38 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
whence, substituting for C the value A+B, we have 
2A+2B=A+E; 
and E=A+2B, giving, as the constituents of the unit of matter considered: — 
Unit of Hydrogen A . . . weighing *089 grm. 
„ Oxygen 2B . . . „ 1*430 „ 
„ Water A+B . . „ *805 „ 
„ Binoxide of hydrogen . A+2B . „ 1*520 „ 
We cannot, from the evidence before us, assign any constitution to the bits of matter 
A and B, nor are we able to make any assertion about these bits of matter, except that 
the bit of matter A weighs *089 grm., and that the bit of matter B weighs *715 grm. 
A bit of matter as to which our knowledge is thus limited is what is here termed a 
“ simple” or “ undistributed weight.” These terms do not refer to the constitution of 
the bits of matter A and B, as to which we have no means of forming an opinion, but 
to a very different thing, namely, our knowledge of that constitution, which is confined 
within narrow bounds determined by our powers of observation and experiment. 
The groups of letters A, 2B, A+B, A+2B, although truly symbols or signs of the 
matter of which the units of hydrogen, oxygen, water, and binoxide of hydrogen consist, 
are not the symbols of those units of matter themselves. A symbol must distinguish 
the thing symbolized from other things, but these expressions do not thus distinguish 
those units of matter. Thus the expression A + 2B indicates (to one who knows the 
meaning here given to the letters) the matter of which the unit of binoxide of hydrogen 
is constituted ; but it indicates to him several other things besides, namely, the matter 
of a unit of hydrogen, A, and the matter of a unit of oxygen, 2B, and also the matter 
of a unit of water, A+B, and the matter of the simple weight B, and also the matter 
of the unit of hydrogen, A, and of two simple weights, B and B. So that when such 
an expression is presented to us (if no more be said) we cannot tell to which of these 
different objects the expression refers. The expression A + 2B indicates something 
common to all these objects, but does not indicate any one object specially. How, then, 
are we to frame such a distinctive symbol \ This question has been fully considered in 
the first part of this Calculus, to which I must refer the reader for information. I will 
here only make one remark. The chemical symbol of a unit of matter, as constructed 
on the principles of this Calculus, is an analytical expression which indicates to one 
acquainted with those principles that special combination of operations by which, in 
the processes of chemical change, the unit has been made up. These operations are 
known to us only through their results, and are defined by those results ; indeed no 
other knowledge of them is practicable ; but this is sufficient for our purpose, which is 
the comparison of those results. 
That operation which I have here termed a chemical operation, and defined as an 
operation performed upon the unit of space, of which the result is “a weight” 
