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of Edinburgh , Session 1873 - 74 . 
In Rankine’s paper of 1849, groups of circular vortices were sup- 
posed to be arranged in spherical layers round the atomic nuclei, 
in order to simplify the investigation. On the 18th December 
1851, he read a paper (Edin. Trans, xx. p. 425) in which it was 
shown that precisely the same results as to the relations between 
heat, elasticity, and mechanical work, follow from the supposition 
of molecular vortices of any figure arranged in any way. In a 
long series of papers he applied the principles of thermodynamics 
to various practical equations relating to the steam-engine and 
other heat engines, and he was the author of the first separate 
treatise in which the science of thermodynamics was set forth 
with a view to its practical application (A Manual of the Steam- 
Engine and other Prime Movers, 1859). In two papers read to 
the Philosophical Society of Glasgow in 1853-1 855 respectively, 
he pointed out how the laws of thermodynamics and of electro- 
dynamics might be regarded as particular cases of general laws 
applicable to energy in the abstract, and especially to transforma- 
tion between the two great classes of tl actual and potential” 
energy. 
Clausius, who, it is well known, discovered the second law of 
thermodynamics consentaneously with Rankine, having taken occa- 
sion in 1866 to lay great weight on his having adopted no special 
hypothesis on the molecular constitution of bodies, hut to have 
deduced the second law from general principles, Rankine, in an 
address to the Philosophical Society of Glasgow, concluded an 
eloquent justification of the mechanical hypothesis of molecular 
vortices in these words : — u I wish it to be clearly understood that 
although I attach great value and importance to sound mechani- 
cal hypothesis as means of advancing physical science, I firmly 
hold that they can never attain the certainty of observed facts ; 
and accordingly, I have laboured assiduously to show that the 
two laws of thermodynamics are demonstrated as facts independent 
of any hypothesis ; and in treating the practical application of 
those laws, I have avoided all reference to hypothesis whatsoever.” 
In March 1854 he was awarded the Keith medal of the Royal 
Society of Edinburgh for the researches above summarised, mostly 
in his own words. His name and fame had become European. 
He was elected Fellow of the Royal Society of London, and con- 
