36 
MR, J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
§ 35. We must now endeavour to show that an atmosphere of mixed media follows 
exactly the same law of equilibrium. 
Atmospheres of different homogeneous media supposed separate from each other 
must evidently have the same height if the mean square molecular velocity at the 
base of each of them is the same, and, consequently, the molecular vis viva in each 
atmosphere will, at the same height, be proportional to the specific molecular weight of 
the medium. If, on the contrary, the molecular vis viva at the base of each is the 
same, then will the height which is proportional to the mean square molecular 
velocity follow the inverse ratio of the specific molecular weight, which is also equal 
to the direct ratio of the mean square molecular velocity (VII.). Thus, a hydrogen 
atmosphere ought to be four times the height of an oxygen atmosphere, &c. When 
mixed, the molecules of each of the media at the same height are necessarily in 
equilibrium of vis viva, and the mean space occupied by each molecule is therefore the 
same (§ VIII.). To see distinctly that the condition of the mixture is exactly that of 
a homogeneous medium of equal specific gravity, or, what is the same, whose specific 
molecular weight is equal to the sum of the products of the specific molecular weight 
of each by its proportionate volume—and thus having in equal volumes the same 
amount of vis viva as the mixture—we have only to recollect that a constant 
increment of descent in the atmosphere corresponds in all parts of it to the same 
constant increment of mean square molecular velocity, whatever the molecular velocity 
may be, or whatever the weight of the molecules with which it is associated, and the 
increment of vis viva in each medium for the same constant increment of mean 
square molecular velocity is as the product of its specific weight by its constituent 
volume. But the increment of mean square molecular velocity in the homogeneous 
being the same as in each of the constituents of the heterogeneous medium, and the 
product of its specific weight by its constituent volume being equal to the sum of the 
products of the specific wmight and constituent volume of each, it is obvious that for 
the same increment of descent through the atmosphere the increment of vis viva in 
the homogeneous is the same as in the mixed medium, and that generally the 
physical condition of an atmosphere consisting of various media mixed together is 
exactly the same as if it were composed of one homogeneous medium whose specific 
gravity is equal to that of the mixture. 
If each constituent of an atmosphere were supposed to form an atmosphere by 
itself, and ranged by each other side to side, and having all the same height, the 
ratio of their densities or proportional number of molecules in a constant volume 
would be the same at all heights, but the molecular vis viva would be respectively as 
the specific weight of each. If in this condition they were brought together so that 
all might occupy the space of one, an immediate change in the molecular vis viva of 
each medium would ensue, the heavy molecules losing and the light molecules gaining 
vis viva until the vis viva equilibrium is established ; and this, as well as their 
united density, corresponds with the same qualities of the homogeneous medium at 
