ADDENDA 263 



by the fact that the correlation between right and left side 

 diminishes distally along the appendage. The correlations 

 for lengths of merus, carpus and propus are, for right-handed 

 males, 0754, 0-698 and 0-473 ; for left-handed males, 0-789, 

 0-699, °'549- He suggests that the chela asymmetry may be 

 responsible for the asymmetry of other parts. 



Marples (Proc. Zool. Soc, 1931, p. 997) has given some 

 interesting facts as to the percentage changes of different 

 parts of birds' wings during development. For calculating 

 growth-coefficients, he has kindly put at my disposal his 

 original data on the Common Tern (the species on which 

 the most numerous measurements were taken). For a proper 

 analysis, considerably more measurements are needed, includ- 

 ing measurements of some standard part of the body ; but 

 provisionally we can see that there are three distinct phases 

 of growth, during each of which the relative growth-rates of 

 different parts of the wing remain approximately constant. 

 The first phase ends at hatching ; the second, juvenile phase 

 goes from hatching (wing-length below 40 mm.) to wing- 

 length about 100 mm. ; the third up to the largest adults 

 (wing-length over 180 mm.). 



The growth-coefficients (approximate only) of the lengths 

 of ulna and radius, relative to humerus length, are as follows : 



Phase. r 23 



Ulna . . . . .1-05 about o-8 1-6 



Radius . . . . .1-2 ,, o-8 1-45 



The growth-gradient appears to centre in the radius in the 

 1st phase (though this may be due in part to the late differ- 

 entiation of this terminal region) ; to be reversed, centering 

 in the upper arm, in the 2nd phase ; and again to change its 

 form, centering in the fore-arm, in the final phase (cf. p. 34). 



I have not discussed the enormous body of data given in 

 Donaldson s The Rat (1924), since all the comprehensive tables 

 there set forth do not give the actual values for the various 

 organs, but calculated values. These values have been 

 calculated in accordance with empirical formulae devised by 

 Hatai to fit smooth curves to the data. 

 These formulae are of the following types : 



y = a log x + b 



y = a (log x -f- c) -f- b 



y = ax + b log x + c 



y = ax -f b (log % -f- c) -\- d 



y = (ax -f- b) -f- b (log x 4- c) + d 



y = ax b 



