160 KERATIN AND KERATINIZATION 



relate the amounts of growth in different parts is the allometric equation : 



y = bx a 

 where x and y are the sizes of two parts and a and b are constants. The 

 equation gives expression to the idea that each part grows by self-multi- 

 plication (giving the exponential law p. 139), but that for reasons depending 

 on their " appetites", their command over or access to food supplies, etc., 

 the exponential factors are not equal in the two separate growth equations 

 (Reeve and Huxley, 1945; Richards and Kavanagh, 1945). 



That the law applies to epidermal growth vis a vis that of the whole 

 organism is suggested by the often noted fact that horns tend to be 

 relatively larger, the larger the animal, but no data really adequate to test 

 it exist. In any case much epidermal growth is strictly accretionary, i.e. a 

 fixed amount of growing tissue is constantly adding to a store of dead 

 material which itself, since it is no longer contributing to the growth, 

 should be subtracted from the measured size before testing the equation as 

 in the modified version proposed by Robb (see Reeve and Huxley, 1945) : 

 y = bx x + c, where c is the " dead weight". The existence of cyclic 

 growth, ecdysis and changes in relative rates due to changes in hormonal 

 patterns following crises such as puberty (equivalent to discontinuous 

 changes in a) are further complications. 



