^^^ G. S. WILSON 



such was not altogether the case. But as the irregularity affected 

 the curves more or less equally in the opposite directions, it is 

 believed that the results obtained by combining all the curves 

 into one composite curve represent the actual facts with a certain 

 degree of accuracy (fig. 2). An examination of this composite 

 curve constructed from the 26 simple curves involved shows that 

 the overcrowding error does not come into play till about 50 bacilli 

 are inoculated per tube. After this point the curve decreases 

 gradually proceedmg obhquely downwards in ahnost a straight 

 line Had it been continued far enough, no doubt the obhquity 

 of the descent would have decreased, otherwise at a certain point 

 It would have reached zero, which would manifestly have been 

 absui-d More than 1200 colonies were not counted, as above this 

 point the error due to counting becomes so considerable as to 

 mvahdate the results obtained. Indeed any number of colonies 

 greater than 800 per tube renders counting a distinctly arduous 

 procedure and the curve was continued beyond this point more 

 lor theoretical than for practical reasons. 



We may now return to the optimum number of colonies de- 

 sired per tube. It was seen that the sampUng and the over- 

 crowding errors varied in opposite directions, and it was therefore 

 necessary to obtain a number which should permit of the mini- 

 mum error of both. But now that the overcrowding error has 

 been worked out in the form of a curve, it is possible to correct 

 one s results in accordance with this curve, so that this error may 

 be left out of account when the optimum number of colonies 

 per tube is considered. The only factors influencing this point 

 now are the sampling error and the actual error of counting It 

 was shown before that if only three tubes are used for each count 

 in order that the deviation of each tube, from the aritlmietic mean 

 may not exceed 5 per cent, between 400 and 800 colonies per tube 

 should be aimed at. The counting error is naturally smallest 

 when the colomes are fewest, but it is of httle import till the 

 number per tube rises to about 400. This error has been ascer- 

 tained by counting the same tube twice in succession. The error 

 involved IS remarkably small, and not until something like 800 to 

 1000 colonies are counted does it become appreciable. The time 



