SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
53 
such combinations of these elements as the units ay 3 , yjz, yv, xy ? . . . and the like % 
But this argument does not come to much. Our only choice lies between the two 
hypotheses in question, and hypothesis a 3 is attended with far graver difficulties ; for 
in this system the real and unreal combinations are mixed up together, which is 
not the case on hypothesis a. On this latter assumption we do not introduce among 
the units made up of the matter of our actual elemental bodies the unit of any 
chemical substance whatever which cannot be thus made up ; so that the system with 
which we have to work makes no false assertion, but is from the beginning properly 
constructed. A sharp line of demarcation is drawn in it between what is and what 
is not, our actual system of chemical combinations appearing to us as a fragment 
of a wider and unrealized system, of which it is a part and in which it is compre- 
hended. 
The relation of the two hypotheses will be readily appreciated from the following 
diagrams : — - 
Hypothesis a 2 . 
Hypothesis a. 
Figure I. represents to us the system of combinations on hypothesis a. The total 
area included within the outer contour indicates what I may term the region of possible 
combinations — that is to say, of the combinations, actual or conceivable, of the simple 
weights of the system a, y, |, a, v . . . by which we may consider it to be occupied. This 
region is divided into two subordinate regions — the region of actual existences, namely, 
the region occupied by the combinations made up of the matter of our actual elemental 
bodies, hydrogen, chlorine, iodine, nitrogen, oxygen, carbon, and the like, indicated by 
the shaded space ; and an unknown or unexplored region, external to this, containing 
the combinations of these same simple weights which are not thus made up and of 
which we have no actual representatives. Were we to write down in each region the 
symbols of the combinations by which we thus consider it to be inhabited, we should 
place within the shaded space the symbols satisfying the conditions given by the law of 
even numbers, and in the open space the symbols which do not satisfy those conditions. 
i 2 
