameda,  California 94501
(Comments and corrections would be appreciated)
First Edition October 1973
Second Edition February 1974

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I.  Sample Collection

        Representative samples from any body of water
   are difficult to take.  Directions can be given for a
   completely statistically valid approach (e.g., random
   sampling), but these would probably be beyond the
   resources  of most laboratories.  Furthermore, the
   approach should be determined in relation to the
   purposes of the study.  This may preclude a random-
   sampling approach or make it unnecessary.

        One of the best ways to assure that a sample is
   representative of a site (whether that site be chosen
   randomly as indicated above or arbitrarily as in this
   section) is to composite 3 or 4 or more equal-volume
   samples from each site.  These can be put into a
   plastic bucket, mixed, and a container filled from
   this bucket.

   A.    Routine Sampling

        1.   Generally, the specific sampling sites are
             chosen because they are accessible, equally
             distant from each other, traditional
             sampling sites, or in locations of importance
             near dischargers or in areas of water use.
             Samples may be taken above and below a dis-
             charge pipe, or they may be taken in the
             receiving water near the discharge pipe.
             Many times the location selected is one
             where a water quality standard may be
             exceeded.

        2.   Rivers, streams,  estuaries

             Sites can be sampled from different depths,
             from different locations around the sides
             of a relatively-stationary large boat,
             and from different locations if a small boat
             is allowed to drift.  Water moving past an

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     anchored boat can be sampled every half-
     minute,  or longer time interval depending
     on time  limitations at the station.  A
     stream should also be sampled in this way
     from the bank, i.e., with samples taken from
     the stream throughout a given time period
     and composited.   A wide-month, liter,
     plastic  container attached to a pole can
     be used  to reach further from shore so that
     flowing  water can be more easily sampled,
     or so that the moving part of a stream can be
     reached.  A wide stream which is not above
     boot-top in depth can be sampled by sub-
     samples  from 4 or 5 locations in a transect
     across the stream.  The subsamples must be
     taken upstream so that they will not be
     contaminated by the stream bottom stirred
     up from  walking.

     Compositing samples is suggested because
     then fewer samples would have to be analyzed.
     However, if variations within time or a
     small space are desired, then the samples
     could be kept discrete, i.e., not composited.
     Spatial  or temporal variations at one one or
     more stations can then be used in statistical
     comparisons between the stations.

3.    Lakes, reservoirs, and ponds

     If five  individual samples for nitrate
     analysis are to be taken from five-acre
     Lake X whose water is being mixed thoroughly
     (e.g., because of fall turnover), then one
     might choose locations so that all parts of
     the Lake would be represented.   (Figure  1).

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          Figure 1.  Lake X, Divided into Sections,
          Five Stations Shown.

          In fact, one could take several samples in
          the area where he was to sample the single
          station and composite the several samples.
          For example, four or five subsamples could
          be taken in an area near sampling Station 1
          (indicated on Figure 1 by circle),  and the
          composited sample would represent Station 1.
          The compositing can be done from sample
          taken at different lake depths.  This com-
          positing approach is very useful where little
          time can be allotted to the execution of the
          sampling or where the project does not
          require a more sophisticated approach.

B.    Random Sampling

     Because of such variations as density, light
     penetration differences and the like, most
     waters would require a stratified random sampling
     approach.

     1.    Random Sampling, Spatial Approach

          First the water body is arbitrarily divided
          into areas which are physically or geogra-
          phically distinct.  Then each area is divided
          into a grid pattern, and each section is
          numbered.  The sections to be sampled in each
          area are selected by using a random numbers
          table.  Only 2 or 3 locations are sampled in
          each physically or geographically distinct
          lake area.  The same number of sections can
          be sampled in each area if the areas are
          approximately of the same size.  The total
          number of samples would depend on resources
          and availability.

          If a long channel is to be randomly sampled,
          it can be divided into separate sections each

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                                                      4.
          with its own subsections.  The difficulty
          with the subsection approach is that the
          areas are hard to delimit on the water, as
          there are no lines marked on the water surface.

     2.   Other random sampling approaches.  As an
          alternative to a spatial design, temporal
          considerations also may be important.  Time
          intervals also can be selected randomly with
          a new set of sections again selected by means
          of a random number table each time samples
          are taken.

          A given approach may be suitable for one type
          of measurement and not for another.  Such
          factors as water movement, animal migration,
          and diurnal fluctuations cannot be overlooked
          in designing proper sampling.

C.   Tests for Random Distribution

          There are several ways in which a biological
     parameter can be tested to see if it is randomly
     distributed.  The simplest way would be to compare
     the variance and means of samples taken from an
     area.  Table 1 shows the significance of three
     such comparisons: S2 = X; S2^>X; s2
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                                                           5.
               The main advantages of a random distribution in
          a comparison of samples or in making statements
          about parameters is that confidence limits can
          be set which will delimit the true mean.   However,
          if just a "yes or no"  answer is required  about
          whether there is a difference between samples,
          then non-parametrical  statistical approaches can
          be used for both randomly and non-randomly
          distributed parameters.

     D.    Non-parametric Statistics

               These procedures  are very useful because
          no presumptions are made about sampling techniques,
          analytical methods, time of collection and, of
          course, distribution of the parameter.  Further-
          more, they are usually simpler tc calculate than
          the parametric tests.   At the selected probability
          level, the results of  the test give an answer
          to the question of whether or not there is a
          difference among the compared sampled means.
          Confidence limits containing the true population
          mean cannot be calculated using these tests.
          This is one of their main drawbacks.  Suggested
          tests are below.  The  Kruskal-Wallis test is
          given in the Statistical Section.  The others
          can be found in the references.
Test
Mann-Whitney U - Test
Kruskal-Wallis Test
An alternative to the t - test
Sample numbers do not have to
be equal

Comparable to a one-way analysis
of variance.  Two or more
samples can be compared.  As
above sample numbers do not
have to be equal

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                                                           6.
Wilcoxon's Signed Rank Test    Use for detecting differences
                               in paired samples

Spearman Rank - Correlation    This is the alternative to
  Coefficient  (rs)             calculating the correlation
                               coefficient for bivariate
                               normal distributions  (r)
                          References

Elliot, J. M., 1971.  Some Methods for the Statistical
     Analysis of samples of Benthic Invertebrates.
     Scientific Publ. No. 25, Freshwater Biological
     Association.  Ambleside, Westmorland, England.
     144 pp.

Snedecor, G. W. and W. G. Cochran.  1962.  Statistical
     Methods.  Iowa State Univ. Press. Ames, Iowa.  534 pp.

Steel, R. G. D. and J. H. Torrie.  Priciples and Procedures
     of Statistics.  McGraw-Hill Book Co., Inc., New York.
     481 pp.

Woolf, C. M.  1968.  Principles of Biometry.  D. Van Nostrand
     Co, Inc., Princeton, N. J.  359 pp.

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Table 1 Significance of the variance and mean.
measurement as indicated.
                            Transform by converting each X
Conditions of
the Samples
 2   - (1)
   = x
S2x
Distribution

Random (Poisson
Statistical
Approach

Use parametic
statistics
Uniform, Regular
(Underdispersion or
evenly spaced)

Contagious, Overdispersion
(clumped or aggregated)
Use non-parametric
statistics
Use non-parametric
statistics or
transform so than
S2 = x
     f\   _
(1) S  = x means approximately equal
Transformation

If numbers are low
transform each value
x = •/ x  or x =
 v/x + 1 if O's are
encountered

None used
Commonly encountered
x = logio x or
x = Iog10  (X + 1),
x is less than 1.0
If upon transformation of the data,  the variance is approximately equal to the mean then
the data can be used in mormal statistical procedures such as t-tests, analysis of
variance,  single and multiple regressions and correlations, analysis of covariance, etc.

S2 is the variance
x is the mean
S is the standard deviation

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II.  Sample Collection Forms

         On subsequent pages are sample collection forms,
    including directions for sample preservation.   The
    sample preservation information is mostly from the
    EPA "Methods for Chemical Analysis of Water and
    Wastewater"; however,  the determinations for which
    the same preservatives are used are placed conti-
    guously.

         The forms are suggestions only and can be modi-
    fied according to needs.

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B.
                SAMPLE COLLECTION FORM

                     INSTRUCTIONS

 Project Director - Indicate measurements, location, date,
 sample points,  sampler, time, samples to be taken and
 whether composite or grab.  Indicate composite frequency.
 Check off these items on Sample Collection Form (one per
 sample).

 Sampler - On same form fill in field data, correct date,
 and time of sampling if this information is different from
 that entered by Project Director (I).
                     x x x x x x x
Location
                                           Date
                                               Time
Sample Point

Sampler(s)
Field Measurements

	  Flow	

     DO
     Settleable Solids
                                    Clarity

                                    PH	
     Specific Conductance
                                    Chlorophyll	
                                    (mis filtered)
 ,1.
          BOD
          COD
          Coliform, Total
          Nitrogen, Total
          NH3-N
          NO3-N
          N02-N
          Odor
          Oil and Grease
          Phenol
          Phosphorus, Total
          Cyanide
C
G
Composite
Grab
Remarks:  I.  Project Director

         II.  Sampler	
                               Suspended Solids
                               Total Solids
                               Volatile Solids
                               Sulfide
                               Total Organic
                                  Carbon
                               Turbidity
                               Pesticides
                               Oil Spill Sample
                               Fish Bioassays
                               Algal Bioassays
                               Benthic Sample
Heavy Metals
  Arsenic
  Chromium
  Copper
  Cadmium
  Iron
  Lead
  Mercury
  Nickel
  Zinc
Specific
  Conductance
Others
(See reverse side and attached pages for sample size, preservative and
container type)

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                                                              3.
           Check Equipment to be Taken for Sampling
(Always take - distilled water or deionized water, jugs, cubi-
tainers, preservatives, rubber bulbs, Van Dorn Bottler or
Kemmerer Sampler, pipettes, squeeze bottles, plastic bucket,
rope, thermometer, towels, record book and/or Sample Collection
Forms.)
          Flow - flow meter, weir apparatus
          DO - DO meter, buret, reagents, thiosulfate soln.,
          starch, beaker, BOD bottles

          Specific conductance - meter, 2 cells  (constants of
          2x and lOx)

          Clarity - Secchi disk and line

          Benthic Samples - dredges, container, formalin

          Chlorophyll - GF/C filters, filter flask, vacuum
          pump (hand or electric), desiccant jars, styrofoam
          container, ice

          Algal count - container, formalin
Other Samples                  Number of Containers

	  Glass jugs           	

	  Cubitainers          	

	  Wide mouth plastic   	
          jars
Preservatives, etc.
          Styrofoam container and ice
          Mailing container
          H2SO4
          10 N NaOH
          HN03
          CuS04 + H3P04
          HgCl2 (Saturated solution)
          2N Zn acetate
          1:1 HNO3

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                                                                4.
Container*
NA

Glass
NA
Cub.
or
Gl.
Parameter
Dissolved
Oxygen
Dissolved
Oxygen
(by
titration)
pH, tempera-
ture, Settable
solids, clarity
Metals, Total
(one or all
can be analyzed
Preservative
Determine on
site
2 ml MnS04 +
2 ml ALK-I
Determine on
site
5 ml HNOs
per liter
Holding
Period
NA

4-8 hours
NA
6 months
Volume
Needed
NA

300 ml
NA
(For all
paramete
1 quart
Gl.


Gl.


Gl.
               from same
               sample)
               Metals,         Filtrate: 3 ml
               Dissolved       1:1 HN03 per
                                 liter
               (With arsenic HN03 interferes with
               reduction method; preserve arsenic
               samples with HC1)
                                        6 months
       Total organic
         carbon
2 ml H2S04 per
liter (pH 2)
       Chemical Oxygen 2 ml H2SO4
         Demand        per leter
       Oil and Grease
               Petroleum
               Products
2 ml H2S04
per liter-4°C

None required
                                                    individual
                                                    analyses
                                                    unless indi-
                                                    cated differ-
                                                    ently.  One
                                                    gallon for
                                                    combinations
                                                    with same
                                                    preservative)
*Cub.
 Gl.
 NA
Cubitainer or polyethylene jar
glass
not applicable
7 days


7 days


24 hours
                                        Bring to
                                        Lab as soon
                                        as possible
1 gallon
            1 quart

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                                                             5.
Container
Gl.
Gl.


Gl.
Cub. or Gl.
Parameter

Pesticides,
   PCB
Organo
Phosphates

Chlorinated
Hydrocarbons

Phenolics
Preservative
Maximum
Holding
Period
Volume
Needed
None required
(Put teflon or
aluminum foil
under cap)
                             2 gallons
                 12 hours
                  2 days
                             2 gallons
                             2 gallons
                             1 gallon
                               1.0 g CuS04/l +  24 hours
                               Cone. H3PO4 to
                               pH 4.0 - 4°C
                               (Use methyl orange indicator.  At pH 4
                               it turns pink upon additions of H3PO4.
                               Use 2 drops indicator/100 ml of sample
                               or use pH meter)
Cyanide

Sulfide



Turbidity


Solids
               Acidity-
               Alkalinity,
               Color, Thres-
               hold Odor

               Biochemical
               Oxygen Demand

               Sulfate, Odor
               Fish Bioassays
2 ml ION NaOH/1  24 hours

                  7 days
                             1 gallon
2 ml 2N Zn
acetate per
liter

None
Available

Refrigerate at
    4°C

Refrigerate at
    4°C
                Refrigerate at
                    4°C

                Refrigerate at
                    4°C

                Refrigerate at
                    4°C
                  7 days


                  7 days


                 24 hours
                                                            1 gallon
                  6 hours


                  7 days


                  6 hours
                             20 gallons of
                             sample.  20
                             gallons of
                             receiving
                             water

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                                                               6.
Container
Cub. or Gl,
Wide-mouth
  Jar
Parameter
Preservative
Algal Bioassays Refrigerate
                  at 40°C
                               None Required
Chloride,
Hardnedd,
Specific
Conductance,
Fluoride,
Calcium
Algal Count     4% formalin

Benthic Sample  10% formalin
               Kjeldahl
               Nitrogen
               Ammonia,
               Nitrate-
               Nitrite,
               Phosphorus
                1 ml/1 of sat
                urated
                4°C
Maximum
Holding
Period

12 hours
                  7 days
                 Indefinite

                 Indefinite


                 Unstable



                  7 days
Volume
Needed

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                                                           1.
III.  Algal Bioassays

           There are two general approaches in carrying out
      algal bioassays:  (1)  Using indigenous algae found
      naturally in a water sample (indigenous); or (2)  adding
      a laboratory-grown single culture of algae.  It is
      sufficient to say here that the use of indigenous
      algae in a bioassay is much easier than adding laboratory
      cultures.  However,  if the results of a bioassay are to be
      expressed as the dry weight of algae, this parameter can
      be more easily derived from single-specied bioassays.
      (There are many more advantages and disadvantages, to
      both approaches.  These are discussed at length elsewhere
      [Tunzi, 1972]).

           Directions to follow in carrying out algal bioassays
      will be divided into several sections:

           Laboratory Bioassay directions
           Cell Mass Measurement
           Measuring Dry Weight
           Measuring Algal Chlorophyll
           Maintaining Algal Curtures in the Laboratory

      A.   Laboratory Bioassay Directions
           (Bioassays utilizing Indigenous Algae)

           Materials

                Glass or polyethylene containers (e.g.,
                     cubitainers) for sample collection.
                Ice chest, ice.
                Filtration apparaters, vacuum pump.
                Erlenmeyer flasks (250 or 500 ml each),
                     acid rinsed (0.1NH Cl), then rinsed with
                     tap water and distilled water; water
                     volume marks should be indicated on
                     side of flask.
                Waterproof labeling pens; black ink
                     Examples:  Sanford's Sharpie #49;
                     Scientific Products #P1226, Fine Tip
                     Marker.

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                                                2.
     Foam rubber stoppers for erlenmeyer flasks;
          rubber stoppers for same.
     Light box capable of 400 ft. candle
          illumination at 20°C; check uniformity
          of light with light meter.

Method

1.   Collect samples in glass or polyethylene
     containers.  Collapsible cubitainers are the
     most convenient.  If the samples are from
     eutrophic water, about 1 quart is sufficient.
     Otherwise collect 1 gallon.  If spiking of
     samples with nutrients or effluent is antici-
     pated, then collect 1 gallon.

