12 
MR. J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
the formula (448 -f- t) A 3 = e ; in which t = temperature, Fahrenheit scale; A 3 = 
density, and e = elasticity. 
The law of elasticity in the hypothetical medium is represented by the formula 
FA 3 = e ; in which v 3 is the mean square molecular velocity ; A 3 = density, and 
e = elasticity. 
The first expresses physical laws that have been found to belong to a certain 
existent form of matter. 
The second expresses physical laws that have been proved to belong to a certain 
possible form of matter. 
The cause of the effect represented by (448 + t) in the first is unknown, but has, at 
various times, by eminent authorities, been referred to molecular motion. 
The corresponding term, v 3 , of the second represents molecular motion. 
Section II.— On the Physical Pelations of Media that differ from each 
OTHER IN THE SPECIFIC WEIGHT OF THEIR MOLECULES. 
§ 7. The synthetical deductions of last section apply to a homogeneous medium 
without respect to the absolute weight of its molecules, if the weight of each molecule 
is the same. This weight, common to all, may be viewed as the specific molecular 
weight of the medium, and distinguishes it from any other medium with a different 
specific molecular weight. We have now to enquire into the relations that subsist 
between the density and molecular velocity of two such media that have the same 
elasticity, or that are in equilibrium of pressure and also of vis viva. 
We deduced from the law of impinging elastic bodies that if v represents the mean 
molecular velocity in feet per second, A the number of molecular impacts in a second 
upon a small elastic plane which is equal in weight to n molecules, then n — -Av. 
2 co 
Let oj represent the specific weight of the molecules, we have con — —Av = e = the 
elastic force exerted by the medium on a unit of surface and as this must in the 
present enquiry be assumed constant, we may easily remark how a change in to affects 
v and A. 
It is evident that since -^Au is a constant quantity and to, A, and v variable, we 
have Av = - ; but e = wA 3 p 2 (5 5) = Av , and, therefore, A°v = -A, or A = f ~A^v, and 
‘to (J CJ 2 
Av — - = A 3 p 3 . Hence it is obvious that if A 3 , the density or number of molecules 
' O) • 
in a constant volume, as well as e, the tension, are constant, while the molecular 
* e is the absolute weight of tlxe small elastic plane that is supported by the succession of A number 
of molecular impacts per second, tbe weight of each of which is w, and their common impinging velocity 
v feet per second. 
