The total weight of fractions plus the weight of  the  material  that  reached  the  pan  comes  to 359.0 g. The weight of the sample originally was 359.1  g;  there  is  an  error  here  of  0.1  g.  At  the lower  right,  you  can  see  how  the  percentage  of error  is  computed.  The  maximum  permissible percentage  of  error  is  normally  (±)  1  percent.  If the  percentage  exceeds  the  maximum,  the  test must be rerun. For an error smaller than the max- imum permissible, correction is made by adding the  value  of  the  error  to  the  largest  amount  listed as retained. The value of the error in this case is 0.1 g. The largest amount retained is 83.3 g for the No. 20 sieve. This amount would be changed to  83.4  g. SIEVE   ANALYSIS   WITH   PREWASH- ING.— When inspection indicates that a sample contains an excessively high portion of superfine material  (material  that  passes  the  No.  200  sieve), analysis  with  prewashing  is  done  as  follows: 1.  Oven-dry  the  sample. 2.  Weigh  and  record  the  total  weight  after cooling. 3.  Place  the  sample  in  a  clean  pan  and  add clean water until it is completely covered. Allow it  to  soak  until  it  is  completely  disintegrated— from 2 to 12 hr. Stir to break up lumps and hasten the  action. 4. Wash the material thoroughly on a No. 200 sieve  under  running  water  and  discard  the  material that  passes. 5.   Oven-dry   and   reweigh.   Record   the   dif- ference  between  this  weight  and  the  original weight as washing loss. 6.  Continue  as  for  sieve  analysis,  dry. Figure  15-32  shows  a  data  sheet  for  sieve analysis with prewashing. The ovendry weight of the original sample was 75.0 g; the ovendry weight after  prewashing  was  55.0  g;  therefore,  the washing  loss  was  75.0  -55.0  or  20.0  g.  The  sum of  the  weights  retained  (53.0  g,  the  total  of  col- umn b) plus the 2.0 g that, in spite of prewashing, was  still  left  in  the  sample  to  pass  the  No.  200 sieve, equals 55.0 g. This was the original weight after prewashing. Therefore, no error was made. Hydrometer Analysis As you learned in the preceding discussion, the determination of grain size distribution by sieve analysis is limited to those materials larger than the No. 200 (0.074-mm) sieve. For uses such as soil classification,  this  is  sufficient  since  grain  size distribution  is  not  used  to  classify  fine-grained soils.  For  determination  of  frost  susceptibility, however,  the  distribution  of  particles  smaller  than the No. 200 sieve is necessary. A soil is considered frost susceptible if it contains 3 percent or more by weight of particles smaller than 0.020 mm in diameter.  Frost  susceptibility  should  always  be considered  in  areas  subject  to  substantially freezing  temperatures,  since  repeated  freezing, and subsequent thawing, of water in the soil can seriously affect the ability of the soil to support a structure. Hydrometer analysis is the test used to determine the grain size distribution of the soils passing  the  No.  200  sieve. Hydrometer analysis is based on Stokes’ law, which relates the terminal velocity of a free-falling sphere in a liquid to its diameter. The relation is expressed  by  the  following  equation. Where: It is assumed that Stokes’ law can be applied to  a  mass  of  dispersed  soil  particles  of  various shapes  and  sizes.   Larger  particles  settle  more rapidly  than  the  smaller  ones.  The  hydrometer analysis is an application of Stokes’ law that per- mits the calculation of the grain size distribution in silts and clays, where the soil particles are given the sizes of equivalent spherical particles. The density of a soil-water suspension depends upon the concentration and specific gravity of the soil particles. If the suspension is allowed to stand, the particles will gradually settle out of the suspen- sion,  and  the  density  will  be  decreased.  The hydrometer is the instrument used to measure the density  of  the  suspension  at  a  known  depth  below the surface. The density measurement, together with  knowledge  of  specific  gravity  of  the  soil particles, determines the percentage of dispersed soil  particles  in  suspension  at  the  time  and  depth of measurement. Stokes’ law is used to calculate the  maximum  equivalent  particle  diameter  for  the material in suspension at this depth and for the elapsed  time  of  settlement.  A  series  of  density measurements  at  known  depth  of  suspension  and at known times of settlement gives the percentages of  particles  finer  than  the  diameters  given  by Stokes’ law. Thus the series of readings will reflect the amount of different sizes of particles in the fine-grained  soils.  The  particle  diameter  (D)  is 15-24