2.   Keep the samples out of the sunlight.  If
     necessary, surround samples by ice, but do not
     freeze.  It is usually not necessary to
     ice if transport time is less than 1 hour.

3.   If the samples are to be shipped a long dis-
     tance, they can be put into styrofoam containers
     and surrounded by ice.  The algae in the samples
     will remain cool and viable for about 12 hours
     during transit.

4.   At the laboratory filter part of each sample
     for dry weight or chlorophyll determination
     (50 to about 400 ml is needed for eutrophic
     and 1 to 2 liters for oligotrophic waters).

5.   Choose sample concentration.  Suggested
     additions of effluent to receiving water are
     1%, 5%, 10%, 50% of total volume.  When pre-
     paring nutrients, prepare high concentrations
     so that additions will be   5 ml/liter of
     sample.  Otherwise the distilled water used
     to dissolve the nutrients will dilute the
     sample so that comparisons with a control or
     with other nutrient additions is difficult
     (see Table 1, components of Macronutrient
   .  Medium for Algal Cultures, Section III-E.

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 6.    Prepare about 1 liter of each concentration
      and mix well before adding the water to the
      replicates.

 7.    Prepare at least 4 replicates per sample type.
      Use black ink,  waterproof pens for labeling.

 8.    Number the sample containing Erlenmeyer flasks
      with a waterproof marker pen.  Replicates
      should be numbered; e.g., 1-1, 1-2,  1-3, 1-4;
      2-1, etc.  Number the flasks permanently on
      the frosted parts.  If a flask has consistent
      erratic results compared to replicates of the
      same series, discard it.

 9.    If samples are  to be incubated without addi-
      tions, the flasks can be filled directly from
      the sample container.  First shake sample
      well;  then put  125 ml into the 250 ml flasks
      or 150 ml into  500-ml flask.  Add the water
      to the volume marks on flasks.  Extreme
      accuracy is not important.

10.    Cover the flasks with foam rubber stoppers.

11.    Take an initial cell-mass measurement on 2
      of the 4 replicates  (see Cell Mass Measure-
      ments) .

12.    Incubate the samples under 400 ft. candles
      of light at 20°C.  If higher temperatures
      are used, the cultures grow too rapidly.
      There does not  appear to be much advantage
      in intermittent lighting.  The main point is
      uniform light.   A light meter should be used
      to check that all areas of the incubation
      shelf are receiving approximately equal
      light ( + or -10%).

13.    Measure the algal mass at about the same time
      every day.

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                                                    4.
    14.    Before measuring the mass, plug the flask
          with a rubber stopper and shake it vigorously.
          This promotes aeration and lessens the possi-
          bility of attached growth.

    15.    Expected growth curve, calculations, and
          reporting forms are shown in Figures 1 and
          2.  A completed reporting form is shown in
          the Statistical Section.

B.   Cell Mass Measurement

     Direct Cell Counting

     Materials

          Whipple micrometer reticule
          Stage micrometer
          At least 4 Sedgwick-Rafter Chambers
          Pasteur pipette or automatic volume delivery
               pipette.

     Procedure

     1.    Calibrate the microscope and Whipple disc
           (see Section 301 C, page 731, Standard
          Methods, 13th Edition), using a stage micro-
          meter.

     2.    Fill each Chamber with water from one of the
          replicates by means of a Pasteur pipette or
          automatic volume pipette.  Let the chambers
          settle for 5 minutes  (Chamber volume is 1 ml).

     3.    Usually 2 strips are counted in each chamber
          and a factor is used to convert the number of
          cells counted to cells per ml for the sample.
          Make two counts of the cells in each chamber
          and record average.

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                                                5.
4.   Dilute aliquots from the flasks  (with distilled
     water) if the cell concentration becomes too
     high.  Serial dilutions may also be made to
     check accuracy of counting technique.

Turbidimetry by Turbidity Meter

Materials

     Hach 2100 turbidimeter or equivalent.,
     Tubes for reading in Hach 2100.

Procedure

1.   Calibrate the Hach Turbidimeter by means of
     the standard  (the one supplied with the machine
     is adequate).  The machine is set at the
     value indicated on the standard tube (usually
     50 - 80 JTU's).

2.   Read turbidity in each sample.

3.   Obtain an average reading by watching the
     needle for 10-15 seconds.  Fluctuations in
     readings are to be expected.

4.   Use the same sample tube for each of the
     replicates of the same samples.  It is not
     necessary to rinse the tube with distilled
     water between replicates of a single sample;
     however, the same tube must be well-rinsed or
     even washed between different samples.

5.   When the maximum turbidity reading is reached
     (after incubation of sample), combine the
     water from the replicates, mix, and use for
     dry weight measurements  (see Section on
     Weighing).  (Maximum growth is reached when
     readings are approximately the same for
     2-3 days [see Statistical Procedures for
     approach to evaluating differences in the
     samples].)

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                                                6.
6.   The lower limits of the detectable turbidity
     is about 2000 cells/ml, but 10 fold increases
     changes turbidity only about 2 units.

Absorbance by Spectronic 20

Materials

     B & L Spectronic 20; Spec 20 tubes

Procedures

1.   Set the wave length at 600 nm.

2.   Using special Spec 20 tubes, read absorbance
     for each sample.  Many tubes are required,
     since the sub-samples have to be poured back;
     generally 20-30 ml volume is utilized at
     each reading, and discarding this would
     deplete the incubating sample too drastically.

3.   Take readings daily at about the same time.

4.   When maximum value is reached and stabilized,
     express terminal values as dry weight.  The
     water from the replicates can be combined to
     give enough volume to yield weight differences
     and the individual reading used for statistical
     comparisons  (see sections on Weighing and on
     Statistical Treatment).

5.   Depending on the size of the algal counts, the
     Spectronic 20 is good starting at about the
     100,000/ml level.  It is an instrument rather
     insensitive to any but large cell number changes.

In Vivo Fluorescence

Materials

1.   Turner Model III Fluorometer  (or equivalent) with
     an ultra-violet light source F4T5, the red-
     sensitive R-126 photomultiplier, Corning 5-60

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                                                7.
     primary .filter and 2-64 emission filter.  The
     general purpose photomultiplier can be used
     for dense cultures (^104 cells/ml and up).   The
     R-126 photomultiplier is sensitive down to
     1000/ml.  In contrast to the turbidity meter,
     10 fold increases in cell number changes
     fluorescence 50-100 units.

Procedure

1.   Zero the machine using the black plastic tube
     which comes with the machine.  Check the zero
     calibration when changing from slit to slit
     or after reading every 3 or 4 samples.  There
     are slits on the machine -IX, 3 X, 10X, 30X,
     the latter allowing the most light to pass
     through.  Do not use the 1 X slit, as response
     of the machine is not linear with this slit.  On
     top of the machine a dial reads from 0-100.
     Record both slit and dial values for each
     reading taken.

2.   Establish a calibration factor for converting
     readings from one scale to another.

3.   Follow sample incubation, etc. under 1-14 of
     the Laboratory Bioassay Directions, IIIA.

4.   Shake the flasks thoroughly immediately
     prior to reading as clumping of algae can
     cause fluctuations in the readings.

5.   Pour 5 ml of water directly into cuvette
     and take reading.  Each reading only takes
     about 5 ml of sample, so that once the
     aliquot is read the water used can be
     thrown away.

6.   Rinse tube as follows:  for replicates of
     the same sample, rinse the tube with a
     subsample from the next replicate; between
     different samples, rinse the tube with dis-
     tilled water.

-------
                                                     8.
     7.   Wipe the outside of the cuvette dry before
          inserting it in the holder.

     8.   Shake the next replicate, then take the
          reading of the tube in the machine.  This
          should give about a 10-15 second period
          between readings.  It is important that the
          time span be consistent.

     9.   When growth reaches a plateau (i.e., the
          amount of fluorescence does not seem to
          increase), combine the replicates for either
          chlorophyll a or weight measurement.  Since
          algal chlorophyll fluorescence is the primary
          cause of sample fluorescence, chlorophyll a
          determination is the more reasonable one to
          make (see Measuring Algal Chlorophyll, begin-
          ning with Filtration, D-2).  There is usually
          not enough sample for both measurements.

C.   Measuring Dry Weight

     1.   Wash 4.25 cm GF/C Whatman filters by placing
          them in a pan of distilled water.  Loose
          fibers will separate from the filters.

     2.   Place filters on a towel to partially dry.

     3.   Place them separately on a sheet of aluminum
          foil.

     4.   Dry them for three hours at 90°C.   (Put
          into a desiccator if filters are to be
          stored for more than 5-10 minutes before
          weighing.)

     5.   Number them lightly on their edges with
          a soft lead pencil.

     6.   Weigh filters to nearest hundredth milligram.
          Handle the filters with tweezers, grasping
          the edges.

-------
                                                     9.
     7.    Put them into small envelopes with their
          weights and number written on the outside
          of the envelope.

     8.    When needed, filter as much sample as will
          go through the filter in about two minutes at
          low vacuum, less than 5 inches of mercury.

     9.    Record volume filtered in liters.

    10.    Double the filter, algal side inward.

    11.    Place filter on aluminum foil and dry for
          at least three hours at 90°C.

    12.    Remove them from oven and, using forceps to
          transfer, weigh them after they have cooled
          for about five minutes.  Cooling in a desiccator
          may be desirable but appears to be of limited
          advantage.

     13.  Subtract original weight of dried filter
          from final weight and express results as mg/1
          of dry weight.

D.   Measuring Algal Chlorophyll

     Introduction

          There are two practical approaches to measuring
     the concentration of indigenous algae in water.
     They can be counted directly or may be enumerated
     indirectly by determining the chlorophyll content
     of a sample of water (or performing some other
     mass measurement).  The following method details
     procedures for measuring chlorophyll concentration.

     Materials and Equipment for Laboratory Analysis

         .Whatman GF/C glass fiber filters, 4.25 cm
               diameter

-------
                                                10.
     Filter-holding apparatus: either
          Millipore or Gelman
     Covered small glass jars containing desiccant
     Freezer
     Scissors
     Tissue homogenizer with teflon pestle: either
          Kontes Glass Co. No. 885-380-0023; or
          A. H. Thomas Co. No. 4288B
     Acetone,  (90% acetone, 10% water) spectro-
          photometric grade
     Centrifuge tubes (if Kontes tissue homogenizer
          not used)
     Centrifuge adapters (necessary only if Kontes
          tissue homogenizer used)
     Pasteur pipettes
     Beckman DU Spectrophotometer, or equivalent
     Cuvettes  (for Spectrophotometer), 1 cm or
          small volume 5 cm ones
     Hydrochloric acid,  IN

Method

1.   Sample Collection

          It is best not to collect a single
     grab sample.  Instead an integrated sample
     should be taken by collecting small (about
     250 ml) equal-volume sub-samples at a given
     site and depth over a time period, such as
     10 minutes.  These sub-samples should be mixed
     together in a plastic busket and transferred
     to a transport container (e.g., a 1-gallon
     cubitainer).

     Consult section on Sample Collection for further
     considerations on representative samples.

2.   Filtration

     1.   As soon as possible after collection
          (the sooner the filtration the more
          valid the data; e.g.,  a sample stored
          in the dark on ice should be filtered

-------
                                                 11.
          within 4-5 hours,  if possible),  filter
          under low vacuum as much water as will
          go through a Whatman GF/C filter within
          about two minutes.

     2.    If possible, prepare 4-5 filtrations of
          water from the same sample.

     3.    Record the water volume that has been
          put through each filter.

     4.    Double the filters, algal side inward
          and put them into a small jar with
          dessicant and then into the  freezer
          for storage.

     5.    Extract for chlorophyll within three
          weeks of filtration.

3.    Extraction Methods
                    	  green
                            white
        Figure 1.   Folded Filter

          Refer to Figure 1.   Using scissors,
          carefully trim off  the white border  to
          the edge of the green algae-contining
          section.  Discard white section.   Cut
          each trimmed filter into smaller  pieces,
          putting  these directly into tissue
          grinder  homogenizer.

      2.    Add 5 ml of acetone.

      3.    Grind filter with  teflon pestle.

-------
                                            12.
 4.    Ground-filter-and-acetone mixture should
      only get slightly warm to touch during
      the process.   Move the tube slowly up and
      down while grinding,  ceasing the grinding
      whenever the  tube becomes warm to touch.

 5.    Keep ground-filter-and-acetone mixture
      out of strong light by covering it with a
      towel.

 6.    Pour the mixture into a centrifuge tube,
      cover with parafilm (or other cover), and
      shake well.   If Kontes tissue grinder is
      used, the container may be centrifuged
      directly (if  adapters are present), thus
      making it unnecessary to transfer the
      ground mixture to a centrifuge tube.

 7.    Let set in the dark for 20 minutes at
      least.

 8.    Shake the centrifuge tube well again after
      the 20-minute waiting period.

 9.    Centrifuge the tubes for 10 minutes at
      2500 - 5000 RPM, preferably at the higher
      RPM's.  Tap the tubes to bring particulate
      matter to the bottom.  Recentrifuge.

10.    By means of a Pasteur pipette, carefully
      draw off enough of the supernatant to fill
      a 1 cm cuvette  (about 4 ml).

11.    Take absorbance readings at 750 nm, blanking
      against 90% acetone.  If above 0.005-0.008
      Optical Density  (O.D.), re-centrifuge.

12.    Take absorbancy at 663 nm, blanking against
      90% acetone.

-------
                                                 13.
    13.   Add 2 drops of IN HC1 to each cuvette and
          re-read absorbancy after 2 minutes at 663 nm.
          One cm cuvettes do not have to be shaken to
          disperse the acid, but it is necessary to
          shake those of larger dimension.

    14.   If the absorbancy of the sample is too
          high for the spectrophotometer scale,
          the sample can be diluted.  Keep an
          accurate measure of the total amount of
          acetone used, as this volume is necessary
          for calculations.

4.    Calculation of Results

     1.   The amount of chlorophyll a_ from algae
          can be calculated as follows:

     ug chl a per liter = 26.7 (ODb ~ ODa) x Ac
                               W x cm
     where:  ODa = optical density at 663 nm of extract
             after acidification (step 13 of Extraction),
             less the OD at 750 nm (step 11 of Extraction).
             ODb = optical density of extract before
             acidification (step 12), less OD at 750 nm
             (step 11) .
             Ac = volume of acetone in ml
             cm = spectrophotometer cell path length in cm
             W  = volume of water in liters

2.    Phaeophytin, a degradation product of chlorophyll,
     may be calculated as follows:

     >ig phaeophytin per liter = 26.7 [1.7 (ODa) - ODbl  x Ac
                                               W x cm

     This value may be 0 or negative, indicating no phaeo-
     phytin in sample.

3.    Total chlorophyll a per liter in any sample is the
     sum of the values obtained in 2 and 3.

-------
                                                     14.
     4.   If more than one filter was prepared, the chlorophyll
          concentration values from the 4 or 5 filters can be
          used to establish the standard deviation, standard
          error, and 95% confidence limits of the chlorophyll
          values for the sampling site  (see Statistical
          Procedures).

Discussion

     As was mentioned in the introduction, there are numerous
ways to determine the amount of algae present in a sample.
These include direct counting, weight measurement  (biomass),
trubidity determinations, and chlorophyll measurement.

     Counting is a slow process.  Its principal drawback
however is that algae vary greatly in size, so that to get an
estimate of the mass of algae in water each separate species
has to be measured and the total volume obtained by multi-
plying the number of each species times its volume.   (This
value can be converted to mg/1 of algae by assuming a
specific gravity of about 1.0 for the algae.)

     An extraction of algal chlorophyll is one of the
standard methods of estimating standing crops in water
(Strickland and Parsons, 1965).  This is true because
chlorophyll is a necessary constituent of green plants,
serving as a catalyst in the initial carbon fixation process.
One problem in determining concentration, though, is that
the ratio of chlorophyll to cell mass can be changed,
especially by varying the light intensity.  The chlorophyll
a_ to cell carbon ratios are in the range 1:40 to 1:100.

