568 Dr. F. A. Bixe^rep/i/ to Mr. G. A. K. Marshall 



being that they should be the same for A and for B. Let 

 us say a population of 1000 for each. Now we will suppose 

 that a certain number of A vary in the direction of B, so 

 as to show the aposeme of B in addition to that of A ; and 

 that a certain number of B similarly vary in the direction 

 of A so as to show the aposeme of A as well as their own, 

 this of course being wliat is meant by a reciprocal approach. 

 The possibility of the occurrence of such variations is 

 allowed by Mr. Marsliall (p. 98) ; what he does not allow 

 is the possibility of their permanent establishment. 



Again, numbers are immaterial ; to keep the illustration 

 as simple as possible we will suppose that the given varia- 

 tion of A amounts to half the number of the species, and 

 that similarly B is eijually divided between its original 

 form and its variation. We now have four classes, each 

 500 strong, which we may call A, Ab, Ba, B; the small 

 letters being used to signify the presence of an aposeme 

 that is adopted and not original. Now we will suppose 

 that 100 young insect-eating birds are let loose upon the 

 butterflies of these four classes. To eliminate Mr. Mar- 

 shall's complication of X, Y and Z birds (pp. 103-105) we 

 will suppose that all the butterflies are exposed to simul- 

 taneous attack by the whole body of their enemies. It is 

 obvious that on an average each class will be attacked by 

 25 birds. For the sake of simplicity we will further 

 assume that the butterflies are so nauseous, or the palate 

 of their enemies so delicate, that one experiment on each 

 aposeme is sufticient to ensure the exemption of that 

 aposeme from further attack by the experimenter. Now 

 let us see what will be the fate of our four classes. The 

 25 birds that attack A will not touch it again. Neither 

 will they experiment on Ab and Ba, which exhibit the 

 same aposeme. But each of them will experiment on 

 B, which has nothing about it to suggest A's aposeme. 

 Hence the result of the attack of batch No. 1 is the 

 destruction of 25 A and 25 B. Batch No. 2 experiments 

 on Ab, destroying 25 of them. But it will attack none of 

 the otlier three classes, because each of these possesses an 

 aposeme which it has learnt to avoid. Similarly the 25 

 birds (batch No. 8) that take toll of Ba will henceforth 

 avoid all the rest, for the same reason. Batch No. 4 devotes 

 its attention to B, which has already suffered, or will suffer, 

 under batch No. 1. Of this class B, 25 will be taken, 

 without supplying any experience for the benefit of A, 



