Mathematics to Chemistry. 281 



common atmospherule, (prop. 3 and I,)*- hence, if it can 

 combine with an additional quantity of the same element, 

 it will be with another atom or group, half an atom being 

 impossible ; after the compound has attained a certain state 

 or quantity, it will not in general, on account of the mu- 

 tual actions of the combined atoms and the ethereal matter, 

 be in a condition to enter into new combinations, except by 

 cohesion, or by the expulsion of some of its elements: 

 hence, the proposition is manifest. 



Prop. 8. Taking each elementary atom as representative 

 of a volume ; then in all strictly chemical combinations, 

 that is, whenever- there is a condensation, the resulting 

 volume is always, without exception, either one or two 

 volumes exactly, whatever number of volumes combine. 



For, since the volume is diminished, the centre of some 

 atom, or those of several atoms, have penetrated the atmos- 

 pherule of some other (prop. 3 and cors.) 



1 . When the atmospherule of one atom or single group 

 is penetrated by the centres of all the other atoms, the 

 result is a single group, and, consequently, (prop. 3 and 

 cors.) that result will be one volume exactly. 



2. When one atom or single group combines with a 

 single group, and all the centres do not rest within the 

 spere of repulsion of one of them ; then one or more of the 

 atoms will be brought, by their mutual actions, to the in- 

 terval between the remaining atoms or single groups, 

 "which combine, and so situated, will (prop. 3 and cors.) 

 supply the effect of the ethereal matter which it displaces ; 

 and the whole will form a double group, and (same cors.) 

 will become two volumes exactly. 



3. When one atom, or single group combines with a 

 double group ; the centres of the combining atoms of the 

 single group, or that of the single atom, will penetrate 

 the atmospherule of the double group ; otherwise there 

 would be only a cohesive combination ; hence, the whole 

 when combined will continue a double group, and will 

 form exactly two volumes (prop. 3, cor. 3) ; except when 

 the mutual actions bring all the centres within the sphere 

 of repulsion of one of them, in which case, (prop. 3, cor. 1) 

 they will become one volume : hence, still we shall have 

 either a single or double group, so that evidently no other 



