The integrals occurring here have been well tabula ted For 

 convenience, let 



Then, after an interchange of order of integration, one obtains 



m =£[ f Pffl] \^r(^ - iff p(i^)- J^j-p(^j) 



Also, 



_ A cr 



Consequently, 



which holds for all values of r and Ro Values for the functions 

 occurring here may be found, in tables of the normal probability- 

 function and the function G(r)/G(<*>) tabulated as a function of 

 r/sr for various values of R/<r« Figure 8 shows a graph of these 

 functions for R/cr s 0, 1, 2, 3j 4„ A cross= plot may now be 

 gbtained from these curves for the particular value 'dr(r/ar, RAt)/ 

 G(e» ? R/oO - o 68o This gives a curve for R/c against r/c shown 

 in Figure 9o The correction to the value of er , say cr Q , obtained 

 from the experimental curve may now be made as follows? First 

 compute R' s R/lr/2 in order to obtain the square opening of 

 area equal to that of the circular opening of radius R Q Then 

 find the point (R'/c* ,l) on the graph The line passing through 

 the origin and this point will intersect the curve at some point 

 (R'./CTi, CT /€Ti)o The value of <T-\ can then be found immediately, 

 and is the corrected value. This correction was made to all the 

 standard deviations taken from data c In one exceptional case, 

 for the data taken 3/4 in« downstream from the injector when this 

 in turn was 15 mesh lengths from the grid ? the line through the 

 point (R'Afpj 1) and the origin did not intersect the curve at all. 

 This fact is difficult to explain, for the indication is presum- 

 ably that the observed value of <T Q is impossible The dilemma 

 was resolved by ignoring the point,, 



It has been mentioned in the report that the total amount 

 of dye passing any one station should be a constants However, 

 since the concentration curves obtained from the experiments 

 have been altered by the effect of the finite size of the . 

 sampler, one might expect that the volume under the rotated 



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