SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
49 
For the interpretation of the symbol of a unit of matter it is essential that we should 
be informed of the conditions which that unit is to satisfy, apart from which no inter- 
pretation is possible, for the same symbol may have its origin in many ways. The way 
in which the symbol originates is defined by the equations ; thus, in the present case, to 
interpret the symbols a n -'/ i n '^ n "z n '", 
n is the ratio of the sum of the units of hydrogen and chlorine formed to the 
number of units of matter decomposed ; 
it! is twice the ratio of the number of units of chlorine formed to the number of 
units of matter decomposed ; 
n" is twice the ratio of the number of units of oxygen formed to the number of 
units of matter decomposed ; 
n'" is t times the ratio of the number of units of carbon formed to the number 
of units of matter decomposed, t being (probably) 1 or 2. 
For example, to interpret the symbols ax, a£. In both cases n= 1. That is to say, 
a% and at are symbols of two units of matter such that the sum of the units of 
hydrogen and chlorine formed by their respective decompositions is equal to the number 
of units thus decomposed. In the case of ax, n'=l, n"= 0, n'"= 0, that is to say, the 
ratio of the units of chlorine formed to the units of matter decomposed is as 1 : 2. No 
oxygen and no carbon are formed in the decomposition. In the case of n' = 0, n"=l, 
n"'= 0. The ratio of the units of oxygen formed to the units of matter decomposed is 
as 1 : 2, no chlorine and no carbon are formed. These properties characterize the 
respective units of hydrochloric acid and of water. Again, in the case of the symbol 
a 2 x^x, (the symbol of the chloride of acetyl), n— 2. The sum of the units of hydrogen 
and chlorine formed by the decomposition of the substance is twice the number of units 
of the substance decomposed, n'— 1, the ratio of the units of chlorine found to the 
units of matter decomposed is as 1 : 2 . n"= 1, the ratio of the units of oxygen found 
to the units of matter decomposed is also 1:2. n"'= 1, the ratio of the units of 
carbon formed to the units of matter decomposed is as 1 : t, where t is assumed to be 
1 or 2. We hence are always able, from inspection of the symbol, to reconstitute the 
equation whence that symbol was derived. 
The preceding reasoning may be extended to the general case. Let m units of any 
chemical substance a’yW 1 ' 2 . . . . . . z n '"h n "' i ... be identical with p units of 
hydrogen a, p' units of chlorine ayj, p" units of iodine aco 2 , p m units of nitrogen av 2 . . ., 
q units of oxygen £ 2 , q ! units of sulphur 0 2 , <f units of selenium A. 2 . . ., r units of carbon z, 
r' units of mercury r" units of zinc £ . . ., so that 
ma n x n 'co nl 'v n ' 2 . . . g n "fl n "‘X n " 2 . . . z n "% n '"' . . . ==pu-\-p , a% 2 +p"aM 2 -\-p" , av 2 -\- . . . 
+q¥+q'0 2 +q"7S+ . . . +rz+r'l+r"t;+ . . ., 
we have then the following equations connecting the positive integers m, n , n', . . . 
p, p\ p", . . . 
