Jandast 11, 1918] 



SCIENCE 



47 



and conversely — or negative means B. coli 

 were not found. 



Problem. — The problem is to derive from a 

 number of such determinations a numerical 

 index of the most probable result to be ob- 

 tained by repetition. 



Definition.— Call the quantities used " Dilu- 

 tions," since the dilution method is the one 

 used for measuring those quantities. Specifi- 

 cally grade the dilutions as follows : 



Quantity.. 10 c.c. 1 c.c. .1 c.c. .01 c.c. .001 c.c, etc. 

 Dilution ... 1 2 3 4 , etc. 



Call the "Dilution Positive" that "Dilu- 

 tion" at which higher "Dilutions" were neg- 

 ative and lower positive, after reverting skips 

 where such occur. 

 Example continued: 



"Dilution 1 2 3 4 



Positive" ... 2 10 7 1 



Average Dilution Positive. — Add the "Di- 

 lutions Positive," and divide by the niimber 

 of samples to find the "Average Dilution 

 Positive." 



Example continued: 



' ' Dilution Positive ' ' 



X 2= 



1 X 10 = 10 



2 X 7 = 14 

 3X1=3 

 4 X 0= 



Total 20 ) 27 

 Average 1.35 



Score. — The decimal part of the "Average 

 Dilution Positive " gives the " Score," and the 

 integral part teUs how many figures to point 

 off. The reason for calling it a " Score " is 

 that it is directly comparable to the bacteri- 

 ological score of oysters."^ In the above ex- 

 ample, the " Score " would be 3.5. For all 

 ordinary purposes, the " Score " is a very 

 good index and can be used directly. 



Geometrical Mean. — The " Score " can be 

 converted into the " Geometrical Mean " from 

 the following table: 



TABLE FOR CONVEKTINQ SCOEE INTO OEOMETEICAL 

 MEAN 



01234 5 67 89 



100 102 105 107 110 112 115 118 120 123 



1 126 129 132 135 138 141 145 148 151 155 



2 159 162 166 170 174 178 182 186 191 195 



3 200 205 209 214 219 224 229 235 240 246 



4 251 257 263 269 276 282 289 295 302 309 



5 317 324 331 339 347 355 363 372 381 389 



6 398 407 417 427 437 447 457 468 479 490 



7 501 513 525 537 550 562 576 589 603 617 



8 631 646 661 676 692 709 725 741 759 776 



9 794 813 832 851 871 891 912 933 955 977 



From the previous example, the " Score " 

 3.5 becomes " Geometrical Mean " 2. 24, which 

 is not very different. Either represents an 

 approximation sufficiently close to be con- 

 sidered the number of B. coli per c.c. 



Percentage Method. — The same results are 

 given by an alternative method, which may 

 sometimes be more convenient. Compute the 

 percentages that are positive in each " Dilu- 

 tion." The resulting figures should extend 

 from a " Dilution " at which 100 per cent, 

 are positive to one at which 100 per cent, are 

 negative. The percentages are then added, 

 and wiU give a number of three figures before 

 the decimal point. The first or hundreds 

 figure is discarded, the other figures giving 

 the " Score " when properly pointed off by 

 inspection. 



Example continued: 



Quantity Per Cent. + 

 10 c.c 100 



1 c.c 90 



.1 c.c 40 



.01 c.c 5 



.001 c.c 



235 



Discarding the 2 gives the " Score " figures 

 of 35. Inspection shows there are more than 

 .35 and less than 35, and thus the same result, 

 3.5, is obtained as by the previous method. 



Reversion Method, (a) Direct. — The prin- 

 ciple of reversion used in figuring the oyster 

 score^ may also be applied in this method. 



Example continued : The + .01 c.c. tube 

 and one of the + •! c.c. tubes revert to the 

 1 c.c. column, leaving seven -|- .1 c.c. tubes 

 out of twenty samples. This gives 35 per cent, 

 of the .1 CO. tubes positive or as before the 

 " Score " 3.5 when pointed off. 



