26 PRINCIPLES OF BIOCHEMISTRY 



very useful. 1 In the treatment of quantitative data and the graphic 

 representations thereof it is frequently necessary or desirable to apply 

 a formula to the curves obtained or to compare them with the curve 

 which may be deduced from theoretical premises. In this extensive 

 field of practice a knowledge of the proper method of dealing with and 

 minimizing the effect of accidental experimental errors is required and 

 the employment of the method of least squares is essential if the best 

 use is to be made of the experimental material which may be available. 2 

 For purposes of fitting empirical formulae to curves, eliminating ex- 

 cessively erroneous results and interpolating probable values between 

 values which have actually been measured, a study of the methods of 

 interpolation and mechanical differentiation is exceedingly valuable 

 and helpful. 3 



But perhaps the most essential branch of mathematical practice in 

 the equipment of the biochemist of the future will consist in the 

 methods of the statistician. When we come to deal with actually 

 living material, as we are compelled to do in order to advance our 

 subject at all in its most significant direction, we are at once con- 

 fronted by the problem created by the inherent variability of living 

 things. No two animals are alike, not even may we find any two living 

 cells which are precisely identical. In agriculture no two plots of 

 ground are alike, no two plants are ever identical. How then, in 

 comparing experimental animals or plants or plots of ground with 

 "normals" or "controls" shall we ever attain to certainty of our 

 results? It would seem that it must always be possible that the 

 differences between any two groups of animals may merely be the pro- 

 duct of chance selection of two groups which might have differed in the 

 observed sense without any experimental manipulation whatsoever. 

 This difficulty, the fundamental character of which is recognized by 

 every biological investigator, is of course not of so much importance 

 in those cases in which the differences for which we are looking are very 

 large, as death contrasted with survival, decisive loss of weight con- 

 trasted with equally decisive gain, or reduction or enhancement of 

 normal qualities by fifty per cent, or more. But phenomena such as 

 these are the obvious ones in any field of science, those which lie at the 

 surface and are garnered by the earliest investigators, and they are not 

 invariably, and in fact not usually, the phenomena upon which we 

 ultimately come to rely for the basis of wide and fundamental generaliza- 

 tions. Such emphatic disparities testify in themselves to the unusual- 

 ness of the conditions invoked, and hence carry the suspicion that the 

 response to such extreme conditions may not be a normal or at least a 

 usual reaction of living matter to its environment. For our deeper 



1 Murray: Introductory Course in Differential Equations, London, 1897. 



2 M. Merriman: Text-book on the Method of Least Squares, New York, 1891. L. 

 Tuttle: The Theory of Measurement, Philadelphia, 1916. 



8 H. L. Rice: The Theory and Practice of Interpolation, Lynn, Mass., 1899. 

 J. Mellor: Higher Mathematics for Students of Chemistry and Physics, London, 1902. 



