132 Dr. A. C. Brown on Sir Benjamin Brodie's 



the author adopts the simplest form of the second hypothesis, 

 and makes (unit of chlorine) = a% 2 . 



The same divergence of the results obtained under the two as- 

 sumptions occurs in all the other members of this class. Thus 



(unit of nitrogen) (unit of hydrogen) 3 = (unit of ammonia) 2 



in our system both of the factors of the first term are squares 

 N 2 and H 6 . In the author's system the second factor cannot 

 be a square, and therefore, as in the case of chlorine (unit of 

 nitrogen), must contain as factors a square and an odd power of 

 (unit of hydrogen) ; and here, as before, he takes the simplest 

 form and makes (unit of nitrogen) =«v 2 *. In all the members 

 of the second class we have : — 



H=2Vs C\ = 2. X s/*> I =2.0)^ 



Br=2./3v/«, N=2.v v /«, P=2.</> 1 /a, 



As = 2. / 3 v /«, B = 2.0 iv /a, Sb = 2.o- v /«, 

 Bi=2./3 2V /«. 



(In the case of silver we have two possible hypotheses — oxide 

 of silver, AgO or Ag 2 ; according to the one we have 

 Ag = 2 . p v according to the other Ag = 2 . p 2 \/ot.) 



Here again we have a difference of unit ; reducing therefore 

 to the same unit (either w(oc) = l and H = 0*5, or w(a)=2 and 

 H = l), we have, taking e and E as general symbols of prime 

 factors and atoms of the iirst class, and p. and M of the second 

 (excepting hydrogen), 



E = e, 

 and 



H= y/ai., and Mrr/i-^/a. 



It will further be observed that all the elements in the first 

 class are artiad, all in the second perissad. So that it is true, 

 as the author remarks, that this system falls with the law of even 

 numbers ; for if we have an odd number of perissads, we have an 

 odd power of V a. 



As every perissad atom is the product of one peculiar prime 

 factor and v'a, and as « does not occur in any other form (ex- 



* There is a third and more general solution of these equations, which 

 would give us as the symbol for hydrogen civ 2 , for chlorine x^ 2 , for nitro- 

 gen uv 2 , &c. To determine the weight of the prime factors u., v, x, v, &c, 

 we have the equations w{ocv 2 ) = \, w(ux 2 ) : =35'5, w{ot,v 2 ) — \A, &c. ; that is, 

 n equations to determine n-\-l unknown quantities. Either, therefore, 

 they must remain undetermined, or we must arbitrarily assume another 

 equation. Sir Benjamin assumes v=l, or w(v)=0, and therefore unit 

 of hydrogen =u; we assume « = 1, or w(a) = 0, and therefore unit of hy- 

 drogen = v 2 . 



