214 PROBLEMS OF RELATIVE GROWTH 



group, is reached by a given species, the growth-mechanism 

 will see to it that new potentialities of relative organ-size are 

 realized. But though the proportions of the organ are new, 

 the same single growth-mechanism is at work. There has 

 been no change in its hereditary basis, determinate or other- 

 wise ; merely new results, potential in it from the first, have 

 been realized. 



If we wish to search for evolutionary parallels, we find that 

 a similar situation has occurred in regard to many time- 

 relations in body-processes of warm-blooded vertebrates, 

 which take place at temperatures well above the lethal tempera- 

 tures for most cold-blooded vertebrates. Accordingly such 

 processes occur at speeds which are never realized in cold- 

 blooded forms. The speed of such processes in the cold-blooded 

 forms varies with temperature in a regular way. The maxi- 

 mum speed in the cold-blooded forms is limited by the tempera- 

 ture which they can tolerate without dying ; but the actual, 

 and much higher, speeds in warm-blooded forms approximate 

 closely to the speeds which are obtained by extrapolating the 

 curve obtained for the cold-blooded forms to the blood- 

 temperature of the warm-blooded. An example of this is 

 seen in the lapse of time between onset of convulsions due to 

 insulin injection in a frog, which dies at about 30 ° C, and 

 in a rabbit, which dies at 37 C. (Huxley and Fulton, 1924). 



The evolutionary importance of the facts lies in this : that 

 whenever we find the rule of Lameere and Smith holding true 

 for a series of separate forms, we are justified in concluding 

 that the relative size of horn, mandible, or other heterogonic 

 organ is automatically determined as a secondary result of a 

 single common growth-mechanism, and therefore is not of 

 adaptive significance. This provides us with a large new list 

 of non-adaptive specific and generic characters. 



The operation of the rule, however, is not constant : it is, 

 in fact, merely a rule, with numerous exceptions. There are 

 a number of cases in which related species of very dissimilar 

 absolute size show secondary sexual characters of the same 

 relative size. Champy (1924, p. 155) lists a number of these, 

 and Dr. Arrow, of the British Museum (Natural History), 

 has informed me that there are numerous other examples to 

 be found in Coleoptera. This should, however, not surprise 

 us. The fact that the growth-ratio of the male chela of Uca 

 changes during the life-history, or that the onset and end of 

 heterogony may vary for the same organ in different types, 



