SECT. 2] AND WEIGHT 389 



and, more recently, still other ways have been devised. The un- 

 prejudiced investigator cannot avoid a considerable measure of 

 scepticism in considering the claims of one way of expressing the 

 facts over another. 



2-4. The Empirical Formulae 



We may first direct our attention to those presentations of the facts 

 which do not carry with them any theoretical superstructure, but 

 aim simply at describing the data in as short a manner as possible. 

 The first of these "empirical formulae" was that of Roberts, who in 

 1906 pointed out that the growth of the human foetus could be 

 regarded as nearly proportional to the cube of the age ; thus, if the 

 weight in grams is W and the age in days T, the formula would be 

 W — T^. But this was only very approximate, and the curve it gave 

 did not fit the curve drawn through the experimental data with 

 any accuracy. Roberts, indeed, stated that his formula gave results 

 correct to "within an ounce at the third month". "Since the weight 

 of an embryo of the third month," was Meyer's remark, "according 

 to the best available evidence, is considerably less than an ounce, the 

 accuracy of Roberts' method must be fully apparent without further 

 comment." 



Tuttle next introduced an equation in which arbitrary constants 

 were introduced, thus W = 50 {T — 2)^. Later still, Jackson, whose 

 work on the human embryo has already been mentioned, proposed 

 the formula : 



where W is the weight in grams and T the age in days. This fitted 

 the experimental points much better than the formulae of Roberts 

 and Tuttle, but was still rather deficient, especially in the very 

 early period and the very late period. Henry & Bastien also pro- 

 posed 



x^ + 2^xj> — 3q>'2 — i62y = o, 



where x = months andj = kilos. 



Duvoir has reviewed the other more or less practical rules which 

 have from time to time been proposed, such as Casper's rule that, from 

 the fifth month onwards, the age of an embryo in man can be found 

 by dividing the height in centimetres by 5. Balthazard & Dervieux 