     Biomass might also be determined.  One disadvantage of
this procedure is that the volume of material available for
filtration is usually small so that the resulting weight of
the cells retained by the filter is not too much greater
than the weight of the filter itself.  This causes a wide
variation in results.  If one wishes to determine cell
weight, though, the method can be employed.  Empirically it
has been observed that the cell dry weight is approximately
equal to two times the cell carbon (Maciolek, 1962).

     A summary of the advantages of chlorophyll as a measure
of mass would include the following points:

-------
                                                     15.
     1.    The amount of chlorophyll is determined
          spectrophotometrically.   The precision of
          this determination is greater than that for
          any cell-count method.

     2.    Large volumes of water can be filtered to
          determine chlorophyll.  Only one ml at most
          is used in direct counts (and hence is not
          too representative).

     3.    The green chlorophyll color of algae is the
          substance seen when one looks at algae in
          water; therefore, measuring chlorophyll in
          water usually is a direct way of quantifying
          the size of an algal bloom.

E.   Maintaining Algal Cultures in the Laboratory

          The EPA Report Algal Assay Procedure -
     Bottle Test (1971) available from Thomas Maloney,
     EPA, NERC, Corvallis, Oregon gives useful infor-
     mation on culturing algae.  Pure cultures of
     algae can be obtained from NERC, Corvallis or
     from the Culture Collection of Algae, Dept, of
     Botany, Indiana Univ., Bloomington, Indiana.
     Direction are available in the Indiana University
     listing for media for specific algae.

General Directions

     These are applicable for Selenestrum, Scenedesmus and
mixtures.

     1.    Stock cultures can be kept viable for months if
          they are kept out of direct light.  They may be
          stored at normal room temperature in a shelf of
          the laboratory where the light is constantly
          subdued or at least off at night.  Cultures kept
          under constantly high light will go through a
          growth phase, exhaust nutrients, and usually die,

-------
                                                 16.
2.   Use aseptic techniques for transferring uni-
     algal cultures.  Pasteur pipettes, flasks and
     stoppers  (or other covers) can be autoclaved or
     heated to 90°C if an autoclave is not available.

3.   Table 1 shows a simple mixture of nutrients
     which will promote growth.  Stock culture can
     be kept in polyethylene or glass bottles.  Micro-
     nutrients are not needed as there appears to be
     ample present as contaminants in the chemicals.
     If they are desired, utilize those given in the
     EPA Corvallis publication  (or add to 1 liter
     macronutrients 1 ml of a solution prepared by
     adding a small amount of bouillon cube to 100
     ml water) .

     Table 1.  Components of Macro-nutrient Medium for
     Algal Cultures

     Component                     Amount in g/1

     NaN03                             6 g/1
     CaCl2                             0.6
     MgS04                             1.8
     NaCl                              0.6
     KH2PO4                            0.875
     K2HP04                            0.375
     NaHC03                           10.0
     Fe(SO4)2  (NH4)2   *  12 HOH      860 mg  Dilute in
         EDTA  •   2 HOH              660 mg  one liter
4.   Add 10 ml of each chemical except the iron solution
     above to a two liter flask and bring volume up to
     1 liter with ion-free or distilled water.

5.   Cover the flask with a beaker and heat to 90 °C or
     autoclave for 20 minutes.

6.   Autoclave the iron solution or heat to 90 °C.  The
     iron solution should be kept in a screw-cap flask.
     Loosen caps when heating or autoclaving and tighten
     when cool.

-------
                                                           17.
           7.   Add 1 ml of iron solution to liter of the macro-
                nutrients when the latter has cooled.

           8.   The nutrient solution can then be dispensed to
                sterile smaller flasks  (250-ml ones are suitable)

           9.   Inoculate the small flasks with the stock algae.
                Put under constant light of about 400 ft-candles.
                Solutions should be densely green in about five
                to seven days and ready for use.

                              References

Anonymous, 1971.  Algal Assay Procedure.  Bottle Test, NERC
      Environmental Protection Agency.  Corvallis.  82 pp.

Maciolek, J. A. , 1962.  Limnological Organic Analyses by
      Quantitative Dichromate Oxidation.  Res. Rept. (50. U.S.
      Fish and Wildlife Service.  61 pp.

Tunzi, M. G., 1972.  Algal bioassays:  Examples, advantages,
      and limitations of current approaches, 173-197 pp. in
      Proceedings of Seminar on Eutrophication and Biostimu-
      lation.  California Dept. of Water Resources.  Sacramento.
      229 pp.

Strickland, J. D. H., and T. R. Parsons.  1965.  A Manual of
      Sea Water Analysis.  Fisheries Research Board of Canada.
      Bull, No. 125.  Ottawa, Canada.

-------
Algal Cell
Concentration

(any type of
 measurement;
  cell count,
  optical
   densityk
  fluorescence,
  chlorophyll
   concentration)
                10
                                                         Days
Algal Growth Data
Sheet Parameters
Initial chlorophyll
Concentration
Peak chlorophyll
Concentration
Increase in chlorophyll
Concentration
Days to reach peak
Maximum Growth rate
u, day ~l
Value from Figure
(A) 10
(E) 90
(E minus A) 80
4 days
J.^JL.) .i$)-i.»
t i
              x0 - cell concentration at beginning of maximum growth

              x,  • cell concentration at end of maximum growth

              t  - time

              n  • maximum specific growth rate, (day "1)

    Maximum growth rate is derived  from the steepest part of the growth curve,
    utilising the log of the  cell concentration at  the beginning and end of
    the curve.
    Fig. 1.   Typical algal  growth response.   The values are the
    means  of the  replicates, whose range are indicated by the
    vertical lines.

-------
I
Sample
Location



-


-



?igure 2












ALGAL GROWTH 1
Average Initial
Chlorophyll
Concentration

L








DATA SHEET
jig Chi a/1
Average Increaae
In Chlorophyll
Concentration

»









Average Maximum
Chlorophyll
Concentration










i
Average Maximum
Growth Rate .
/\ . — -i
«!,» days 1











No. Of
Days to
Reach Peak










The results below connected by underlining are not different from each  other at the 951 confidence level.
                                          on the results of four replicates.
            Average based
    fiample Numbftr
    Concentration
 Increase jig Chi a/1
       »le Humber
 Concentration Maximum
     jig Chi a/1
          Nmhur
 Maximum Growth Rate
 Fig. 2.   Data reporting  sheet with multiple range  section on the  lower  part,
 for elaboration.
See  statiscal section

-------
IV.     Statistical Procedures

       A.   Introduction
                Statistics is a scientific method involving
           collection,  analysis,  and interpretation of
           numerical data.  An understanding of basic statis-
           tical principles and procedures is helpful to both
           field and laboratory workers.   The mathematics
           involved is  simple except for  advanced procedures
           which are infrequently used.

                The data collected for statistical treatment
           are measurements or observations of a characteristic
           of a population.  The  population can be the cells
           in a series  of flasks, the nitrate ions in a lake,
           the oligochaetes in the sediments of a bay, etc.
           Thus the population can have discrete physical
           boundaries or ones which the planner sets himself.

                Almost  without exception  we cannot make all
           the desired  measurements of a  population, so that
           instead we take a sample from  the population.  From
           the sample mean, predictions can be made about the
           same characteristic in the entire population.  By
           sample  is meant a series of measurements, although
           in reality we would have to take a separate sample
           for each measurement.

                Greek letters are used for population statis-
           tical terms  and English letters for sample: ones.
           The measurements from a population are called
           parameters and those of the sample called statistics.

                Assuming that we  have measurements from a
           population,  the above  can be clarified by the following
           table.

                                  Population         Sample
                                  Parameter          Statistic

                Mean                p (Mu)               x
                                     2                   2
                Variance            &                   S

                Standard
                Deviation           ©• (Sigma)            S

-------
B,
                                                 2.
Definitions
    1.   Mean (x) .  The average value calculated by

         dividing the sum of the measurements by the

         number  (n) of measurements.


    2.   Variance  (s2).  The variability or spread of

         the data about the mean  (See Figure 1).
    3.
    4.
          >, l
          u
          c
          0)
          3
          cr
          0)
                                    Mean
         Figure 1.  Two sample measurements with

         equal means but differing variances.
     The standard deviation  (s).

     of the variance.
The square root
     The standard error or the standard error of

     the mean (S^).  The standard deviation of the
     sampling distribution of means.
    5.   Degrees of freedom - usually equal to i\ -1.


    Calculations


         The calculations for the above statistics

    are very simple.


         Given the data below collected from a

    population with individual measurements listed

    under x.
X
11
12
15
16
11
x - x
-2
-1
2
3
-2
(x - x)2
4
1
4
9
4
x2
121
144
225
256
121
    65
                               22
         867

-------
                                              3.
  (x-x)2 is the sum of the squared deviations which
is called the sum  of the squares (SS).

x2 is calculated because it is used in the working
formula for the variance.
The mean being: n
               £
       x =      1
                n
=  6_5_  =  13
   5
The variance is:
               n
       s2 =
   =  22  =  5.5
               n-1
The working formula is simpler because the sum of
the squares does not have to be calculated.
        n
 ,2  _
       Ix2-
                    \
                  n
            n-1
Standard deviation
     .5
           867 -  (65)
           _ 5
                                  2.35
                                            = 5.5
Standard error
       x
By use of the standard deviation confidence limits
for the measurements can be set:
      x  + IS includes 68% of the sample measurement
      etc. (see below).
       Xr ........
     <•
                95
                99
   -3S -2S  -IS
+1S  +2S  +35
This assumes that the sample measurements are
normally distributed.

-------
                                                  4 .

    Confidence limits of the population are much
    more important.  That is we want to set limits
    which bracket the true population mean or average
    ( Ai  ).

    This can be done by using the standard error S^
    and  t   table values for the degrees of freedom
    in our sample.

    x  +  s~    will include the true population mean
    (ja ) 68 out of 100 times.

    x  +  (t Q QC) sx will include ;u 95 out of 100 times,

    x  +  (t o.Ol) sx wiH include u 99 out of 100 times
    The difference between sample confidence limits
    and population confidence limits must be clearly
    understood.

    Using the last formula in the above data:

    x +  (4.60) (1.05) = 13± 4.83

    The t(04Q5) and t/Q Q-J\ are found in a t table for
    a range of n-1 values  (a few values are given below)
                          Degrees of Freedom  (n-1)

              6 DF   5 DF   4 DF    2 DF     1 DF

    t(0.05)   2.45   2.57   2.78    4.30     12.71

    t(0.01)   3.71   4.03   4.60    9.93     63.66
    By utilizing the t values for various degrees of
    freedom, we can see the importance of high numbers
    of replicates in sampling.

D.  Group Comparison of Two populations

    1.   A comparison consist of two steps.

         a.  At test to determine if the sample means
             come from one or two populations.

         b.  Confidence limits can be set for the sample
             means if the t test is significant.

-------
                                                  5.
    Special formulas for group comparisons

                                2
                               s
    a.    ;u  =  x  +  t (0.05)    p
                                n

         Note:  If the t test is not significant then
         both samples come from the same population.

         The confidence limits for the population means
         may overlap slightly even when the t test
         is significant.
b.   Pooled variance

            n   ;>    / n   \ „     n    _   / n
           2
               V—  ':  _ / s—    2    S	  2  _k~ x  2
                                                2
                                             "2
         These formulas can be used whether or not
         n1 = n2.

3 .   Example of a group test



X
x2
X
V
X
32
31
52
44
159
6625
39.75
? 6625 -
X2
17
35
22
24
98
2574
24.50
(159)2 2574 - (98)2
4 + 4
                     (4-1) + (4-1)

-------
s 2 =  6625 - 6320  +  2574  - 2401
s 2 =  478   =  79.7
 fr      £
       39.75  -  24.50        15.25
                                     =  2.42
       79.7(1/4+1/4)          39.85
For 6 degrees of freedom t[0.05] = 2.45.  Therefore,
there is no difference between the set of data.

-------
                                                         7.
E.   Comparison of Two Groups by Pairing

     1.   If two samples are not independent, then a pairing-
          test can be used to compare them.  Of course,
          nl = n2-  Generally, high values in one sample are
          associated with high values in another.

     2.   Example of the data from a pairing test:

                            K! - x2
x± X2 difference d^
10 19
9 18
8 17
11 19
14 22
12 18
/_ 64 113
x 10.64 18.83
f n \
\ \2
l_ d
L 	 =2401
. 1 1
Variance of the? dif
-9 81
-9 81
-9 81
-8 64
-8 64
-6 36
-49 407
xd= -8.17
n
*\~~ d2 = 407
1
/n\
21 d2 - E d 2
i \i/
2 n
:ference sd = 	
                                                    n - 1
                 407 _ (49)2      407 _  2401
          sd2 =          6       	6	 =  1.4

-------
                                                         8.
          The standard error is:
          s       /
           xd   = / I-4    -  ./0.233 =  0.48
                 V   6        v

          t  =   I *d |    =   8.17    =   17.0
                 s_          0.48
                  xd

          Since the t value of 17.0 is greater than the t
          value for 5 degrees of freedom (0.05), there is a
          significant difference between the sample means.

          The 95% confidence limits for the difference
          between the samples can be calculated by using the
          following formula:

                      xd   +   t(0.05)
                                          n

F.   Comparison of data from more than two groups

     1.   Analysis of variance is the technique used to
          compare one characteristic from three or more
          populations.

          Three or more populations cannot validly be
          compared by the sequential use of a t test.  It
          is especially bad to single two groups out of a
          large number and subject them to a t test to see
          if they differ.

          The completely randomized design is used for
          comparing the means from three or more populations.

     2.   The following calculations for unequal sample size
          can also be used when the same number of measurements
          are made for all samples:

-------
                                                      9.
r
Sample
1
10
11
12
13

x 46
x2 534
n 4
x 11.50
(Zx)2 529
n
Correction
Total Sum
Treatment


2
6
12
14


32
376
3
10.67
341.3
(133)

3
10
12
10
9
14 _
55 )_ = 133
621 ^_= 1531
5 2 = 12
11.00
605 }_ = 1475.3
2
Factor =12 = 1474.1
of Squares = 1531 - 1474.1 = 56.9
Sum of Squares =
Analysis of
1475.3 - 1474.1 = 1.2
Variance Table
       Source  of  Variation      DF     SS     Mean  Square

                   Total        11    56.9

                   Treatment     2     1.2       0.6         0.097

                   Error         9    55.7       6.2

            Treatment mean square
       F   =  Error  mean square

       F  values  for 2 degrees of freedom  in the  numerator
       and 9 in  the denominator for  the 0.05 probability
       level is  4.3, much higher than our F value.   There-
       fore, there  is no significant difference  between
       our sample means.

-------
                                                        10.
     3.   If the F value is significant, a multiple range
          test must be used to determine which samples
          actually differ.  Duncan's new multiple range
          test for equal replication (p. 107) and unequal
          replication (p 114)  are good ones to use (Steel
          and Torrie, 1960).

G.   Non-parametric methods

          These approaches are useful when it is not certain
     that the normality of the population distribution and
     its means and variance are the same as that of the sample,

          One of the more useful tests is the Kruskal-Wallis
     test which compares medians from 2 or more populations.,
     An example of this ranking test is given below:
Data







Median =
Set I
6
8
8
12
14
30
23
12
Rank
2
3.5
3.5
6
7
11
10
m =7
Rn =43
Data Set II
21
15
4
11



Median = 13
Rank
9
8
1
5



n2
Ro







=4
= 23
     Median-the middle value for odd number of values, and
     the mean of the two middle values for even number of
     values
                 11 + 15
=  2_6   =  13
    2
     An H value is then calculated where-

        k = number of samples

        T = total number of measurements in all sets

-------
                                                   11.
   k-^ = degrees of freedom

   R = sum of the rank

   n = number of measurements

  12 = a constant


H -  T-rinr    F- -g-  "3


For the above data:

H -   12        432   +  232
H ~ 11 (12)     —7—    —4—

H = 0.035

     The hypothesis made is that the populations are
identical.  When the H value is greater that the chi-
square value for k-1 degrees at the 0.05 probability
level, then there is a difference between the sample
medians.   For 1 degree of freedom this =3.84.   So the
hypothesis is accepted.  (Chi-square tables are found
in most mathematical handbooks and statistic books.)

