562 Dr. F. A. Dixey's reply to Mr. G. A. K. Marshall 



the change of seasons can be taken as exact for all regions 

 where the phenomena of mimicry obtain. For the country 

 that has been the scene of his own admirable observations 

 he can of course speak with the highest authority. But 

 he appears to have left out of account the fact that it is 

 not merely a question of young birds, but also of the 

 emercjence of new insects. The seasonal forms of butter- 

 flies are often so different from one another that a fresh 

 brood may have to be learned as if it were a new species. 

 Again, although in a given locality the insectivorous 

 migrants may have departed, it is only to resume their 

 activity among the insect provender, possibly quite new to 

 them, of some other district. However this may be, 

 the contention that the Miillerian factors vary in im- 

 portance Avith the time of year, whether well-founded or 

 not, does not seem to be very material for the points at 

 issue. 



We now come to an important section of Mr. Marshall's 

 paper, in which on the strength of some very clever a priori 

 reasoning, he asserts (I quote his words) that " a Miillerian 

 approach will only take place in one direction, namely, 

 from a rarer species towards a more abundant one, and no 

 species can in this way approach another which has fewer 

 individuals than itself." Equality (of number) he says, is 

 " a condition which effectually prevents the Miillerian 

 selection from producing any mimetic results" (p. 100). 

 This contention rests principally on the arithmetical work- 

 ing out of certain supposed cases. 



Before dealing specifically with Mr. Marshall's arithme- 

 tical demonstration, I would remark that experience shows 

 the danger of trusting too much to a priori reasoning in 

 matters of this kind, especially when its results do not 

 accord with the facts of observation. In reference to an 

 able treatise on a different subject,* lately published, it 

 has been forcibly said that " readers are apt to assume that 

 the statements are necessarily correct as being based on 

 unimpeachable mathematical data. It will be well if they 

 remember that mathematical deductions under the best 

 conditions are like the Hour that comes from a mill. 

 If the original corn is impure, the flour will be unwhole- 

 some ; . . . similarly arguments built up on insufficiently- 

 observed phenomena, when subjected to the mill of mathe- 

 matical reasoning, are exceedingly apt to have any faulty 

 * "Theories Modernes sur la Matiere," by M. Pozzi-Escot. 



