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XLI. — The Lam of the Volumes of Aeriforms extended to Dense Bodies. By 

 Rev. J. G. Macvicar, M.A., D.D., Moffat. 



(Read 18th April 1864.) 



It is certain that the unities which constitute aeriform media, when they have 

 been fully separated from each other by an adequate temperature, and relieved 

 from excessive pressure, are all equal to each other in volume, whatever the 

 aeriform may be, either singly or in couples, or in pairs of couples, double pairs 

 of couples, &c., giving such ratios as 1:^:4:8, &c. 



More than this cannot be affirmed, except by hypothesis or convention. But 

 this is a great deal. By this, many formulse justly entitled to the name of 

 rational (for they are representative of the molecules of bodies, both as to 

 quality and quantity), become probable. But the construction of such formulae 

 is limited to such molecules as can be raised into the aeriform state. And the 

 discovery of some such law in reference to such bodies as are permanently 

 dense, is at this moment a great desideratum in science; for the doctrine of 

 atomic volume, as insisted upon by some distinguished chemists, is beset with 

 endless embarrassments, and is, besides, plainly wanting in that simplicity and 

 breadth which belong to all laws which are really those of nature. 



What the author here proposes is to show, that the same law which has been 

 discovered in reference to aeriforms holds good also in reference to dense sub- 

 stances — viz., that the molecules of which they consist, whatever the dense body 

 may be, are all equal to each other in volume, either singly or in couples, &c. 



The method which he here adopts to prove this is, first, To construct out of 

 the least chemical units, or the aeriform elements of bodies, such molecules as 

 have the highest intrinsic verisimilitude in their favour; and, secondly. To show 

 that these molecules, as measured by their atomic weights, give the specific gravi- 

 ties as found by the balance, — the argument being the same in form as that which 

 has settled the question as to the volume of aeriforms. 



By intrinsic verisimilitude, is meant the probable reality arising from that 

 fact which forms the basis of all demonstrated science— viz., that nature is a 

 dynamical system, or system of applied or concrete mathematics. 



But to begin : In having to do with molecules, we have obviously to do with 

 structures in which the constitutive forces are in a statical condition. This suggests 

 at once, as the forms of molecules, the regular polyhedra of geometry, towards 

 an adequate discussion of which all Euclid's labours and the ancient geometry 

 aspired, and may I not say the modern geometry now again aspires. They are 

 only five in number, which, beginning with the most perfect, stand thus : — 



VOL. XXIII. PART III. 7 S 