-------
       Sample   3/17/70
TABLE 1 - BIOASSAY DATA WITH MULTIPLE RANGE STATISTICAL PRESENTATION

                       ALQAL GROWTH DATA SHEET

                          V9 Chl a/1
Location
Redwood City Sewage
Treatment Plant


downstream location



•
San Francisco Bay
Number
12
1
2
3
4
5
6
15
Average Initial
Chlorophyll
Concentration
7.2
2.0
2.0
2.1
2.1
2.5 -_
2.8
3.0
Average Increase
In Chlorophyll
Concentration
2.0
33.6
0.0
66.6
69.8
40.3
26.1
6.8
Average Maximum
In Chlorophyll
Concentration
9.2
35.6
2.0
68.7
71.9
42.8
28.9
9.8
Average Maximum
^Growth Rate
Pb. days -1
0.13
'0.94
0.00
1.09
0.61
1.67
1.57
0.93
Ho. of
Days to
Reach Peak
6
6
0
3
3
3
3
2
The results below connected by underlining are not different from each other at the 95 percent  confidence  level.   Average
based on the results of four replicates.
Sample Number
Concentration
Increase >ig Chl a/1
Sample Number
Concentration Maximum
jig Chl a/1
Sample Number
Maximum Growth Rate
ub, day'1
2
0.0

2
2.0
2
0.00
12
2.0

12
9.2

12
0.13
578 ITTI

15 6
978 287?

0715 0.93

1
3375
3575
	 1

7673
¥O
T~oc

3 4
5575 597ff
3 4
5877 71.9

6 5
> T757 T75T

-------
                                                           1.
V.  Fish Bioassays

    Sources of Fish

    1.   Collection
              Test fish may be collected from a large body of
         water using a seine; from a small slough, one can use
         dip nets.  Usually a collection permit is required
         (get this from state fish and game departments).

              Since collection of suitable and adequate number
         of fish is somewhat uncertain, it should be done only
         if time is of little importance, if the locations of
         the desired fish are well-known, and if there is no
         other way to obtain fish.

              After collection, place fish in a suitable
         transport container.  A five-gallon plastic bucket
         with a snap-on lid can hold 100 small  (up to 2 inches)
         fish for short distances.

              If one collects his own fish, he must have
         several good battery-operated aerators  (e.g., the
         Jorgensen portable aerator - $7.00; Lewis Air Pump -
         $3.50).  Take extra batteries and check at least
         every hour to see that they are not run down.  Aerate
         fish on the way back to the laboratory.

              Aeration is accomplished by connecting aerator
         to a flexible line with an airstone at the end.  The
         airstone should be weighted or it will float to the
         water surface.  A large  (No. 10) rubber stopper with
         a hole in it  (to put the tube through) will hold the
         aerator under water.
    2.   Purchase
              Commercial aquarium and fish stores generally
         charge too much to make them a reasonable source of
         fish.  Names of dealers who supply fish for bioassay
         are generally available from agencies such as State
         Water Resources Control Boards and fish and game
         agencies or from other persons who carry out fish

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                                                  2.
bioassays.  The price per fish delivered  is
usually 20-50 cents, depending upon the species.
This is normally the most economical way  to get
fish.  Be sure not to acquire more fish than
needed.  It is usually easier to purchase fish in
lots as required than it is to maintain fish for
many weeks in an expectation that they might be
needed.

     Possible sources of fish from agencies include:
 (Normally the hatcheries supply fish only to other
public agencies)

     Striped Bass
          Bureau of Reclamation, Tracy
          Phone  209-935-3122
     Rainbow Trout
          American River Hatchery
          Phone  916-351-0314
     Salmon, Steelhead Trout
          Nimbus Fish Hatchery
          Phone  916-351-0383
     Black Bass, Blue Gill, Shad> Catfish
          Elk Grove Hatchery Phone  916-685-9555
    Two    commercial fish dealers in the San
Francisco Bay area are:
     William Putman
          5449 Modoc St. Richmond, CA   94804
     Alex Fish Company
          2235 Juniperberry Drive
          San Rafael, CA
A list of commercial fish dealers in California is
available from the California Fish and Game Department

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                                                       3.
Recommended Species

     Ideally, the best fish to use are the most abundant
or economically significant young small ones found in the
receiving water area.  However, this may be impractical or
impossible to carry out as they would be too difficult
to catch or only available during specific seasons.

     A standard test species available throughout the
year would make comparisons between tests more meaning-
ful.* Fish most commonly used in California are:

               euryhaline

     3-spine stickleback    Gasterosteus aculeatus
     Threadfish shad        Dorosoma petenese
     Killifish              Fundulus parvipinnis
     Striped bass           Roccus saxatilis

               Fresh Water

     Golden shiner          Notemigonus chrysoleucas
     Channel catfish        Ictalurus punctatus

Maintenance of Fish

1.   Disinfection

     a.   A new group of fish should be disinfected by
          putting them (for about 5-10 minutes) in
          water containing both .025 ml/1 of formalin and
          0.05 mg/1 malachite green (Leteux and Meyer,
          1972).

     b.   Fifty fish can be put into approximately two
          gallons of water.

     c.   Watch them carefully, and remove them immediately
          if they show signs of distress (floating up
          slightly sideways).

2.   Aeration

     a.   Before adding fish to water, aerate water for
          12-24 hours.
*Table 3 lists animals suitable for bioassay in Hawaii

-------
                                                       4.
     b.   A twenty-gallon aquarium can hold 100 small fish
          if it has two activated charcoal filters and
          one to two airstones running constantly.  Some-
          times it is better to replace the water or part
          of it every three or four days, but aerate the
          water for 12-24 hours before adding it to the
          tank.

     c.   One example of an activated charcoal filter
          is the large-size Halvin which attaches on
          the side of the aquarium.  Examples of
          electric air pumps are the Silent Giant
          ($15), Oscar and Star ($8).  Activated
          charcoal should be changed every two days.
          The charcoal can be reused if fired in an
          oven at 450°C for an hour.  Less heat will
          not destroy the organics absorbed in the
          charcoal surfaces.

     d.   If one uses a compressor as an air source,
          the air should first be passed through one
          tube:  the first half holding non-absorbant
          cotton and the second half holding activated
          charcoal.  The cotton and charcoal should be
          changed every month.

     e.   A large sand filter fiberglass system is shown
          in Figure 1.  This can be used for 200-300 fish.
          The pump can be run constantly.  Its size should
          be sufficient to circulate the water in the tank
          once per hour.

          Back-flush the sand filter every 3 weeks.  Turn
          off the pump when feeding the fish.

3.    Temperature for Fish Maintenance

     a.   Cold-water fish should be kept at 13-14°C in
          order to remain disease-free.  Warm-water fish
          also are usually less apt to contact disease
          when kept at these cool temperatures.

-------
                                                       5.
     b.    There are several ways to maintain these cool
          temperatures.   One of these is a water bath with
          a refrigerant system.  Another is a walk-in box
          with a refrigerant system.

4.    Feeding Fish During Maintenance Period

     a.    When feeding fish, turn off the aerators and
          any filtration system (including activated
          charcoal).

     b.    Throw in food slowly until fish cease eating;
          this usually takes 10 to 15 minutes.

     c.    Look at the individual fish and remove any
          that have any discoloration and, of course,
          any dead ones.  Generally only 1 or 2 fish
          will die out of a hundred, and these in the
          first days after delivery.

     d.    Fish should be fed 3 times a week; however,
          they can do without feeding on the weekends.

     e.    Do not over feed.

     f.    Fish food may be purchased as pellets or in
          frozen form.  Fish food is available in bulk
          in pellet form of various sizes.  No. 2 is
          suitable for small fish, but larger pellets
          can be ground in a mortar if only one size is
          available.   Brine shrimp can be purchased
          frozen.  Chunks can be broken off as needed.
          Put the frozen chunks into a beaker of water
          until they melt apart.  Stir them and let the
          shrimp settle to the bottom.  Pour off the
          supernatant water, add more water and repeat the
          process.  In this way, less debris is added
          along with the shrimp.  (If one is feeding fish in
          large tanks, the brine shrimp chunks can be
          thrown in directly).

     f.    Fish are not to be fed 2 days before the
          commencement of any test.

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                                                  6.
Holding and Dilution Water

     Most fish are either marine or fresh-water, but
some fish can live in water of varying salinity.
These are termed euryhaline fish.  If freshwater
discharges into a freshwater receiving water are being
tested for their toxicity, then a freshwater species
can be used and a marine species for saline discharges
into the ocean.

     However, when low-salinity water is discharged
into an estuary or the ocean, then a euryhaline
species is the appropriate one to use.  The euryhaline
species can be kept in a 1:1 mixture of marine and
tap water.  It will withstand without great stress
transferral from this mixture into both the effluent
and sea water.  These extremes in salinity would
be present in the test waters because the concentra-
tions used would include both sea water and effluent
and mixtures of the two.

     Fresh water holding water and the dilution
water can be tap water that has been aged or
aerated for 12 hours.  For some of the reasons
given above, there are usually two controls, one
the holding water and the other the dilution
water.  If the fish are kept in the holding water
within the laboratory-maintained temperature range,
then the fish left in the holding water can be
considered controls.

     When both the receiving water and the effluent
from the discharger are suspected to be toxic, a
double control can be made.  Dilution water could be
river water upstream of the effluent in which a
double control should be used.  Control 1 being
the river dilution water; control 2 the aged tap
water.  Sometimes results will vary if you use
existing receiving water as a diluent instead of

-------
     using tap water as diluent.  For example, when
     salts are high in receiving waters, this may have
     a positive or negative effect on effluent toxicity.
     If one has two controls  (river water and tap water)
     and there is mortality due to the receiving water
     (river) rather than the effluent, use of the second
     control, tap water, will make this obvious.

Bioassay Procedure

Materials Required

     Bioassay containers.  These may be five-gallon
          (19-liter) aquaria, pickle jars or battery
          jars which are available in sizes up to one
          gallon; the size depends upon size of fish -
          one gm fish per one liter water; fish nor-
          mally require 10-15 liters per test sample.
     Container-cleaning facilities (large thick rug;
          garden hose).
     Aluminum foil or lids for bioassay containers.
     Temperature controllers.   (Capable of maintaining
          20°C + 2°C for warm-water fish and 15°C + 2°C
          coldwater ones).
     Aeration device
     Dissolved oxygen meter.  DO can be measured by
          siphoning but then large-volumed containers
          are required.  See Fig. 2.
     Thermometer.   (Either a recording thermometer or
          a small thermometer in a jar of water).
     Optional:  devices for measuring pH, conductivity,
          turbidity, and hardness.
Data recording sheets (See attachment, Figure 3)
Bioassay organisms  (e.g. fish)  [fish must be held at
     experimental temperatures for 10 days prior to
     commencement of bioassay for legal purposes].
Method
     Scrub bioassay glass containers clean and rinse
     them well with tap water.  If the containers are
     large, it is safer to do this on a large thick
     rug, using a light garden hose for rinsing the
     jugs.  This is best done out of doors on a cement
     platform.

-------
                                                       8.
2.    Let the containers drain for about one hour, then
     let them air dry inside the laboratory.  After
     they are dry, cover them with aluminum foil or
     lids to keep dust-free, or store upside down.

3.    Normally ten fish are added to each container.  The
     weight of the fish cannot exceed 1 gram per liter of
     water.  If fish are too large for 1 container, put
     five fish into each of two separate containers
     containing the same sample solution.

4.    There are several ways to increase the reliability of
     the tests:

     a.    Increase the number of fish from 10 to 20 per
          container (remaining consistent with the
          weight to volume restriction above).

     b.    Prepare replicates of each concentration so
          that there would be two or more of each test
          solution (with 10 fish per container).

     c.    Prepare concentrations with closer increments of
          toxicants e.g., instead of 10%,  20%,  30% there
          would be 10%, 15%, 20% etc. additions.

5.    a.    Preparation of concentrations

          The graph shown in Figure 4 is a standard plot
          of log of concentration versus regular arithmetic
          increments.   This plot is based upon experimental
          results which show that effect of a toxicant
          upon an organism is logarithmic rather than
          arithmetic.   That is to say that, in general,
          if one doubles the concentration one does
          not double the mortality.

          Actual additions of toxicant are in logarithmic
          increments.   An excerpt from Standard Methods
          is given in 5b.  It includes Table 1 which
          shows some log increments; a more complete

-------
                                                       9.
          range is expressed in Figure 4.   Figure 4 shows
          concentrations ranging from 100% to 10%.   If
          a wider range of concentrations  were to be
          employed, then several-cycle semilog paper
          would be used - e.g., a range of 100% to
          0.1% would require four-cycle semilog paper -
          or divide values in Fig. 4 by 10 or multiples
          of 10.

          If possible,  the actual concentrations chosen
          would be based on a preliminary  test of 12-24
          hours with toxicants added in concentrations
          covering a wide range of values.  For an
          unknown substance this might be  100%, 50%, 10%,
          1%, and 0.1%.  Regardless of the preliminary
          results, if possible, always include a 100%
          full strength test sample because many
          toxicity standards are based on  percent
          survival in the pure test sample.

     With experience and a preliminary test, the concen-
trations can be selected so that containers very close to
the TLso value will be the most numerous.   A preliminary
test using 2-4 fish per concentration can  be carried out
if the test material does not degrade.  For example, if
the preliminary test using two fish per liter showed the
following results

     Concentration of

       Test Solution               Survival

          100%                        0
           50                         0
           25                         1
           10                         2
            1                         2

     Then the following concentrations could be set up:

                    100%  (Optional)
                     56
                     32
                     24
                     18
                     10

-------
                                                  10.
     Excerpt from Standard Methods, 13th Ed., p. 565
     "Although a TLso may be determined by testing any
     appropriate series of concentrations of the sub-
     stance or waste assayed, the geometric series
     of concentration values given in Table 1 is often
     most convenient and has been widely used.  These
     values can represent concentrations expressed
     as percent by volume or as milligrams per liter,
     etc.; they may all be multiplied or divided, as
     necessary, by any power
   TABLE 1:  GUIDE TO SELECTION OF EXPERIMENTAL
  CONCENTRATIONS, BASED ON PROGRESSIVE BISECTION
         OF INTERVALS ON LOGARITHMIC SCALE

Col. 1  Col. 2     Col. 3     Col. 4     Col. 5

10.0
                                          8.7
                               7.5
                                          6.5
                    5.6
                                          4.9
                               4.2
                                          3.7
         3.2
                                          2.8
                               2.4
                                          2.1
                    1.8
                                          1.55
                               1.35
                                          1.15
 1.0
of 10.  For example, the two values in the first
column may be 10.0 and 1.0 as shown, or they may be
100 and 10, or 1.0 and 0.1, with the values in the
other columns changed accordingly.  The values of

-------
                                                        11.
      the series 10.0, 5.6, 3.2,  1.8, and 1.0 (i.e.,
      Cols.  1-3),  or 10.0, 7.5, 5.6, 4.2, 3.2, etc.
      (Cols.  1 through 4), are evenly spaced when
      plotted on a logarithmic scale."

 6.    At the  beginning of the bioassay, measure dissolved
      oxygen  (DO)  in each container.  If it is below
      4  mg/1, aerate that container until the DO is
      above 4 mg/1.

 7.    Additional optional measurements (in order of
      importance)  include pH, conductivity, turbidity and
      hardness (titration, expressed as EDTA as CaCO3).
      Figure  3 shows a blank data sheet.   Figure 5 shows a
      typical data sheet with observations recorded.

 8.    Record  the temperature daily  (on Data Sheet,
      Figure  5, range of temperature is recorded following
      reading on 7-day recording thermometer).

 9.    Keep room semidark and do not let people wander need-
      lessly  in to frighten fish.

10.    When transferring fish, do so gently so as not to
      harm them.

11.    Add fish in groups of two to the jugs.  Random
      placement of jugs and random addition of fish is
      recommended (see section on Random Sampling).

12.    Using data sheet, record mortality and D.O. at
      least every 24 hours along with any other information
      about the bioassay that may be subsequently of
      interest.  Remove dead fish as soon as they are
      observed.

 Calculation  of Results

 1.    The TLso (concentration of toxicant killing 50% of
      the fish) at 96 hours should be calculated by
      plotting toxicant concentration on the ordinate
      scale of semilog graph paper and survival on the
      abscissa (normal scale axis).

-------
                                                        12.
     For example,  if  the  96-hour results were obtained
     from a toxicity  test as below  (in Table 2)  the
     TLso can be  seen from  Inset in Figure  5 to  be
     68%.

