814 SIK B. C. BEODIE ON THE CALCTLUS OF CHEMICAL 0PEEATI0N8. 



changes this selection is attended with no difficulty. It will be found by trial that the 

 symbol of oxygen, S^, that symbol in which it is expressed by the smallest number of 

 prime factors in the above equation, will satisfy all other known conditions. 



There is only one other known compound of oxygen and hydrogen, the peroxide of 

 hydrogen. Our knowledge as to this substance is very imperfect, but let us assume 

 that it can be decomposed with the formation of water and oxygen, in the ratio of two 

 units of water to one of oxygen. Then putting z as the unknown number of the 

 volumes of the peroxide decomposed, and y as the number of volumes of oxygen formed, 

 and ^3 as the symbol of peroxide of hydrogen, 



z<Pi=^<p+y<p2, (1) 



whence, substituting for (p its value <Pj+ y' 



and putting a''!'"' as the symbol of the peroxide of hydrogen, a as the symbol of hydrogen, 



and ^ of oxygen, 



za''|'''=2ya + 2y« (2) 



and 



whence 



2p=2y, 



Now, Up and j>j be positive integers, since z is prime to y, z must be either 1 or 2. 



If 



z=l, ^=2y, _pi=4y; 



if 



2=2, p=y, i)i=2y. 



In either case the above equation (2) is of the form 



{ul^y'=y^{u+l^). 



Now, although it undoubtedly cannot be considered that this equation is established with 



the same certainty as the equation 



2a|=2a + |2, 



yet regarded as a question of probability the evidence in favour of this view is very con- 

 clusive. For the only hypotheses involved in it are (1) that in this equation the symbol 

 of the peroxide of hydrogen can be expressed by an integral number of prime factors, 

 and (2) that the symbol of hydrogen can be expressed as a, and the symbol of oxygen as 

 §2, in favour of which hypotheses we have (as will hereafter be seen) the evidence of an 

 extensive and uniform experience. 



We may proceed by the aid of further hypotheses, and still with great probability, to 

 determine the value of y-^ in this symbol. The most probable hypothesis is that yi=l, 

 and that the symbol of peroxide of hydrogen is a^^, in which case the above equation is 

 thus expressed, 



