210 [August 



both continents is, that no distinctions have yet been discovered on 

 careful study." At this rate, if I choose to assert that the Insects of 

 Illinois difter specifically throughout from those of the other States, I 

 may successfully defend that absurd hypothesis against the whole world 

 by the same curious method of argumentation. Surely the large per- 

 centage of forms asserted on the very best authority to be identical, 

 cuts the ground away from under such reasoning as this. Suppose, 

 which is scarcely a supposable case, that it is only an even chance 

 that Loew is right, in deciding that the Dipterous North American 

 form A, is identical with the European form Ej ; then the chance of 

 his being mistaken in this particular instance will be J, and the com- 

 pound chance of his being mistaken in every one of n similar cases, as 

 to species xi.^ and Eo, A3 and E3, An and En, will be 



— which when n is large becomes so exceedingly small that it is 

 2n, o 



scarcely worth taking into account. But in this case n is exceedingly 

 large and consequently — almost inconceivably small, so that the chance 

 of Loew being mistaken throughout amounts almost, according to the 

 Theory of Chances, to a negative certainty.* Or are facts and figures 

 to o'o for nothing', and are we to form our theories first, and afterwards 

 ignore or deny all fiicts and all reasonings that run counter to those 

 theories ? 



In order to throw further light upon this question, I have prepared, 

 from the very limited resources at my disposal, the following imperfect 

 list of species in all the Orders, which are asserted by authors to be 

 found both in North America and in the Old World. I have followed 

 Loew's example in including in the list all species common to both 

 countries, even those which I believe myself to have been introduced, 

 because to attempt to draw any line between introduced and indige- 

 nous species would be begging the question at issue. The authority 



* Assuming the chance of Loew's being mistaken in a single average case to 

 be as large as it may seem proper, say ^=^- taking f pretty large, yet when n 

 is so exceedingly large as it is here, the chance of his being mistaken through- 

 out, or C'^=-^)^, will always be a very small quantity indeed. 



