FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION 3 
general facts, as well as numerical values furnished by observation.... The 
original principle itself involves an assumption which seems to me very difficult to 
admit, and by no means a satisfactory basis for a mathematical theory, viz., that the 
elasticity of a medium is to be measured by supposing its molecules in vertical motion, 
and making a succession of impacts against an elastic gravitating plane.” These 
remarks are not here quoted with the idea of reflecting upon the judgment of the 
referee, who was one of the best qualified authorities of the day, and evidently 
devoted to a most difficult task his careful attention ; but rather with the view of 
throwing light upon the attitude then assumed by men of science in regard to this 
question, and in order to point a moral. The history of this paper suggests that 
highly speculative investigations, especially by an unknown author, are best brought 
before the world through some other channel than a scientific society, which naturally 
hesitates to admit into its printed records matter of uncertain value. Perhaps one 
may go further and say that a young author who believes himself capable of great 
things would usually do well to secure the favourable recognition of the scientific 
world by work whose scope is limited, and whose value is easily judged, before 
embarking upon higher flights. 
One circumstance which may have told unfavourably upon the reception of 
Waterston’s paper is that he mentions no predecessors. Had he put forward his 
investigation as a development of the theory of D. Bernoulli, a referee might have 
hesitated to call it nonsense. It is probable, however, that Waterston was 
unacquainted with Bernoulli’s work, and doubtful whether at that time he knew 
that Herapath had to some extent foreshadowed similar views. 
At the present time the interest of Waterston’s paper can, of course, be little 
more than historical. What strikes one most is the marvellous courage with which 
he attacked cpiestions, some of which even now present serious difficulties. To say 
that he was not always successful is only to deny his claim to rank among the very 
foremost theorists of all ages. The character of the advance to be dated from this 
paper will be at once understood when it is realised that Waterston was the first to 
introduce into the theory the conception that heat and temperature are to he 
measured by vis viva. This enabled him at a stroke to complete Bernoulli’s expla¬ 
nation of pressure by showing the accordance of the hypothetical medium with the 
law of Dalton and Gay-Lussac. In the second section the great feature is the 
statement (VII.), that “ in mixed media the mean square molecular velocity is 
inversely proportional to the specific weight of the molecules.” The proof which 
Waterston gave is doubtless not satisfactory ; but the same may be said of that 
advanced by Maxwell fifteen years later. The law of Avogadro follows at once, 
as well as that of Graham relative to diffusion. Since the law of equal energies was 
actually published in 1351, there can be no hesitation, I think, in attaching Water¬ 
ston’s name to it. The attainment of correct results in the third section, dealing 
with adiabatic expansion, was only prevented by a slip of calculation. 
b 2 