          Table 2.  Survival of Fish vs. Toxicant,
          Typical  Data

              Survival
           (per 10  fish total)          % Toxicant

                  0                        100
                  3                        75
                  6                          65
                  9                          56
                10                          42
                10                          24
                10                          10

Statistical Treatment of  Fish Bioassay Results

     The TLso value can also be calculated  by using the
Reed-Muench Method  (Woolf,  1968).  This method also
allows one to calculate the 95% confidence  limits which
contain the true TLso value.
     Utilizing the data given on the sample record
sheet for the "Northwest  STP", the calculations  are
given in Figure 6.  Natural logs can be used in  place
of logs to the base 10, if  this is more convenient.
If the lowest dose in mg/1 or percent volume of
toxicant is less than one, multiply the dose values by
10 or 100 as logs values  less than one are  negative.
Then divide the resulting final values by the same
multiple.  Express the TL values as whole numbers in
the example given.

                          REFERENCES

Leteux, F. and F. P.  Meyer.  The Progressive Fish
     Culturist 34.  1972.   "Mixtures of Malachite
     Green and Formalin for Controlling Ichthyophthirius
     and other Protozoan  Parasites of Fish."
Woolf, C. M.  1968.  Principles of Biometry.  D. Van
     Nostrand Company.  Princeton, N. J.  359 pp.

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                                     Table  3
                TEST  ORGANISM SUITABLE FOR THE STATE OF HAWAII
                  University of Hawaii at Manoa
                                 i)(!,'nrlmont of Zoology
                              Edmiiiuisiiii Hall* 2538 The Mall
                                 Honolulu, Hawaii 96622
                          Suggested Native Hawaiian Fauna
                               for Aquatic Bioassay

                      (John A. Maciolek - Associate Professor)


      The following  fresh  and brackish waters animals are available  on most islands
in Hawaii and generally  can be kept without undue difficulty in aquaria  and holding
tanks.

A.  Freshwater species.

    1.  Shrimp:   Atya  bisulcata = opae kalaole, "mountain opae".   Occurs in fast-
        flowing streams  to about 3,000' elevation.  Very abundant  in pristine streams,
        but on Oahu, it  is common only at higher elevations.  Filter-feeds on stream
        seston and epilithic algae.  Normally completes its life cycle in freshwater
        but larvae can tolerate salinity.  Size:  to about 2".

    2.  Fish:  Awaous  stamineus = o'opu nakea and Sicydium stimpsoni = o'opu nopili.
        Doth species are abundent in the lower to middle reaches of  perennial streams
        on neighbor  islands; much less common on Oahu.   Larvae  develop in ocean and
        migrate upstream as post-larvae (hinana), often in great numbers, during
        several months of  the year.  Juveniles and adults do not tolerate saline
        water.  Feed on benthic algae (especially nopili) and small  invertebrates.
        Size:  hinana  about 1"; nakea adult to 12"; nopili adult to  7".


B.  Brackish water species:  the following shrimp and fishes are broadly euryhaline
    (freshwater to seawater).

    1.  Shrimp:   Palaemon debilis = opae huna, "glass shrimp".  Most common in estu-
        aries and brackish shoreline ponds, but is also found in most protected
        inshore marine areas.  Omnivorous, feeds on plant materials, detritus, etc.
        Can complete its life cycle in brackish water.   Size:  to  1.5".

    2.  Fish:  Kuhlia  sandvicensis = ahole, aholehole.   Occur in estuaries and inshore
        marine areas.  Juveniles (to 3") invade lower reaches of streams.  Carnivorous;
        predaceous on  invertebrates (shrimps, worms) and small  fishes.  Size:  to 12".

    3.  Fish:  Mugil cephalus = amaama, grey mullet.  Habitat similar to Kuhlia, but
        is herbivorous—feeding on phytoplankton, bottom sediments,  etc.  Fry and
        small juveniles  common in estuaries.  Size:  to at least 2 feet.

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                                          Holes increase in size from middle to end
xPVC pipe 3/4" diam

            2"
              Sand
              Filter
     Hose 3/4" diam.
                                                 (doe   O
                                    .Spreader
                                                   PVC Pipe (bottom view)
                                  Board at angle   Water goes through holes in PVC
                                                   pipe onto spreader board.
                              " diam. PVC
                                                         ergency overflow
                                                       (in event of sand clogging)




Pump
i i/«" aiam vaive \ i R\
If- PVC (Y "II
II '
-< L-1
                       Fish Tanks with Filtering System
      8" depth sand
  (No. 12, White Monterey)
   6" depth pea gravel
 12" depth rock (l"-3" in size)

row of PVC collector pipe
           i
                                                                3/4" diam.
 Sand Filter, Details
 (side view)

urface of sand in square feet
hould be approximately equal to
he flow in gallons per minute
                                                                           cap

• ' t


^2" diam.

^outlet (2" diam.)
V
PVC Collector Pipes, Details
                      (viewed from above)

                      Each pipe has holes of 3/8" - 1/2" diam.
                      spaced regularly at 2" intervals along
                      length.
         Figure 1.  Diagram of Fish Tanks with Filtering  System
                    (Details of Sand Filter and Collection Pipes  Included)

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                           GLASS TUBING
                              FLEXIBLE TUBING
                                        PINCH CLAMP
                                           BUCKET
                                           BOD BOTTLE
Figure 2  .   The siphon is first filled with distilled water.



After putting the glass tubing into the test water, the pinch



clamp can be released and enough water siphoned into the



bucket to displace the distilled water by test water.  Then



the end of the tube is put into the BOD bottle all the way to



the bottom.   After overflowing the bottle about twice, slowly



withdraw the tubing, allowing the water to flow until the tube



is out of the bottle.  Start with the control water and



proceed from the lower toxicant additions through the more



concentrated ones.  Then the siphon can be utilized without



rinsing it with distilled water.  Stopper the BOD bottles and




measure the dissolved oxygen by the routine Winkler method.

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    Figure 3 - Data Recording Sheet
Source



Number and Kinds of Individuals
                                 Collection Date
Bioassay Date



Temperature Range
Time
0
hour
i
t
24
hour
48
hour
72
hour
96
hour
Parameter
DO, mg/1
pH
EC, jumhos/cm
EDTA, as mg/1
CaCO3
JTU initial
1 hr
Survival
DO, mg/1

Survival
DO, mg/1

Survival
DO, mg/1

Survival
DO, mg/1
PH
EC , ^wmhos/cm
EDTA, as mg/1
CaCO-*
JTU

Control
Holding






















Dilution






















Waste Concentrations




















































































































































i


































-------
100


 90
 80   ' 87
 60
 50
 40
  30
  20
  10
         f
                              Inset indicates determination  of
                                 from percent survival and concen-
                             trations given in Table  2.  Plot 30%
                              survival at 75% concentration  and
                               60% survival at 65% concentration
                                 Draw straight line between  points.
                                   Line intercepts 50% survival at
                             42      point of 68% concentration.
 (For Insejt Percent Survival cjf Fish in Experiment)
                    i

L    i ijo  I	2$-     |3^L.    y I	sp     ep     7^i..   __sp	;_S^L..
            Regular Arithmetic Increments of the Log Scale
      Figure 4.  Guide to Fish Bioassay Concentration Selection

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        Figure 5  -   Completed Data Form

Source No^TKufit'  STf*        Collection  Date

Number and Kinds of  Individuals   \Q  ST) cKle b*cft / )•£

                          9£fc  C.*f«
-------
                               Figure 6

        CALCULATIONS FOR FISH BIOASSAY STATISTICAL CONFIDENCE LIMITS
Dose
18%
32
42
56
65
75
100
Log of
Dose
1.2553
1.5052
1.6232
1.7482
1.8129
1.8751
2.0000
No.
10
10
10
10
10
10
10
Number
Dead
0
0
3
10
10
10
10
Alive
10
10
7
0
0
0
0
Accumu!
Dead1
0
0
3
13
23
33
43
ated
Alive1
27
17
7
0
0
0
0
Total
27
17
10
13
23
33
43
Cumulated
% Mort.2
0
0
30
100
100
100
100
 (S.E.) Standard error =  /0.79 hR
                             n
h = interval between doses
R = interquartile  range which is TL?s - TL25-  If either of these TL50
    values are not found, use either 2(TLso - TL25) or 2(TLys - TLso)
    as the R value.

0.79 is a constant

n = number of organisms in each concentration (use mean number if variable)

h = 0.2499 + 0.1180 + 0.1250 + 0.647 + 0.0622 + 0.1249
h = 0.1241

TL2s = 1.5052 +
                30
                            = 1.6035 = 40.1%
TL50 = 1.6232 + 20 (0.1250) = 1.6589 = 45.6%
                70"

TLy5 = 1.6232 + 45 (0.1250) = 1.7036 = 50.5%
                To"
R = 1.7036 - 1.6035 = .1001

SE =  /0.79 x 0.1241 x .1001  =   .0313
     v/         !0
                                       95% confidence  limits  equal:

                                       TLso ±1.96  (SE)

                                       1.6589-1.96  (.0313)  =  1.5976  = 39.5%

                                       1.6589+1.96  (.0313)  =  1.7202  = 52.5%

                                          95% CL = 40%  -  52%
1.  Accumulative dead are derived from adding downwards in the numbers
    dead column and those alive by starting at the bottom of the numbers
    alive column and adding upwards.

2.  Cummulative % Mortality = Accumulative dead .1 total d^tf x 100

3.  Interpolation to determine log value between 0 and 30% mortality.

-------
                                                            1.
VI.  Use of Random Numbers

     A.   A table of random numbers is given in Table 1.  This
          listing can be used in randomization processes needed
          for sample collection or experimental design.

          For sample collection, the numbers selected would
          be used to pick the locations to be sampled.  It
          would be essentially a process of limiting the
          number of sample points, all points having an equal
          probability of being selected.            /

          In experiments the random numbers are used to
          assign positions of flasks, sequence of inoculation,
          etc.  The uses of random tables for the two purposes
          will be explained below.

          First it will be necessary to select the numbers
          from the table.  This consists of (1) selecting
          the starting point and  (2) listing sequentially
          a sufficient amount of numbers.

          1.   Selecting the starting point

                   Table 1 has the columns and rows each
               numbered 0-49.  Without looking, put your eraser
               or finger-tip on any location in the table.
               Assume the point is at the intersection of
               column 20 and row 30.  The numbers there are
               4113.  Then we can start using numbers at
               column 41 row 13.  If the number selected is
               too high, just move along the row until a number
               under 50 is encountered or find another starting
               location.

          2.   Listing the numbers

                   Using the above location, write down the
               numbers.  When getting to the end of the row start
               back in the reverse direction in the next lower

-------
                                                       2.
B.
     row.  Group the numbers singly or in pairs
     depending on whether more or less than 10
     samples have to be randomized.

         Assume that we have 15 samples to put
     in random order, then starting at our above
     location we would have:  93  15  11  80  45  81
     51  41  80  16  57  42  87  53  95  65  36  etc.,
     continuing until we have encountered numbers
     1-15.  In actual practice we would not write
     down the numbers until one 15 or under was
     encountered.

Use of the tables in experiments

Fish bioassays

     In these experiments, we would like at least
to randomize the position of the jugs on the bench,
and add 2 fish per jug in the randomized order.  For
example if we had the following jugs:
              Control
                   1%  10%  25%  50%  75%  100%
     Given
     Numbers      1      234567

          Utilizing the single sequence of numbers above,
     we would have on the bench the jugs so:
     10%
      Control
50%
25%
75%
100%   1%
          We could re-number the jugs as they appear now
     on the bench 1, 2, 3 	 and utilize a new selected
     sequence of numbers for adding 2 more fish per jug.
     However, time considerations would probably preclude
     this approach, although its advantage should not be
     overlooked in a completely randomized experiment.

-------
                                                  3.
     Variations to the above approach, will probably
be obvious.

Algal Bioassay Flasks

     Randomization is possible in the sequence of
adding algae, placement of flasks on shelves, mass
measurement order, etc.  The importance of randomi-
zation in bioassays probably should be secondary to
an orderly sequence which would minimize errors.

-------
Table  1
TEN THOUSAND RANDOM DIGITS

00
01
02
03
04
05
06
07
OS
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
4")
46
47
48
49

00-04
88758
35661
26335
60826
95044
83746
27998
82685
18386
21717
18446
66027
51420
27045
13094
92382
16215
09342
30148
23689
25407
25349
02322
15072
27002
66181
097 7'J
10791
74833
17583
45G01
60683
29!.>56
91713
85704
17921
13929
03248
50583
10636
43896
76714
22393
70942
92011
66456
96292
19680
07347
05-09
66605
42832
03771
74718
99896
47694
42562
32323
13862
13141
83052
75177
96779
62626
17725
62518
50809
14528
79001
19997
37726
69456
77491
33261
31036
83316
01822
07700
55767
24038
40977
33112
81169
84235
86588
26111
71341
18880
17972
46975
41278
80963
46719
92042
60326
00126
4434!!
07146
51142
95888 59255
10-14
33843
16240
46115
56527
13763
06143
63402
74625
10988
22707
31842
47398
54309
73159
14103
17752
49326
64727
03509
72382
73099
19693
56095
99219
85278
40386
45537
87481
31312
83701
39325
65995
18877
75296
82837
35373
80188
21667
12690
09449
42205
74907
15-19
43623
77410
88133
29508
31764
42741
10056
14510
04197
68165
08634
66423
87456
91149
00067
53163
77232
71403
79424
15247
51057
85568
03055
43307
74547
54316
13128
26107
76611
28570
09286
64203
15296
69875
20-24
62774
20686
40721
91975
93970
38338
81668
85927
18770
58440
11887
70160
78967
96509
68843
63852
90155
84156
39625
80205
68733
93876
37738
39239
84809
29505
51128
24857
67389
63561
41133
18070
94368
82414
67822 95963
86494
89827
48266
48277
01311 ! 61806
00452
45986
10425
16890
93766
34672
66560
15492
02083 62428 45177
22776
86346
45685
47761 13503
26738 OI9U3
67607 i 70796
25-29 30-34
25517
26656
06787
13695
60987
97694
48744
28017
72757
19187
86070
16232
79638
44204
63565
44840
69955
34083
73315
58090
75768
18661
18216
79712
36252
86032
82703
27805
04691
00098
34031
65437
16317
05197
35-39 40-44
09560 41880 85126
59698
95962
25215
14692
69300
08400
80588
71418
08421
08464
67343
68869
92237
93578
02592
93892
35613
18811
43804
77991
69018
81781
94753
09373
34563
75350
42710
39687
60784
94867
13624
34239
66596
83021 90732
01888
65735
07229 i 71953
80201 47889
16414
46916
59967
27489
57562
16037
04186
01889
20898 i 02227 76512 i 53185
53951 10935 ' 23333 76233
01212
63881
90139
06067
49243
30875
41388
98128
03057
13706
24536 60151 05498 64678 ! 87569
06898 99137
t
50871 j 81265 42223
t (
86241 13152
60841 j 91788
72237
71039
99864
83124
14756
81133
23872
20565
36205
49062
29969
24756
88572
70445
35670
86230
94548
72641
10332
32245
41450
69471
93204
25179
63471
13596
76098
1 1849
90896
031543
13083
32661
05315
16128
83052
27964
83117
73563
22287
31748
80754
03848
13599
61375
20502
65066
83303

06337
34165
19641
19896
54937
69503
03036
74390
50036
02196
49315
10814
03107
00906
10549
99682
82693
95386
83137
84081
30944
15606
72973
86104
08804
88730
84217
75171
80945
66081
46278
64751
79328
65074
31029
02766
53947
29875
19760
64278
47491
78354
93710
10760
45-49
60755
49187
86386
73439
21297
15083
18805
76379
44037
34208
36541
59411
55109
11804
15185
90169
57002
07468
828%
22799
70138
88257
18436
53912
77209
90760
40638
23455
86850
34997
57682
71987
12242
73498
83903
13367
28782
06023
28786
95218
79033
13056
05731
96012
14964
23974
26889
60405 ! 09745
17790
48694
55413
81953


