422 M. A. Naquet on the Calculus 



one ought to be preferred which is the more limitative. In 

 other words, if a hypothesis A accounts for all the facts and 

 does not suggest any improbable phenomenon, while another 

 hypothesis A x accounting equally for all the known facts 

 suggests a considerable number of unknown and improbable 

 facts, it is hypothesis A which we ought to select. 



We fully accept these principles; but let us see their con- 

 clusions. The hypothesis a 2 , Sir B. C. Brodie says, permits 

 the regular explanation, by means of integral positive factors, 

 of the symbols of all the known facts. But it admits besides 

 of the similar construction of symbols of an equal number of 

 substances which the law of even numbers rejects as impossible 

 to realize. The hypothesis a, on the contrary, while per- 

 mitting the expression by symbols, by means of integral posi- 

 tive factors, of known facts, excludes the possibility of repre- 

 senting in the same way, by means of symbolic expressions, 

 the substances which do not obey the law of even numbers. 

 The hypothesis a is therefore superior to the hypothesis a' 2 . 



Such is the argument of Sir B. C. Brodie ; and we should 

 consider it irreproachable if hypothesis* a were not, though 

 more limitative on one side ; more extensive on the other, and 

 if, from this point of view, what is gained in one sense were 

 not lost in an opposite sense. 



But, first, the hypothesis a compels us to admit that chlo- 

 rine, bromine, iodine, nitrogen, phosphorus, arsenic, antimony, 

 bismuth, potassium, sodium, etc, are compound bodies cor- 

 responding to the general formula HB 2 or H 2 K 4 . This is a 

 serious obstacle against accepting this hypothesis; for though 

 there may be nothing impossible in this supposition, neither is 

 there anything demonstrated : we anticipate experience, and 

 thus we enter upon a path which threatens to lead us far. 



This is not all. The existing theory, which considers chlo- 

 rine, bromine, iodine, nitrogen, etc. as elementary bodies, leads 

 us to consider as products of " substitution " the compounds 

 resulting from the action of chlorine, bromine, or iodine on 

 organic hydrogenized bodies, as well as the compound ammo- 

 nias produced by the action of simple ethers on ammonia. 

 The number of these products is thus limited. 



Let us take, for example, the action of chlorine on marsh- 

 gas, CH 4 . Theory, indicates that this action ought to pro- 

 duce four bodies, and four bodies only, as indicated in the 

 the following equations : — 



CH 4 + C1 2 = HC1 + CH 3 C1, 

 CH 3 CI + Cl 2 = HC1 + CH 2 Cl 2 , 

 CH 2 C1 2 + C1 2 ==HC1 + CH Cl 3 , 

 CH C1 3 + C1 2 =HC1 + CC1 4 . 



