244 STEPHEN DEM. GAGE 



1903, the difference between the highest and lowest values being 

 i.oi, and the greatest variation in the monthly ratios occurred 

 in 1901, the difference between the highest and lowest values being 

 2.48. 



Normal ratios. That the labor of computing the ratios between 

 the various bacterial constituents is repaid by the additional informa- 

 tion acquired as to the character of the water, is clearly demonstrated 

 in the preceding chapters. The bacterial ratios may also be made 

 to serve as a check upon the bacterial determination, and by point- 

 ing out fluctuations in the bacterial contents of different samples 

 of water from the same sources, which would otherwise have passed 

 unnoticed, indicate the direction in which further investigations 

 must be made to convert the hitherto unexplainable discrepancies 

 between analytical results into significant facts. In order that we 

 may have a clear understanding of the significance of the different 

 ratios, and of the relative numbers from which they are computed, 

 it is important that we should know what are the normal ratios 

 for different classes of waters. The determination of the normal 

 value for any set of variable characters is distinct from the determina- 

 tion of the average of those characters, and consists in arranging 

 the individual values in groups, each group containing all values 

 which are between certain limits, and the normal value for characters 

 which have been arranged in this manner will then lie within the 

 limits of the group which contains the greatest number of individual 

 values. 



In Tables 12-15, inclusive, certain of the bacterial ratios have 

 been grouped in this manner, the size of each group being expressed 

 as the percentage which the number of samples included in the group 

 is of the total number of samples examined. The various 50 ratios 

 have been omitted, for the reason that a fair normal value cannot 

 be obtained by the group method when the investigation covers 

 less than 25 samples. On the other hand, determinations of bac- 

 teria and B. coli in Merrimack River water have been made on 

 thousands of samples, while on certain other classes of samples 

 many hundred determinations have been made, with the result 

 that the normal ratios for such waters are correspondingly accu- 

 rate. 



