428 Sir B. C. Brodie on the Calculus 



four times and no more. Similarly in ammonia (NH 3 ) three 

 analogous substitutions are possible. Whence we have, for 

 example, the three ammonia bases, methylamine, dimethyl- 

 amine, trimethylamine. Again, in chloride of ammonium 

 (NH 4 CI) we may have four such substitutions ; and extend- 

 ing this principle, we are able to anticipate in numerous cases 

 the precise number of similar derivatives. All this, it is as- 

 serted, is The work of the atomic method. Now the theory 

 before us, says M. Naquet, does nothing of the kind, and, 

 indeed, is incapable of doing it. We have o?k^ as the symbol 

 of chloroform, and « 2 #x 4 as ^ ne tetrachloride of carbon. All 

 that is here done to form the chlorine derivatives of marsh-gas 

 is to add the weight ^ over and over again to the weight ol 2 k. 

 Go on in the same direction, the next step brings you to x 2 /c% 5 , 

 an utterly impossible, or at least an eminently improbable, 

 entity, which yet is not excluded from the system. 



The reply to this is that M. Naquet does not give a correct 

 account of the process by which these derivatives are con- 

 structed. We cannot make « 2 /c% 5 by the same process as that 

 by which <z 2 a:% 4 is manufactured. After a 2 /e% 4 is placed an insur- 

 mountable barrier to progress in this direction which he does 

 not see. He can go so far, but no further. 



M. Naquet's criticism is based on a distinction for which he 

 certainly is not responsible, as it is made in every chemical 

 treatise, which is necessitated by the material mode of treat- 

 ment of the atomic theory, but which, in this Calculus, does 

 not exist, namely the distinction between Addition and Sub- 

 stitution of atoms. For us the two processes are merged in 

 one. (Part II. Section III. (9).) 



Let us consider the equation which expresses the relation 

 between the chloride of iodine and its constituents, 



«X 2 + «&> 2 = 2axft>, 

 or 



a^ 2 + otoi 2 — 2a%ft) = 0. 



This equation vanishes when % = o>. It may be written 



thus 



«(%- ®)(x— »)=o. 



In this event a is constant, and it occurs in two ways by the 

 substitution of o> for %, which substitution is expressed by the 

 symbol (^ — co), and we have : — 



Symbol of the unit of chlorine a XX> 



„ „ chloride of iodine... a&>^, 



„ „ iodine acaco, 



in which symbols the relation of substitution connecting these 

 units is apparent. 



