36 
SIE B. 0. BRODIE ON THE CALCTJLTJS OF CHEMICAL OPERATIONS. 
sion, b^ a system of arbitrary signs, to certain mental conceptions and combinations of 
conceptions which enter into exact chemical inquiries. This involves an analysis of 
those conceptions. But something more, too, is there effected. For the study of these 
questions necessitates the reconstruction (to a certain extent) of the fundamental ideas 
of the science and, .especially, the reconsideration of a problem supposed to have been, 
long since, finally determined, namely, the constitution of the units of ponderable 
matter, of which I have given a new theoretical analysis. I shall not attempt to give 
any summary of these results, which, in my previous Memoir, have been discussed as 
briefly as is consistent with clearness. At the same time I should observe that the 
following pages can only be intelligible to those who have already made themselves 
acquainted with the principles of this Calculus, and to such alone they are addressed. 
There is, however, a point of fundamental importance which as yet has been only inci- 
dentally touched, namely, the origin of the hypothesis that the unit of hydrogen is an 
“ undistributed weight,” which is the keystone of the system here adopted, and the 
reasons by which that hypothesis is justified, on which it is desirable, before proceeding 
further, to offer a somewhat fuller explanation. The following slight outline of the 
treatment of the subject pursued in this Calculus is given merely with the view of 
introducing these questions. 
For the effective consideration of the chemical properties of matter it is necessary to 
refer these properties to a common standard of comparison. Our first step, therefore, 
was the definition of the “Unit of ponderable matter” (I. Section I. (10)). In the 
selection of this unit we are guided by the same principles as those on which we select 
the unit of length, the unit of weight, the unit of heat, our choice being in all such 
cases determined by what is convenient for the special purpose in view. Now the 
objects of our study are the chemical nature and transformations of gaseous 
matter. If, therefore, we wish to reason with impartiality, we must compare the 
properties of equal volumes of gases existing under the same conditions of temperature 
and pressure, for no reason can be assigned for comparing unequal volumes. All gases 
must be treated alike. 
We are thus led to the notion of the “ unit of space,” a peculiar and essential feature 
of this Calculus. This “ unit of space ” is the empty measure in which we measure out 
the “units of matter.” The measure chosen is 1000 cub. centims. ; and were we to 
measure out the volumes of gases in this standard measure at a temperature of 0° C. 
and a pressure of 760 millims., we should be in possession of the “units of matter.” 
We shall consider this estimate to have been, in some way, made. 
Here we are met by the preliminary difficulty that this estimate involves numerous 
assumptions, so that our results are by no means conclusive. Even in the case of actual 
gases and vapours we cannot determine our units without, at least, assuming the truth 
of the law of Mariotte and of the recognized variation of volume due to changes of 
temperature. But the greater number of chemical substances do not exist for us as 
gases at all. Here we are driven to select as the “ unit of matter ” that quantity of 