-------
VII.  APPENDIX



     Contents                                            Page

Equivalent Values                                         1

Physical Constants                                        4

Specific Conductance Conversion Figure                    4

Mathematical Formulae                                     5

Oxygen Solubility and Nomograph                           6

Interconversion Tables
   Centegrade to Fahrenheit                          .     7
   Meters to Feet                                         8

Plankton Neeting Aperture Size and Grades                 9

Sediment Size Classification                              9

Sieve Scales - Wentworth, Tyler, and U.S.
  Sieve Series                                           10

Formula Weights                                          11

Atomic Weights                                           13

Relative Humidity                                        14

Stock Solutions                                          15

Composition of Commercial Acids and Bases                15

Exponential Arithmetic                                   16

Significant Figures                                      17

Use of Logarithms and Exponents                          18

-------
                            -1-
                             .KO.UVAI.KNT VALUES
Depth
  \ fathom = 6 feet
           = 1.829 meters

Area
  1 square incli — 6.42 s(jiuirc centimeters
  1 s(|imrc foot -- 929.03 square centimeters
  1 S(|ii;irc yard -- 0.836 square meter
  1 acre = 43,560 square feet
        = 4840 square yards
        = 160 square rods
        = 10 square chains (Guntcr's)
        = 0.4047 hectare
  1 section = 640 acres
           = 1 square mile
  1 square mile — 640 acres
               = 259 hectares
               = 2.59 square kilometers
  1 square millimeter =  0.0015 square inch
  1 square meter — 10.758 square feet
  1 hectare = 10,000 square  meters
           = 2.5 acres (approximately)

Volume
  1 cubic inch = 16.386 cubic centimeters
  1 cubic foot = 28,316 cubic centimeters
              — 7.48 gallons
              = 0.0283  cubic meter
  1 cubic yard — 0.7646 cubic meter
  1 acre-foot = 325,850 gallons
  1,000,000 cubic feet = 22.95 acre-feet
  1 cubic centimeter = 0.061 cubic inch
  1 cubic meter -- 35.314 cubic feet
               -•= 1.308 cubic yards
Length
  1 inch = 25.40 millimeters
        =  2.54 centimeters
  1 foot = 0.305 meter
        = 30.5 centimeters
  1 yard = 3 feet
        = 0.914 meter
  1 rod = 16.5 feet
        =  5.5 yards
  1 mile (statute) = 63,360 inches
                 = 5280 feet
                 = 1760 yards
                 = 320 rods
                 = 1609 meters
                 = 1.609 kilometers
                 = 0.867 geographic mile
  1 millimeter = 0.0393 inch
  1 centimeter = 0.393 inch
  1 meter = 39.37 inches
          = 3.281 feet
          = 1.0936 yards
          = 0.000621  mile
  1 kilometer = 3281  feet
             = 1000 meters
  1 chain (Guntcr's) = 792 inches
                    = 66 feet
                    = 4 rods
                    = 0.0125 mile
  1 link (Guntcr's) == 7.92 inches
                   = 0.04 rod
  1 chain (engineer's) = 100 feet
  1 link (engineer's) = 1 foot

-------
                            F.(»UIVAU-:.NT YAI.UKS

        Capacity
           1 U.S. pint = 473.IS cubic centimeters
           1 U.S. quart = 2 pints
                       = 946 cubic centimeters
                       = 0.946 liicr
           1 U.S. gallon = 231 cubic inches
                        = 4 quarts
                        = 3784 cubic centimeters
                        = 3.784 liters
           1,000,000 gallons = 3.07 acre-feet
           1 liter = 61.027 cubic inches
                 = 2.11 pints
                 = 1.0567 quarts
                 = 1000 cubic centimeters

        Miscellaneous
           1 atmosphere pressure = about 15 pounds per square inch
                                 = about 1 ton per square foot
                                 = about 1 kilo per square centimeter

        Angles
           1 circumference = 360 degrees
           1 degree = 60 minutes
           1 minute = 60 seconds
          METRIC  SYSTEM                            ENGLISH SYSTEM

                               Units of Length
Meier (in.) = 39.37 inches (in.)              Yard = 0.914-1 in.
Centimeter (cm.) = 0.01 in.                 Inch (U.S.) = 2.51 cm. (Fig. 1-5)
Millimeter (mm.) = 0.001 ni.
Kilometer (km.) =  1000 in.                 Mile (U.S.) = 1.609 km.
Angstrom unit (A.U. or A) = 10~* cm.'

                               Units of Volume
Liter  (I.) = volume of 1 kg. of water         Liquid qunrt (U.S.)  = 0.9163 I.
Milliliter (ml.) = 0.001 I.                    Cubic foot (U.S.) = 28.316 I.

                               Units of Weight
Gram (it.) = weight of 1 ml. of water         Ounce (oz.)(avoirdupoi3) = 28.35 g.
  Ql 'V \j
Milligram (ing.) = 0.001 g.                  Pound (Hi.) (avoirdupois) = 0.1336 kg.
Kilogrmii (kg.) = 1000 g.                    Ton (short) = 907.1«3 kfj.
Ton (metric) = 1000 kg. = 2201.62 Ib.        Ton (long) = 221011). = 1.016 metric tons

-------
                       -3-
                       NUMKKICAL EQUIVALENTS
             l.KNGTII
           1 in. = 2.540cm
            1 fl = 30.48 nil
           1 in'i-- 1.609km
          1 cm = 0.3937 in.
           1 in =39.37 in.
          1 km = 0.6214 mi
           1 in = 3.28 ft

              Sl'KKU
      15mi/lir=22ft/sec
        1 mi/lir= 1.467 ft/src
        1 ini/lir — 44.7 cm/sec
       1 km/hr = 27.78 cm/sec

              FORCE
         1 g.Xvt = 980 dynes
        1 kg-wt = 2.205'lb
           1 ox = 28.35 R-wt
           1 llj = 453.6g-\vt
          '1 lh = 4.448 X 10" dynes
           1 II) = 4.448 newloiis
      1  ncwton — 10" dynes
      1  ncwton = 3.60 oz

             PRESSURE
1 in. of mercury =
1 cm of mercury
1 cm of mercury
    1 ft of water
  1 in. of water
  1 cm of water
  1 cm of water
       1  Ib/in.2
          1 bar =
          fl.ar
  1 atmosphere
  1 atmosphere
 = 0.491 Ib/in.2
  0.1934 Ib/in.2
  0.0133 bar
  0.433 Ib/in.2
  0.0361 Ib/in.2
  0.0142lb/in.2
  0.980 millibar
  0.0690 bar
 = 10" dynes/em2
= 14.5 Ib/in.2
= 1.0132 bars
= 14.7lb
1 atmosphere = 1.058 tons/ft2
1 atmosphere = 76 cm ol mercury

       WORK AND KNKKGY
      1 joule = 107 ergs
      1 joule = 0.738 fi-lb
      1 joule = 0.000000278 kw-hr
      1 joule = O.OOOU00373  hp-hr
      1 joule = 0.239 cal
       1 ft-Ib= 1.35 joules
       1 ft-lb= 1.35 X 107ergs
       1 ft-lb = 0.324 cal
       1 fi-lb= 0.001286 Htu
        1  cal = 4.18 joules
        1  cal = 3.086 ft-lb
       1 Bin = 252 cal
       1 Btu= 778ft-lb
       1 Btu = 1055 joules
     1 kw-hr = 3.6 X 10(i joules
     1 kw-hr =2.655 X 10(i ft-lb
     1 kw-hr = 1.341 hp-hr
      1 hp-hr = 1.98X 10" ft-lb
      1 hp-hr = 2.68 X 10" joules
      1 hp-hr = 0.746 kw-hr

             POWER
        1  hp = 746 watts
        1  hp= 178cal/sec
    1 Utu/hr = 0.293 walls
        1  kw= 1.34 li|>
      1 wall = 0.239 cal/sec

     ELECTRICAL QUANTITIES
      10 amp = 1 em  unit
 10 coulombs = 1 em  unit
   1 coulomb = 3 X 10" es units
    300 volts = 1 es unit
 1 microfarad = 9 X 10"' es units
 1 millihenry = 10''em units

-------
                        -4-
              ACCEPTED VALUES OF CERTAIN QUANTITIES
Velocity of light in vacuo	
Gravitation constant	
Electronic charge	
Electronic charge	
Number of molecules at  0° C atmospheric pressure
Number of molecules in 1 gram-molecular weight at
  0° C  atmospheric pressure (Avogadro's number)
Mass of hydrogen atom	
Mass of electron	
Mass of electron in atomic mass units	
Mass of proton   	
Unit of atomic mass	
Unit of atomic mass equivalent to	
1 electron-volt   	
Planck's constant (h)	
 299,776 km/sec
 6.670X 10~8cgsunit
  4.80 X 10~10esunit
  1.60X 10-'9coul
  2.69 X 1019 per cm2

6.0233 X 1023
  1.67 X 10~24g
  9.11 X 10-28g
 5.486 X 10~4 amu
  1.67X 10-24g.
 1.660X 10-24g
 0.00146 erg .
  1.60X 10-12erg
 6.624 X 10~27 erg-sec
                    SOME GEOMETRICAL RELATIONS

                    TT= 3.1416, or 3f approximately
                    Circumference of a circle = 2 TTT
                    Area of a circle          = irr2
                    Area of a sphere         = 4 irr2
                    Volume of a sphere      = 3 irr3
                     SOME TRIGONOMETRIC RELATIONS
            sin 6 = rr F or 7 = R sin 0.

            cos 6 — — • or x = R cos 0.
                   K
               n   y   sin 6             n
            tan u — •*- =	2» ory = x tan u.
                   x   cos o
                       cos
                          e
               n   A    cua i/             /i
           cot 0 — - — -—a' or x —y cot u.
                   y    sin a
l./U
1.60
1.50
1.40
o
& 1.30
*5
'•a 1.20
ir
3
2
1.10
1.00
0.90
nnn
\
>








\
\









\
\








V










\









\

                                                 Factors for converting  specific
                                                 conductance of water to equiva-
                                                 lent values at 25 C (based  on
                                                 0.01 A/ KC1 solution).
                    5    10   15   20   25
                      Temperature of Sample-°C
                                            30

-------
           A1 ATIiI-..NiATICAi.  FORMULAS
Given
                                  Sought
                           Formula
Triangle
    1. Base (b) and
      altitude (a')
    2. Area (a) and base (/;)
      or altitude (a')
    3. Three sides (d, d', d")
   4. Base (/;) and perpen-
      dicular  (•/)) of right-
      angle triangle
   5. Base  (b)  or perpen-
      dicular  (p)  and  hy-
      potenuse (h) of right-
      angle triangle

Trapezoni
   (>. Sides (s and /)  and
      altitude (/)

Trapezium
   7. Diagonal (d) and  per-
      pendiculars   (p   and
      p')  to diagonal drawn
      from  vertices of  op-
      posite angles
Circle
   8. Radius (r)

   9. Circumference (c)

  10. Radius (r)
Sphere
  11. Radius (/)

  12. Radius (r)

Cylinder
   13. Radius  (r)  and
      altitude (a')
Cone
   14. Radius  (r)  and
      altitude (a')
   15. Radius  (r)  and
      slant height (/.')

Frustnnn of Cone
   16. Areas  of both  bases
      (b  and />')  and  alti-
      tude (a')
   17. Circumferences     (c
      and  c')   and   slant
      height (b)
Area (rt)

Base  (b), or
   altitude (rt')
Area (a)
                 I lypotcnusc (A)
Base  (/;),  or per-
  pendicular (p)
                 Area  (a)


                 Area (a)
                                         b
-------
                      Solubility of oxygen, from a wet atmosphere at a pressure of
             760 mm. Hg, in mg. per liter, at temperatures from 0° to 35° C.
Temp.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
0.0
14.16
13.77
13.40
13.05
12.70
12.37
12.06
11.76
11.47
11.19
10.92
10.67
10.43
10.20
9.98
9.76
9.56
9.37
9.18
9.01
8.84
8.68
8.53
8.38
8.25
8.11
7.99
7.86
7.75
7.64
7.53
7.42
7.32
7.22
7.13
7.04
0.1
14.12
13.74
13.37
13.01
12.67
12.34
12.03
11.73
11.44
11.16
10.90
10.65
10.40
10.17
9.95
9.74
9.54
9.35
9.17
8.99
8.83
8.67
8.52
8.37
8.23
8.10
7.97
7.85
7.74
7.62
7.52
7.41
7.31
7.21
7.12
7.03
0.2
14.08
13.70
13.33
12.98
12.64
12.31
12.00
11.70
11.41
11.14
10.87
10.62
10.38
10.15
9.93
9.72
9.52
9.33
9.15
8.98
8.81
8.65
8.50
8.36
8.22
8.09
7.96
7.84
7.72
7.61
7.51
7.40
7.30
7.20
7.11
7.02
0.3
14.04
13.66
13.30
12.94
12.60
12.28
11.97
11.67
11.38
11.11
10.85
10.60
10.36
10.13
9.91
9.70
9.50
9.31
9.13
8.96
8.79
8.64
8.49
8.34
8.21
8.07
7.95
7.83
7.71
7.60
7.50
7.39
7.29
7.20
7.10
7.01
0.4
14.00
13.63
13.26
12.91
12.57
12.25
11.94
11.64
11.36
11.08
10.82
10.57
10.34
10.11
9.89
9.68
9.48
9.30
9.12
8.94
8.78
8.62
8.47
8.33
8.19
8.06
7.94
7.82
7.70
7.59
7.43
7.38
7.28
7.19
7.09
7.00
0.5
13.97
13.59
13.22
12.87
12.54
12.22
11.91
11.61
11.33
11.06
10.80
10.55
10.31
10.09
9.87
9.66
9.46
9.28
9.10
8.93
8.76
8.61
8.46
8.32
8.18
8.05
7.92
7.81
7.69
7.58
7.47
7.37
7.27
7.18
7.08
6.99
0.6
13.93
13.55
13.19
12.84
12.51
12.18
11.88
11.58
11.30
11.03
10.77
10.53
10.29
10.06
9.85
9.64
9.45
9.26
9.08
8.91
8.75
8.59
8.44
8.30
8.17
8.04
7.91
7.79
7.68
7.57
7.46
7.36
7.26
7.17
7.07
6.98
0.7
13.89
13.51
1,3.15
12.81
12.47
12.15
11.85
11.55
11.27
11.00
10.75
10.50
10.27
10.04
9.83
9.62
9.43
9.24
9.06
8.89
8.73
8.58
8.43
8.29
8.15
8.02
7.90
7.78
7.67
7.56
7.45
7.35
7.25
7.16
7.06
6.97
0.8
13.85
13.48
13.12
12.77
12.44
12.12
11.82
11.52
11.25
10.98
10.72
10.48
10.24
10.02
9.81
9.60
9.41
9.22
9.04
8.88
8.71
8.56
8.41
8.27
8.14
8.01
7.89
7.77
7.66
7.55
7.44
7.34
7.24
7.15
7.05
6.96
0.9
13.81
13.44
13.08
12.74
ll41
12.09
11.79
11.50
11.22
10.95
10.70
10.45
10.22
10.00
9.78
9.58
9.39
9.20
9.03
8.86
8.70
8.55
8.40
8.26
8.13
8.00
7.88
7.76
7.65
7.54
7.43
7.33
7.23
7.14
7.05
6.95
n F jctt»t lor Otyftn
n «t Various A
Altitude
FW
0
110
6'j5
980
1310
1640
1970
2OT

2950
3260
3(10
3940
4270
4600
4910
5250
5WO
5910
6240
6560
6900
7?1'0
?yx>
Mrirei
0
ion
200
100
400
' 500
600
700

900
1000
1100
lAiO
1300
1400
T.OG
1(05
imO
1800
1'IUrt
?oco
?l«l
2?00
2(110
Plt\Mt
mm
760
750
741
732
721
714
705
696
687
679
671
661
6
-------
                                    TEMPERATURES—CENTIGRADE TO FAHRENHEIT*
Ttwp. ° C. | 0
0
10
20
50
40
50
32.0
50.0
68.0
86.0
104.0
122.0
;
33.8
51.8
69.8
87.8
105.8
123.8
2
35.6
53.6
71.6
89.6
107.6
125.6
3
37.4
55.4
73.4
91.4
109.4
127.4
4
39.2
57.2
75.2
93.2
111.2
129.2
5
41.0
59.0
77.0
95.0
113.0
131.0
C
42.8
60.8
7.8.8
96.8
114.8
132.8
7
44.6
62.6
80.6
98.6
116.6
134.6
5
46.4
64.4
82.4
100.4
118.4
136.4
9
48.2
66.2
84.2
102.2
120.2
138.2
   •Temperatures in degrees Centigrade expressed in left vertical column  and in  top  horizontal row; corresponding  temperatures  in
degrees Fahrenheit in body of table.
                                    TEMPERATURES—FAHRENHEIT  TO CENTIGRADE*
Temp. ° /•'.
30
40
50
60
70
SO
90
100
0
- 1.11
4.44
10.00
15.56
21.11
26.67
32.22
37.78
/
- 0.56
5.00
10.56
16.11
21.67
27.22
32.78
38.33
•7
0.00
5.56
11.11
16.67
22.22
27.78
33.33
38.89
3
0.56
6.11
11.67
17.22
22.78
28.33
33.89
39.44
4
1.11
6.67
12.22
17.78
23.33
28.89
34.44
40.00
5
1.67
7.72
12.78
18.33
23.89
29.44
35.00
40.56
c
2.22
7.78
13.33
18.89
.24.44
30.00
35.56
41.11
-
2.78
8.33
13.89
19.44
25.00
30.56
36. !1
41.67
5
3.33
8.89
14.44
20.00
25.56
31.11
36.67
42.22
9
3.89
9.44
15. CO
20.56
26.11
31.67
37.22
L ? ~C
. _ . / \j
   'Temperatures in degrees Fahrenheit expressed in left vertical column and in  top  horizontal rov.-; corresponding  temperatures  in
decrees Centigrade in bodv of table.

