SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
51 
And reasoning as before, since m is prime to some one, at least, among the numbers 
p, p p", p'", . . . q, q", q'" . . . r, r 1 , r" . . ., if m be prime to some one among the 
numbers r, r", ... m= 1. If m be prime to any one among the numbers p', p ", p'", 
• . . q, g', q", and be not prime to any one among the numbers r, r ', r " . . ., m= 2. If m 
be not prime to any one among the numbers p',p", p'", . . .q, q q", . . . r, r', r", ... m is 
also not prime to^?, which is contrary to the construction. Therefore m= 1 or m— 2. 
If m = 1 , n —p + X(p'), 
if m=2, 
%(n')=2t(p'); 
P+t{p’) 
— o ’ 
t{ri)=t{p% 
the condition being that^+SQV) is to be an even number. 
We have also 
2% (p 1 ) _ 
n ~p + 2(p ' )’ 
whence, in addition to the conditions 
not <0 not >2, 
?? 55 
we have 
If n '\ 
^ not >2. 
The symbol a v yfco n ''. . . . . . z n '"Y"' ... is to be interpreted on the same principles as 
the symbol a n y j n '^ n "z n '" previously considered. Thus to interpret the symbol ayp, here 
n=l, the sum of the units of hydrogen, chlorine, and iodine formed by the decom- 
position of the substance when decomposed into these elements is equal to the 
number of units of the substance thus decomposed, n'= 1, n[—l ; of the units of 
hydrogen, chlorine, iodine thus formed \ are units of iodine and ^ units of chlorine, 
no hydrogen being formed. These are the characteristic properties of the unit of 
chloride of iodine. 
This reasoning may be further extended so as to include the case of the elements 
phosphorus a 2 <p 4 and other elements similar to it in form. 
Both hypotheses, therefore, so far agree that each covers the whole ground, and 
includes all known compounds of carbon, hydrogen, oxygen, chlorine . . . But the 
MDCCCLXXVII. 
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