2 MR. J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
the simple ratio of the velocity instead of the square of the velocity—being in this 
apparently led astray by the definition of motion generally received—and thus was 
baffled in his attempts to reconcile his theory with observation. If we make this 
change in Mr. IIerapath’s definition of heat or temperature, viz., that it is propor¬ 
tional to the vis viva, or square velocity of the moving particle, not to the momentum, 
or simple ratio of the velocity, we can without much difficulty deduce, not only the 
primary laws of elastic fluids, but also the other physical properties of gases enume¬ 
rated above in the third objection to Newton’s hypothesis. In the Archives of the 
Boyal Society for 1845-1846, there is a paper “ On the Physics of Media that 
consists of perfectly Elastic Molecules in a State of Motion,” which contains the 
synthetical reasoning upon which the demonstration of these matters rests. The 
velocity of sound is therein deduced to be equal to the velocity acquired in falling 
through three-fourths of a uniform atmosphere. This theory does not take account 
of the size of the molecules. It assumes that no time is lost at the impact, and that 
if the impacts produce rotatory motion, the vis viva thus invested bears a constant 
ratio to the rectilineal vis viva, so as not to require separate consideration. It also 
does not take account of the probable internal motion of composite molecules ; yet 
the results so closely accord with observation in every part of the subject as to leave 
no doubt that Mr. PIerapath’s idea of the physical constitution of gases approxi¬ 
mates closely to the truth. M. Kronig appears to have entered upon the subject in 
an independent manner, and arrives at the same result; M. Clausius, too, as we 
learn from his paper “ On the Nature of the Motion we call Heat” (‘Phil. Mag./ 
vol. 14, 1857, p. 108).” 
Impressed with the above passage and with the general ingenuity and soundness 
of Waterston’s views, I took the first opportunity of consulting the Archives, and 
saw at once that the memoir justified the large claims made for it, and that it marks 
an immense advance in the direction of the now generally received theory. The 
omission to publish it at the time was a misfortune, which probably retarded the 
development of the subject by ten or fifteen years. It is singular that Waterston 
appears to have advanced no claim for subsequent publication, whether in the Trans¬ 
actions of the Society, or through some other channel. At any time since 1860 
reference would naturally have been made to Maxwell, and it cannot be doubted 
that he would have at once recommended that everything possible should be done to 
atone for the original failure of appreciation. 
It is difficult to put oneself in imagination into the position of the reader of 1845, 
and one can understand that the substance of the memoir should have appeared 
speculative and that its mathematical style should have failed to attract. But it is 
startling to find a referee expressing the opinion that “ the paper is nothing but 
nonsense, unfit even for reading before the Society.” Another remarks “that the 
whole investigation is confessedly founded on a principle entirely hypothetical, from 
which it is the object to deduce a mathematical representation of the phenomena 
of elastic media. It exhibits much skill and many remarkable accordances with the 