-------
                                                 METERS TO  FEET*
Meters
0
111
20
30
41)
50
60
70
80
90
100
0
0.00
32.S1
65.62
98.43
131.24
164.04
196.85
229.66
262.47
295.28
328.09
;
3.28
36.09
68.90
101.71
1 34.52
167.33
200.13
232.94
265.75
298.56
331.37
2
6.56
39.37
72.18
104.99
137.80
170.61
203.42
236.22
269.03
391.84
334.65
3
9.84
42.65
75.46
108.27
141.08
173.89
206.70
239.51
272.31
305.12
337.93
4
13.12
45.93
7S.74
111.55
144.36
177.17-
209.98
242.79
275.60
308.40
341.21
5
16.40
49.21
82.02
114.83
147.64
1 80.45
213.26
246.07
278.88
3 1 1 .69
344.49
6
19.69
52.49
85.30
118.11
150.92
183.73
216.54
249.35
282.16
314.97
347.78
7
22.97
55.78
88.58
121.39
154.20
187.01
219.82
252.63
285.44
318.25
351.06
5
26.25
59.06
91.87
124.67
157.48
190.29
223.10
255.91
288.72
321.53
'354.34
9
29.53
62.34
95.15
127.96
160.76
193.57
226.38
259.19
292.00
324.81
357.62
"Length in meters expressed in left vertical column and in top horizontal row; corresponding lengths in feet  in body of tal>lc.
                                                                                                                                            I
                                                                                                                                           CO
                                                                                                                                            I
                                                  FEET  TO METERS*
t'ett
0
10
20
30
40
50
60
70
80
90
100
0
0.000
3.048
6.036
9.144
12.192
15.239
18.287
21.335
24.383
27.431
30.479
;
0.305
3.353
6.401
9.449
12.496
15.544
18.592
21.640
24.688
27.736
30.784
2
0.610
3.658
6.706
9.753
12.801
15.849
18.897
21.945
24.993
28.041
31.089
i
0.914
3.962
7.010
10.058
13.106
16.154
19.202
22.250
25.298
28.346
31.394
•?
1.219
4.267
7.315
10.363
13.411
16.459
19.507
22.555
25.602
28.651
31.698
5
1.524
4.572
7.620
10.668
13.716
16.763
19.811
22.859
25.907
28.955
32.003
6
1.829
4.877
7.925
10.972
14.020
17.068
20.116
23.164
26.212
29.260
32.308
7
2.134
5.182
8.229
11.277
14.325
17.373
20.421
23.469
26.517
29.565
32.613
8
2. 438
5.486
. 8.534
1 1.5 8 2
14.630
17.678
20.726
23.774
26.822
29.870
32.918
9
2.743
5.791
8.839
11.8S7
14.935
17.983
21.031
24.079
27.126
30.174
33.222
'Length in feet expressed in left vertical column and in top  horizontal row; corresponding lengths in meters in body of table.

-------
                     -9-
AU.U.\<;K A
                          01  SI.\M>AIU> (JKAUK ])KHU:K HOI.TIM; SII.K
Silk No.
0000
000
00
0
1
2
3
4. •
5
6
7
8
9
Mesbe*
per
Inch
IS
23
29
3S
•IS
54
58
62
66
74
82
86
97
,S/:c of
Aperture
(linn.)
1.364
1.024
0.752
0.569
0.417
0.366
0.333
0.318
0.282
0.239
0.224
0.203
0.168
Silk No.
10
11
12
13
14
15
16
17
18
20
21
25

/I/.'J/.'O
per
Inch
109
116
125
129
139
150
157
163
166
173
178
200

                                                             She of
                                                            Aperture
                                                             (•linn.)

                                                             0.158
                                                             0.145
                                                             0.119
                                                             0.112
                                                             0.099
                                                             0.094
                                                             0.08'6
                                                             0.081
                                                             0.079
                                                             0.076
                                                             0.069
                                                             0.064
           GRADES AND Sl/K KAMil'.S OK SlLK Bol.TING Cl.OTII
Grade
Sundard
X quality
XX quality
XXX qunlitv
Grit gauze
XXX Grit gauze
Jtaiige of Sizes
Nos. 0000-25
Nos. 6-17
Nos. 0000-16
Nos. 6-18
Nos. 14-72
Nos. 14-72
WENTWORTH'S CLASSIFICATION OF COARSER SEDIMENTS BASED UPON  SIZE
                             OF PARTICLES
Diameter of I'article
in win.
More than 256
256-64
64-4
4-2
2-1
1-0.5
0.5-0.25
0.25-0.125
0.125-0.062
0.062-0.004
Less than 0.004
Name Applied to
Particle
Boulder
Cobble
Pebble
Granule
Very coarse sand
Coarse sand
Medium sand
Fine sand
Very fine sand
Silt
Clay

-------
                 -10-
WEMAVOKTH GRADE SCAI.K, \/2 Sc.\i >. $2 SCAII:. COKHKSTONDING TYLKR
  SIEVE OPKMM;S AND MESH, AND COKI-.HSI'ONDING MKSII OK U.S. SIEVE
                            SERIES
Wentwonh Grade
Scale
(iinn.)
4
Granule


2
Very coarse sand

1
Coarse sand


0.500 (%)
Medium sand


0.250(14)
Fine sand


0.125 (y8)
Very fine sand

0.062 ('/!„)
Silt
The Openings
Increase in the
Ratio of
\fior
1.414 mm.
4.00

2.83

2.00
1.41

1.00

0.707

0.500

0.354

0.250
0.177

0.125
O.OSS

0.062
•^/2 or
1.189wm.
4.00
3.36
2.83
2.38
2.00
1.68
1.41
1.19
1.00
0.840
0.707
0.595
0.500
0.420
0.354
0.297
0.250
0.210
0.177
0.149
0.125
0.105
0.08S
0.074
0.062
Tyler Screens
Mm.
3.96
3.33
2.79
2.36
1.98
1.65
1.40
1.17
0.991
0.833
0.701
0.589
0.495
0.417
0.351
0.295
0.246
0.208
0.175
0.147
0.124
0.104
O.OSS
0.074
0.061
Mesh
5
6
7
8
9
10
12
14
16
20
24
28
32
35
42
48
60
65
80
100
115
150
I/O
200
250
U.S. Sieve
Series,
Mesh
5
6
7
8
10
12
14
16
18
20
25
30
35
40
45
50
60
70
80
100
120
140
170
200
230

-------
11-
                    •;:; i q.
AgBr
AgBrOj
AgCNS 	 	
AgCI
Ag,CrO4
Agl 	
AglO,
AgNO,
Ag2O
Ag,PO4
Ag2S
Al,0, 	
AI(OH),
AI2(S04),
AsjO, 	 	 _... 	 	
As205
As2S,
BaCO) 	
Ba(CNS)2
BaCI2
Ba(CIO«),
BaCrO4
BaO
BaO2
Ba(OH)z
Ba,(P04)2
BaSO4 	
Bi2S,
Cai(AsO4)2
CaBr, 	
CaCO,
CaC2O4
CaF,
Ca(IO,),
CaO
Ca(OH)2
Ca,(P04),
CaSO4
Ce02
Ce(S04)2
H,Ce(S04)4
(NH4),Ce(NO,)t
(NH,)2Ce(S04),-2H20
CO,
CO(NH2)2 (urea)
Cr,0,
CuCO,
Cul
CuO
Cu;O
Cu5O4-5H2O
187.80
235.80
165.96
143.34
231.77
. 234.79
282.79
169.89
231.76
418.62
247.83
101.96
78.00
342.16
. 197.82
229.82
246.02
197.37
253.53
208.27
336.27
253.37
153.36
169.36
171.38
602.03
233.43
514.20
398.06
199.91
100.09
128.10
78.08
389.90
56.08
74.10
310.19
136.15
172.13
332.26
528.42
548.26
500.44
44.01
60.06
1 52.02
123.55
190.45
79.54
143.08
249.69



















































CuS
Cu2S
FeCO,
Fe(Cr02)2 	
FeO
FeiOj 	 __
Fe,04
Fe(OH),
Fc(OH),.. 	
FeS2
FeSO.-7H2O
FeSO4-(NH4)2SO4-6H2O
Fe2(S04),
HBr
H2C2O4-2H2O (oxalic) ._
HC;H,O2 (acetic)
HC,H5O2 (benzoic)
HCI .
HCIO4
HNO,
HNH2SO, (sulfamic)
H202
H,P04
H,S
H2SO,
H2SO4
Hg(NO,)2
HgO
HgS
Hg2Br2 	
Hg2CI2
Hg2l2
KBr
KBrO,
KCN
KCNS
K2CO,
KCI
KCI03
KCIO4
K2Cr04
K2Cr20,
K,Fe(CN)t
K«Fc(CN)»
KHC2O4
KHC2O4-H2C2O4-2H2O
KHC4H4O4 (tartrate)
KrjC9H4O4 (phthalate)
KH(IO,)2
KH;P04
K,HPO4 f

159 11
1 1 5 •:,'
223 :.,'
71.8S
.159.7 '3
231 5S
8987
.10637
1199i
27803
392.16
399.9:)
80.92
126.07
60.05
122.12
36.46
100.46
63.02
97.10
34.02
98.00
34.03
82.03
98.08
324.63
21661
232.68
561.05
472.13
655.04
119.02
167.02
65.12
97.19
138.21
74.56
122.56
138.56
194.2!
294.2'.?
329.26
363.36
128.13
25-M'-1
183.1;;
20-5.2;
389. V;
137CV
175 1:

-------
-12-

no,
MO. 	 	
t '.V'O,
>->.,O.
••jo', . 	
» o
r.OH
K.PlCI,
>. so,
I. CO)
Id .. . ._....
i. .so,
VqCO,
Vg CIO<),
M(jNH,PO4
WqO
Vq OH),
Mq P,O,
MqSO.
M-iO,
Mn.O,
Mn:O,
MM 'OH),
V.o.P.Q,
No.AiO,
No.B.O,
NaBr
NoBrO,
NaC.H.O, .
NoCN
NoCNS
No;CO,
No.C;O,
NnCI
NoCIO
NuCIO, 	 	
NnHCO,
^J(ll
NoNO,
No O
-'•'O.O; .. . . ..' 	
f.'nOH
N» PO,
••o.S
'•!• SO,
•o.SO.
'• - S;O, 5H,O
NH,
NI'<,
ff-'i.KiO,
166.01
214.01
230.01
158.03
85.11
101. VI
94.20
56.11
486.03
174.27
73.89
. 42.40
109.95
84.33
223.23
137.34
40.32
58.34
222.59
120.39
86.94
157.88
228.82
88.96
283.83
191.88
201.26
102.91
150.91
82.03
49.01
81.08
106.00
134.01
58.45
74.45
90.45
84.02
149.90
85.00
61.98
. 77.98
40.00
163.95
78.05
126.05
142.05
248.19
17.03
32.05
124.10
^
r.

















































NH4CI
NH4NO,
NH4OH
(NH4)3PO4-12MoO,
(NH4)2PtCI6
(NH4)2S04 .
P2O5
PbCO,
PbC2O4
PbCrO4
Pbl2
.Pb(l03)2
PbMoO4
Pb(N03)2
PbO
PbO2
Pb304
Pb3(P04)2
PbSO4
Sb203
Sbz04
Sb2O5
Sb2S3
Si02
SnCI2
SnO2
SO,
S03
SrCO,
SrC2O4
SrO
Sr3(P04)2
SrSO4
TiO2
UF6
U03
U30,
V205
ZnBr2
ZnO
Zn2P2O7
ZnS
ZnSO4
Wafer for Hydrates:
1 H2O
2 H2O
3 H20
4 H2O
5 H2O
6 H2O
7 H2O
53.50
80.05
35.05
1876.50
443.91
132.15
141.95
267.22
295.23
323.22
461.03
557.03
367.16
331.23
223.21
239.21
685.63
811.58
303.27
291.52
307.52
323.52
339.72
60.09
189.61
150.70
64.07
80.07
147.64
175.65
103.63
452.84
183.70
79.90
352.07
286.07
842.21
181.90
225.21
81.38
304.71
97.45
161.45

18.02
36.03
54.04
72.06
90.08
108.10
126.11

-------

Element
Actinium
Aluminum
Americium
Antimony
Argon
Arsenic
Astatine
Barium
Berkclium
Beryllium
Bismuth
Boron
Bromine
Cadmium
Calcium
Californium
Carbon
Cerium
Cesium
Chlorine
Chromium
Cobalt
Columbium (see
Copper
Curium
Dysprosium
Einsteinium
Erbium
Europium
Fermium
Fluorine
Francium
Gadolinium
Gallium
Germanium
Gold
Hafnium
Helium
Holmium
Hydrogen
Indium
Iodine
Iridium
Iron
Krypton
Lanthanum
Lead
Lithium
Lutetium
Magnesium
Manganese
-
Svmbol
"M'^
Al
Am
Sb
A
As
At
Ba
Bk
Be
Bi
B
Br
Cd
Ca
Cf
C
Ce
Cs
Cl
Cr
Co
Niobium)
Cu
Cm
Dy
E
Er
Eu
Fm
F
Fr.
Gd
Ga
Ge
Au
Hf
He
Ho
H
In
1
Ir
Fe
Kr
La
Pb
Li
Lu
my
Mn
' ' Oj
At.
89
13
95
51
18
33
85
56
97
4
83
5
35
48
20
98
6
58
55
17
24
27

29
96
66
99
68
63
100
9
87
64
31
32
79
72
2
67
1
49
53
77
26
36
57
82
3
71
12
25
.*«•
uJ^-
No At.Wt.
227
2698
[2431
12176
39.944
74.91
[210|
137.36
[245|
9.013
209.00
10.82
79.916
112.41
40.08
|248|
12.011
140.13
132.91
35.457
52.01
58.94

63.54
[245]
162.51
[254|
167.27
152.0
[252|
19.00
[2331
157.26
69.72
72.60
1970
178.59
4.003
164.94
1.0030
114.82
12691
1922
5585
83 GO
13392
20/21
6 940
17499
243?
5474
:y)slXfi§
Element
... .. H-'levium
f.-tcuiy
11 •:)-bclenum
'.-odyinium
•,r on
•. j.timium
-. ,l.rl
'. rbium
•. irogen
Oi mium
Cuygcn
fcjiladium
Frospliorus
r.otinum
Plutonium
Polonium
Potassium •
Praseodymium
Promethium
Protoactinium
Radium
Radon
Rhenium
Rhodium
'.'uhidium
Ruthenium
Samarium
Scandium
Selenium
Silicon
Silver
Sodium
Strontium
Sulfur
Tantalum
Technetium
Tellurium
Terbium
Thallium
Thorium
Thulium
Tin
Titanium
Tungsten
Uranium
Vanadium
Xenon
Ytterbium
Yttrium
Zinc
Zirconium

