574 MR W. J. M. RANKINE ON THE 
where J is Joutn’s equivalent, and a function of the temperature, the same for 
all substances, to be determined empirically ; and consequently, 
hyp. log. Gerdes fade 
ais d¢r 
or, ealad NA cay 
; é ~*. (SL) 
ay orc ( 
my ere ose s 
These expressions will be recognised by those who have studied Professor THom- 
son’s papers on the Dynamical Theory of Heat. By introducing the value given 
above of the quantity of heat in unity of weight, into the formule of the preceding 
articles of this section, they are at once transformed to those of Professor 
Tuomson, and in particular, the formulze 79 and 82 become the following :— 
. LL wae Lf wae Lf nae 
* Effect of Machine _ ¢ —€ Coe 
Heat Expended es =1-¢€ . (85.) 
of pdr 
re 
Sus-SECTION 3.—On the Hypothesis of Molecular Vortices. 
(56.) The use of a Mechanical Hypothesis in the Theory of Heat, as in other 
branches of physics, is to render it a branch of Mechanics, the only complete phy- 
sical science; and to deduce its principles from the laws of Force and Motion, 
which are better understood than those of any other phenomena. 
The results of the investigations in the preceding part of this section are con- 
sistent alike with all conceivable hypotheses which ascribe the phenomena of 
heat to invisible motions amongst the particles of bodies. 
Those investigations, however, leave undetermined the relation between tem- 
perature and quantity of heat, except in so far as they shew that it must follow 
the same law of variation in all substances. 
By adopting a definite hypothesis, we are conducted to a definite relation be- 
tween temperature and quantity of heat; which, being introduced into the formule, 
leads to specific results respecting the phenomena of the mutual transformation 
of heat and visible mechanical power; and those results, being compared with 
experiment, furnish a test of the soundness of the hypothesis. 
Thus the hypothesis of Molecular Vortices, which forms the basis of the in- 
vestigations-in the first five sections of this paper, and in a paper on the Centri- 
fugal Theory of Elasticity, leads to the conclusion, that, if temperature be mea- 
* It is to be observed, that in Professor Tiomson’s notation, heat is supposed to be measured 
by an arbitrary unit, whose ratio to a unit of mechanical power is denoted by J ; while in this paper, 
the same unit is employed in expressing quantities of heat and of mechanical power. 
