16 
MR. J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
mean square velocity of the B molecules, &c.). The mean value of /3~ + p is, there¬ 
fore, fifp, but the mean value of /3 3 is also evidently equal to fifip, as above; hence, 
the mean value ofy> is 0, or the positive values of p balance the negative values. In 
the same way, it may be shown that the mean of the values of q is also 0. Hence, 
we deduce that fifiB = B m 2 D, or that in mixed media the mean square molecular 
velocity is inversely proportional to the specific iveight of the molecules * . VII. 
This is the law of the equilibrium of vis viva. 
§ 11. Thus, it appears that the inverse ratio of the specific molecular weight is 
that which is naturally assumed by the mean square molecular velocity of media in 
contact, and according to the foregoing reasoning (§ 10), this is also the ratio that 
ensures an equilibrium of pressure between media of the same density, or which have 
the same number of molecules contained in the same volume. Tims, by combining 
V. with VII. we deduce that media in equilibrium of pressure and vis viva are of 
equal density, or have specific gravities respectively proportional to their specific 
molecular weights .VIII. 
§ 12. We may likewise remark that as the mean value of the product /3 ~B is equal 
to the mean S 3 D, or B„ 3 = 8„ 3 D, there is the same amount of vis viva or mechanical 
force contained in equal volumes of all media that are in equilibrium of pressure and 
vis viva.IX. 
§ 13. If different media are placed in contact they must diffuse themselves through 
their common volume with velocities proportional to their mean molecular velocity ; 
but this velocity being in each inversely as the square root of its specific molecular 
weight, which is equal to the square root of its specific gravity, we may deduce, by 
combining VI. with VII., that media in equilibrium of pressure and vis viva diffuse 
themselves through their common volume with velocities inversely proportioned to the 
square root of their specific gravity .X. 
§ 14. Such are the principal points by which different media are related to each 
other. Their analogies to the properties of gases may be stated as follows : 
(1.) The specific gravities of gases of the same temperature and pressure are respec¬ 
tively proportional to their atomic weight. [The combining equivalents or proportions 
may be viewed as simple multiples or divisors of the atomic weight or specific gravity.] 
This is analogous to tne VIII. deduction. Media in equilibrium of vis viva and 
pressure have specific gravities proportional to their molecular weight. It will be 
remarked that here again we have temperature represented by vis viva. 
(2.) It is considered as almost proved that gases in equilibrium of pressure and 
temperature have, in equal volumes, the same absolute quantity of heat. 
* [This is the first statement of a very important theorem. (See also ‘Brit. Assoc. Rep.,’ 1851). The 
demonstration, however, of § 10 can hardly be defended. It bears some resemblance to an argument 
indicated and exposed by Professor Tait (‘ Edinburgh Trans.,’ vol. 33, p. 79, 1886). There is reason to 
think that this law is intimately connected with the Maxwellian distribution of velocities, of which 
Waterston had no knowledge.-—R.] 