Symbol
Mv
Hg
Mo
Nd
Ne
Np
Ni
Nb
N
Os
O
Pd
P
Pt
Pu
Po
K
Pr
Pm
Pa
Ra
Rn
Re
Rh
Rb
Ru
Sm
Sc
Se
Si
Ag
Na
Sr
S
Ta
Tc
Te
Tb
Tl
Th
Tm
Sn
Ti
W
U
V
Xe
Yb
Y
Zn
Zr

At.
101
80
42
60
10
93
28
41
7
76
8
46
15
78
94
84
19
59
61
91
88
86
75
45
37
44
62
21
34
14
47
11
38
16
73
43
52
65
81
90
69
50
22
74
92
23
54
70
39
30
40

NO At. Wt
[2561
200.61
95.95
144.27
20.183
[237]
58.71
92.91
14.008
190.2
16.
106.4
30.975
195.09
[242]
210.
39.100
140.92
[145]
231.
226,05
222.
186.22
102.91
8548
101.1
150.35
44.96
78.96
28.09
107.880
22.991
87.63
32.066
180.95
[99]
127.61
158.93
204.39
232.05
168.94
118.70
47.90
183.86
238.07
50.95
131.3
173.04
88.92
65.38
91.22

-------
RELATIVE HUMIDITY
Dry-Bulb Ther-
mometer: Degrees,
Fahrenheit
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
Difference between Dry-Bulb and Wet-Bulb Thermometers
1°
93
94
94
94
94
94
95
95
95
95
95
95
95
95
96
96
96
96
96
96
96
96
96
96
2°
87
87
88
S3
89
89
89
90
90
90
90
91
91
91
91
92
92
92
92
92
92
92
93
93
3°
80
81
82
82
83
84
84
85
85
85
86
86
86
87
87
87
88
88
88
88
88
89
*t
89
4°
74
75
76
77
78
78
79
79
80
81
81
82
82
82
83
83
84
84
84
85
85
85
86
86
5°
67
69
70
71
72
73
74
74
75
76
77
77
78
78
79
79
80
80
81
81
81
82
82
82
6°
61
63
64
65
67
68
69
70
71
71
72
73
74
74
75
75
76
77
77
77
78
78
79
79
7°
55
57
59
60
61
63
64
65
66
67
68
69
70
70
71
72
72
73
73
74
75
75
75
76
8°
50
51
53
55
56
58
59
60
61
63
64
65
66
66
67
68
69
69
70
71
71
72
72
73
9°
44
46
48
50
51
53
54
56
57
58
60
61
62
63
63
64
65
66
67
67
68
69
69
70
10°
38
40
43
44
46
48
50
51
53
54
55
57
58
59
60
61
62
63
63
64
65
65
66
67
11°
33
35
38
40
42
44
45
47
49
50
52
53
54
55
56
57
58
59
60
61
62
62
63
64
12°
27
30
32
35
37
39
41
43
45
46
48
49
50
52
53
54
55
56
57
58
59
59
60
61
13°
22
24
28
30
33
34
37
38
40
42
44
45
47
48
49
51
52
53
54
55
56
56
57
58
14°
16
20
23
25
28
30
32
34
36
38
40
42
43
45
46
47
48
49
51
52
53
54
54
55
15°
11
15
IS
21
24
26
28
30
32
34
36
38
40
41
43
44
45
46
48
49
50
51
52
53
16°
6
10
13
16
19
22
24
27
29
31
33
35
36
38
39
41
42
44
45
46
47
48
49
50
17°
1
5
8
12
15
18
20
23
25
27
29
31
33
35
36
38
39
41
42
43
44
45
46
47
18°
0
0
4
8
11
14
16
19
22
24
26
28
30
31
33
35
36
38
39
40
41
43
44
45
                                                   *>.
                                                   I

-------
          -15-
Slock Solutions of Cations (SO mg. of cation per ml.)
Croup Ion Formula of Sail
I AR+ ABNO,
Pl>++ P1)(NO3),
Ilg,-1-1" Hg,(NO,),
II Pb++ P1>(NO,),
Bi+++- ]Ji(NO,),-5 H2O
Cu++ Cu(NO,V3 l(,0
Cd++ Cd(NO,),-4 11,0
Hg++ HgCli
As++t As4O<

Sb+++ SbCI,

Sn++ SnCli-2 H,O


Sn++++ SnCl4-3H20
III Co++ Co(NO,),-6 H,O
Ni++ Ni(NO,),-6 II 5O
Mn+* Mn(NO,)j-6 II,O
Fe*++ Fc.(NOi)j-9 HjO
Al+++ AI(NO,),-9 11,0
Cr+++ Cr(NO,),
Zn++ /n(NO,),
IV Ba++ BaCI,-2II,O
Sr++ Sr(NO,),
Ca++ Ca(NO,)s-41I20
V MB++ Mg(NO,),-6H,0
NH«+ NII«NO,
Na+ NaNO,
K+ KNO,

8.0
8.0
7.0
8.0
11.5
19.0
13.8
6.8
3.3

9.5

9.5


13".3
21.7
21.8
26.2
36.2
69.5
23.0
11.5
8.9
12.0
29.5
52.8
22 2
18.5
13.0
Crams />cr i(>0 ml. cij Solution


(dissolve in 0.6 M UNO,)

(dissolve in 3 M UNO,)



(heal in 50 ml. of 12 M HCI, then
tidd 50 nil. of wuler)
(dissolve in 6 M 1ICI, and dilute
with 2 M IIC1)
(dissolve in ,r,0 ml. of 12 M I1CI.
Dilute to 100 ml. with water.
Add a piece of tin metal)
(dissolve in 6 M 1IC1)














Composition of Commercial Acids and Bases
Arid or Base
Hydrochloric
Nitric
Sulfuric
Aortic
Atjucous ammonia
Specific
Gravity
1.19
1.42
1.84
1.05
0.90
I'ercenlage
by Weight
38
70
95
99
28
Molarily
12.4
15.8
17.8
17.3
14.8
Normality
12.4
15.8
35.6
17.3
14.8

-------
     Exponential Arithmetic
-16-
  In chemistry we use the exponential method of expressing very large and very
small numbers. These numbers arc expressed as a product of two numbers.  Tin-
first number of the product is called the digit term. This term is usually a ninnlxT
not less than 1 and not greater than 10.  The second number of the product i*
called the exponential  term and is written as 10 with an exponent.  Some example*
of the exponential method of expressing numbers are given below.
                      1000 = 1 X 103
                       100 = 1 X 10*
                        10 = 1 X 101
                         1 = 1 X 10°
                        0.1 = 1 X 10-'
                      0.01 = 1 X 10-2
                      0.001 = 1 X 10-»
                      2386 = 2.386 X 1000 = 2.386 X 10*
                      0.123 = 1.23 X .1 = 1.23 X 1f
10 and take the difference of the digit terms.
  EXAMPLE.  Subtract 4 X  I0~7 from 5 X lO"6
  SOLUTION.  4 X 10~7 =  0.1 X 10-"
              (5 X lO"6) - (0.4 X  10 '6) = 4.6 X 10-'
  3. Multiplication  of  Exponentials.  Multiply the digit  terms in the usual  way
and add algebraically the exponents of the exponential terms.
  EXAMPLE.  Multiply 4.2 X 10~8  by 2 X 103
  SOLUTION.  4.2 X 10~8
               2 X 103
             8.4 X 10-»
  4.  Division of Exponentials.   Divide  the digit  term of the  numerator by the
digit term of the  denominator and  subtract algebraically the exponents of the
exponential terms.
  EXAMPLE. Divide 3.6 X 10~6 by 6 X 10~4
             16x1 fl-~6
  SOLUTION,  '-j^p- - 0.6 X 10~l = 6 X 10~2

  5.  The Squaring of Exponentials.  Square the digit term in the usual way  and
multiply the exponent  of the exponential term by 2.
  ExAMPLK. Square the number 4 X 10~6
  SOLUTION.  (4 X l()-«)5 = 16 X 10-'- = 1.6 X 10"11
  6.  The Cubing of Exponentials.  Cube the digit term  in  the usual way and
multiply the exponent  of the exponential term by 3.
  EXAMPLE. Cube the number 2XI03
  SOLUTION.  (2 X 103)3 = 2x2x2x109 = 8x H)9
  7. Extraction of Square. Hoots of Exponentials.   Decrease or increase the expo-
nential term so that the power of ten is evenly divisible by 2.  Extract the square
root of the  digit term  by  inspection or by  logarithms and divide the exponential
term by 2.
  EXAMPLE. Extract the square root of 1.6 X 10~7
  SOLUTION.   1.6 x 10~7 = 16 x 10~8
            VI6 X 10-" - VI6 X X/lF5 = 4 X 10-4

-------
                             -17-
     Significant Figures

  A bee keeper reports thai lie has 525,341 bees.  The last three figures of the num-
ber are obviously  inaccurate,  for during the time the keeper was counting the
bees, some of them would have died and others would have hatched;  this would
have made the exact number of bees quite difficult to determine.  It would have
IKX-II more accurate if he had reported the number 525,000.  In other  words, the
last three figures arc not, significant, except to set the position of the decimal point.
Their exact values  have no meaning.
  In reporting any information in terms of numbers,  only  as many  significant
figures should be used as are warranted by the accuracy of the measurement.  The
accuracy of measurements is  dependent upon  the sensitivity of the  measuring
instruments  used.   For example, if the  weight of an  object has been reported as
2.13 g., it is assumed thai the last figure (3) has been estimated and that the weight
lies between 2.125 g. and 2.135 g.  The quantity 2.13 g. represents  three signifi-
cant figures.   The weight of this same object as determined by  a more  sensitive
balance may have been  reported as 2.131 g.  In this case one would assume the
correct weight to be between 2.1335  g. and 2.1315 g., and the quantity 2.134 g.
represents 4  significant figures.  Note that the last figure  is estimated  and is also
considered as a significant figure.
  A zero in  a number may  or may not be significant,  depending upon the manner
in which it is used.  When one  or more zeros are used in locating a decimal point,
they are not significant.  For example, the numbers 0.063, 0.0063, and  0.00063,
each have two significant figures.  When zeros appear between digits in a number
they arc significant.  For example, 1.008 g. has four significant  figures.  Likewise,
the zero in 12.50 is significant.  However,  the quantity 1370 cm. has four signifi-
cant, figures provided the accuracy of the measurement includes  the zero as a sig-
nificant digit;  if the digit 7 is estimated, then the number has only three significant
figures.
  The importance of significant figures lies in  their application to fundamental
compulation.  When adding or subtracting, the last digit that is retained in the
sum or difference should correspond  to  the first  doubtful decimal place (as indi-
cated  by underscoring).
  KXAMPLK.  Add 4.383 g.  and 0.0023 g.
  SOLUTION. .4.383 g.
              0.0023
              4.385 g.

When  multiplying or dividing, the product or quotient should contain  no more
digits than the least number of significant figures in the numbers involved in the
computation.
  EXAMPI.K.  Multiply 0.6238.by 6.6
  SOLUTION.   0.6238 X 6.6 = 4J.
  In rounding off numbers, increase the last digit retained  by one if  the following
digit is five or  more. Thus 26.5 becomes 27, and 26.4  becomes 26  in the rounding-
off process.

-------
                             -18-
     The Use of Logarithms and Exponential Numbers

  The common logarithm of a number is (lie power to which the number 10 must
be raised to equal that number.  For example, the logarithm of 100 is 2 because the
number 10 must be  raised to  the second power to be equal to  100. Additional
examples are as follows:
Number
10,000
1,000
10
1
0.1
0.01
0.001
0.0001
Number Erpresaed
Exponentially
10«
10'
10'
10°
10-'
io-»
10-'
io-«
IjMjarithm
1
3
1
0
-I
	 9
-3
—I
  What is the logarithm of 60?  Because 60 lies between 10 and 100, which have
logarithms of 1 and 2, respectively, the logarithm of 60 must lie between 1 and 2.
The logarithm of 60 is 1.7782, i.e., 60 - 101-7785.
  Every logarithm is made up of two parts, called the characteristic and the man-
tissa.  The characteristic is that part of the logarithm which lies to the left of the
decimal point;  thus the characteristic of the logarithm of 60 is 1.  The mantissa
is that part of the logarithm which  lies to I he right of  the decimal point; thus
the mantissa of the logarithm of 60 is .7782.  Tin- characteristic, of the logarithm
of a number greater than 1 is one less than the number of digits to the left of the
decimal point in the number.
Number
60
600
6000
52840
Clmraclerislic
1
2
3
4
Number
2.340
23.40
234.0
2340.0
Characteristic
0
1
2
3
The mantissa of the logarithm of a number is found in the logarithm table (see
Appendix B), and its value is independent of the position of  the decimal point.
Thus 2.340, 23.40, 234.0, and 2340.0 all have the same mantissa.  The logarithm
of 2.340 is 0.3692, that of 23.40 is 1.3692, that of 234.0 is 2.3692, and that of 2340.0
is 3.3692.
  The meaning of the mantissa and characteristic can be better understood from
a consideration of their relationship to exponential numbers.   For example, 2310
may be written 2.34 X 10s.   The  logarithm of  (2.34 X 10') = the logarithm of
2.34 + the logarithm of 101.   The logarithm of 2.34 is .3692  (mantissa) and the
logarithm of 10* is  3 (characteristic).  Thus the logarithm of 2340 = 3 + .3692,
or 3.3692.

-------
                           -19-
   The logarithm of a number less than 1 has a negative value, and a convenient
 method of obtaining the logarithm of such a number is given below.  For example,
 we may obtain the logarithm of .00231 as follows: When expressed exponentially,
 .00231 = 2.31 X 10~3.  The logarithm of 2.31 X 10 ' = the logarithm of 2.31  + the
 logarithm of I0~3. The logarithm of 2.31 is .3692 (mantissa) and the logarithm of
 10-3 is -3 (characteristic).  Thus the logarithm of .00231  = .3692 + (-3) = .3692 -
 3 = -2.6208.  The  abbreviated  form for  the expression (.3692 - 3) is 3.3692.
 Note that only the  characteristic has a negative  value in the logarithm 3.3692,
 and that the mantissa is positive. The logarithm 3.3692 may also be written as
 7.3692 - 10.
   To multiply two numbers we add the logarithms of the numbers.  For example,
 suppose we multiply 412 by 353.
                        logarithm of 412     =2.6119
                        Logarithm of 353     = 2.5478
                        Logarithm of product = 5.1627

 The  number which corresponds to the logarithm 5.1627 is 145400 or 1.454 X 10s.
 Thus 1.45 X I05 is (lie product of 412 and 353.
   To divide two  numbers we subtract the logarithms of the numbers.  Suppose
 we divide 412  by 353.
                        Logarithm of 412      = 2.6149
                        Logarithm of 353      = 2.5478
                        Logarithm of quotient = 0.0671

 The number which corresponds to the logarithm 0.0671  is 1.17. Thus 412 divided
 by 353 is 1.17.
    Suppose we multiply  5132 by 0.3121.   Add the logarithm of 0.3124 to  that of
 5432.
                       Logarithm of 5132       = 3.7350
                       Logarithm of 0.3124     = 1.4918
                       Logarithm of the product = 3.2298
 The number which corresponds to the logarithm 3.2298 is 1697 or  1.697 X 10s.
    Let us divide 5132 by 0.3121.  Subtract the logarithm of 0.3124 from  that of
 5432.
                      Logarithm of 5432       = 3.7350
                      Logarithm of 0.3124      = 1.4948
                      Logarithm of the quotient = 4.2402

 The number which corresponds to  the logarithm 4.2102  is 17390 or 1.739 X 10*.
    The extraction of roots of numbers by means of logarithms is a simple pro-
 ccdure.   For example, suppose we extract the cube root of 7235.  The logarithm
 of >X7235 or (7235)* is equal to % of the logarithm of 7235.
                          Logarithm of 7235 = 3.8594
                                £of 3.8591 = 1.2865
 The number which corresponds to  the logarithm 1.2865 is 19.34.   Thus, 19.34
 is the cube root of 7235.
•& GPO 7!XU2:t

-------