456 THE SCIENTIFIC MONTHLY 



starting across the Bridge of Life, and growing in stature as they ad- 

 vance, till at the far end of the bridge we see only the gray-beard, and 

 the 'lean and slippered pantaloon.' As they pass along the causeway 

 the throng is more and more thinned; five Deaths are posted at different 

 stages of the route longside the bridge, and with different skewness of 

 aim and different weapons of precision they fire at the human target, 

 till none remains to reach the end of the causeway — the limit of life." 



This whole, somewhat fanciful, conception of Pearson's needs a 

 little critical examination. What actually he has done is to get a good 

 empirical fit of the d x line by the use of equations involving all told 

 some 17 constants. Because the combined curve fits well, and funda- 

 mentally for no other reason, he implicitly concludes that the fact that 

 the fit is got by the use of five components means biologically that the 

 d x line is a compound curve, and indicates a five-fold biological hetero- 

 geneity in the material. But it is a very hazardous proceeding to draw 

 biological conclusions of this type from the mere fact that a theoretical 

 mathematical function or functions fits well a series of observational 

 data. I have fully discussed this point several years ago (Pearl: 

 Amer. Nat. Vol. XLIII) where I pointed out: 



"The kind of evidence under discussion can at best have but in- 

 ferential significance; it can never be of demonstrative worth. It is 

 based on a process of reasoning which assumes a fundamental or nec- 

 essary relationship to exist between two sets of phenomena because the 

 same curve describes the quantitative relations of both sets. A little 

 consideration indicates that this method of reasoning certainly can not 

 be of general application, even though we assume it to be correct in 

 particular cases. The difficulty arises from the fact that the mathe- 

 matical functions commonly used with adequate results in physical, 

 chemical, biological, and mathematical investigations are comparatively 

 few in number. The literature of science shows nothing clearer than 

 that the same type of curve frequently serves to describe with complete 

 accuracy the quantitative relations of widely different natural phe- 

 nomena. As a consequence any proposition to include that two sets 

 of phenomena are casually or in any other way fundamentally related 

 solely because they are described by the same type of curve is of a 

 very doubtful validity." 



Henderson has put Pearson's five components together in a single 

 equation, and says regarding this method of analyzing the life tables: 



. . . it is difficult to lay a firm foundation for it, because no 

 analysis of the deaths into natural divisions by causes or otherwise has 

 yet been made such that the totals in the various groups would conform 

 to those frequency curves." The italics in this quotation are the pres- 

 ent writer's for the purpose of emphasizing crucial points of the whole 

 matter, which we shall immediatelv discuss in more detail. 



