Ill] 



OF Multimodal curves 



135 



This S-shaped "summation-curve" is what Francis Galton called a 

 curve of distribution, and he "Uked it the better the more he used it." 

 The spread or "scatter" is conveniently and immediately estimated 

 by the distance between the two quartiles ; and it happens that this 

 very nearly coincides with the standard deviation of the normal curve. 



40 



50 60 70 



Micrometer-scale units 



80 



90 



100 



Fig. 26. A plankton-sample of fish-eggs: North of Scotland, February 1905. 



(Only eggs without oil-globule are counted here.) 



A. Dab and Flounder. B, Gadus Esmarckii and G. luscus. 



C, Cod and Haddock. D, Plaice. 



There are biological questions for which we want all the accuracy 

 which biometric science can give; but there are many others on 

 which such refinements are thrown away. 



Mathematically speaking, we cannot integrate the Gaussian curve,, 

 save by using an infinite series; but to all intents and purposes we 

 are doing so, graphically and very easily, in the illustration we have 

 just shewn. In any case, whatever may be the precise character of 

 each, we begin to see how our two simplest curves of growth, the 

 bell-shaped and the S-shaped curve, form a reciprocal pair, the 

 integral and the differential of one another "^ — hke the distance travelled 



* It is of considerable historical interest to know that this practical method of 

 summation was first used by Edward Wright, in a Table of Latitudes published in 

 his Certain Errors in Navigation corrected, 1599, as a means of virtually integrating 

 sec X. (On this, and on Wright's claim to be the inventor of logarithms, see Florian 

 Cajori, in Napier Memorial Volume, 1915, pp. 94-99.) 



