448 ON INCREASE IN SIZE [pt. iii 



constant a, already referred to, and an intensity factor which is the 

 corrected product of the instantaneous percentage growth-rate and 

 the time, i.e. Cvt. The relative extensity factor is obtained by 

 determining the time which is taken by the organism or the 

 organ to grow i mm. in length, thus reversing the process by which 

 a was originally found. The size of the anlage is also included, and 

 called the mass factor. By the aid of all this apparatus, Schmalhausen 

 compares organs on a common basis, i.e. the time taken for i mm. 

 increase in length to be made. Thus the extensity factor of the chick 

 embryo brain [r) is 1-27 and that of the duck embryo brain 1-26, 

 which means that the sizes of the respective organs are in their 

 earliest stages almost identical. But the relative instantaneous per- 

 centage growth-rate (intensity factor, k, or Cv) differs considerably, 

 for in the chick it is 1-87 and in the duck 2-01, which means that the 

 duck embryo brain grows distinctly more rapidly than that of the 

 chick embryo and finally attains a larger size. Again, for the stomach 

 of the chick embryo the extensity factor, r, is 0-244 ^^^ ^^^ the duck 

 0*324, but the intensity factor is 3-59 for the chick and 2-86 for the 

 duck, or, in unquantitative terms, the stomach is rather bigger to 

 start with (relatively) in the duck than in the hen, but the chick 

 stomach grows faster and reaches eventually a larger proportion of 

 the body. 



This work on disproportionate or heterogonic growth led Schmal- 

 hausen into a field which had been in course of investigation by 

 Huxley and others. Schmalhausen was able to obtain Huxley's 

 formula from his own, and concluded with some justice that his own 

 were of fairly general validity and did not hold only for embryonic 

 growth. On the other hand, owing to the absence of a true extensity 

 factor in Huxley's formula, the latter could not be applied to the 

 embryo; for, although in post-embryonic growth-curves the ages of 

 all the organs can be taken as approximately identical with the age 

 of the animal, this is by no means the case in embryological work, 

 where the time of formation of the various " anlages " is of the greatest 

 importance. The investigations on heterogonic growth are not im- 

 mediately germane to the theme of this book, but they may at any 

 moment become very important for the chemical physiology of the 

 embryo, and it is necessary therefore to be aware of them. Schmal- 

 hausen's work is really an extension to the embryo of the conceptions 

 of Pezard and Champy, as worked out in recent years by Huxley 



