26 GEOBGE JOHN EOMANES issi- 



both these predecessors. However, to proceed to the 

 next point, I agree with you, that the sole object of 

 the Sphex stinging the larvae is now to cause them 

 to c keep,' and that natural selection must have 

 worked upon this for perfecting the instinct. But 

 the point is, what was the origin of the selective 

 stinging ? If merely chance congenital variations, 

 would unity to billions express the chances against 

 their ever arising ? Get some mathematician to cal- 

 culate giving as data superficial area of caterpillar 

 on the one hand and that of nine ganglia on the other. 

 Even neglecting the consideration that the variation 

 must occur many times to give unaided natural 

 selection a chance to fix it as an instinct, the chances 

 against its occurring only once would be represented 

 by the following series, where x is the superficial area 

 of the caterpillar minus that of eight ganglia, and 

 unity is superficial area of one ganglia : 



'x'xVxVx'xV 

 xxxxxxxxx 



If, as I suppose, x may here be taken as 100,000, 

 the chances against the variation occurring once 

 would be written in figures expressing unity to one 

 thousand million billion trillions. Of course I do not 

 rely on calculations of this kind for giving anything 

 like accurate results (mathematics in biology always 

 seems to me like a scalpel in a carpenter's shop), but 

 it makes no difference how far one cuts down such 

 figures as these. Therefore, if Lamarck won't satisfy 

 such facts, neither do I think that Darwin minus 

 Lamarck can do so. We must wait for the next man. 



