Ill] OF PRE-NATAL AND POST-NATAL GROWTH 73 



But when you take percentages of y, you are determining dyly, and when 

 you plot this against dx, you have 



dijly dy 1 dy 



dx y . ax y ax 



that is to say, you are multiplying the thing you wish to represent by another 

 quantity which is itself continually varying ; and the result is that you are 

 dealing with something very much less easily grasped by the mind than the 

 original factors. Professor Minot is, of course, dealing with a perfectly 

 legitimate function of x and y ; and his method is practically tantamount to 

 plotting log y against x, that is to say, the logarithm of the increment against 

 the time. This could only be defended and justified if it led to some simple 

 result, for instance if it gave us a straight line, or some other simpler curve 

 than our usual curves of growth. As a matter of fact, it is manifest that it 

 does nothing of the kind. 



Pre-natal and fost-natal groivtli. 



In the acceleration-curves which we have shown above (Figs. 

 2, 3), it will be seen that the curve starts at a considerable interval 

 - from the actual date of birth ; for the first two increments which 

 we can as yet compare with one another are those attained during 

 the first and second complete years of life. Now^ we can in many 

 cases "interpolate" with safety between known points upon a 

 curve, but it is very much less safe, and is not very often justifiable 

 (at least until we understand the physical principle involved, and 

 its mathematical expression), to "extrapolate" beyond the limits 

 of our observations. In short, we do not yet know whether our 

 curve continued to ascend as we go backwards to the date of 

 birth, or whether it may not have changed its direction, and 

 descended, perhaps, to zero-value. In regard to length, or 

 stature, however, we can obtain the requisite information from 

 certain tables of Riissow's*, who gives the stature of the infant 

 month by month during the first year of its life, as follows : 



Age in months 12345 67 8 9 10 11 12 



Length in cm. (50) 54 58 60 62 64 65 66 67-5 68 69 70-5 72 



[Differences (in cm.) 4 4 2 2 2 1 1 1-5 -5 1 1-5 1-5] 



If we multiply these )nonthlij differences, or mean monthly 

 velocities, by 12, to bring them into a form comparable with the 



* Quoted in Vierordt's Anatomische...Daten und Tabellen, 1906. p. 13. 



