12 Mr. W. J. M. Rankine on the Mechanical Action of Heat. 



has a sensibly uniform value, which is a function of the tempe- 

 rature and of certain unknown molecular forces. 



The integration of a differential equation representing the 

 third condition of equilibrium, indicates the /or»i of the approxi- 

 mate equation 



logP = a-^-\, (XIV.) 



the coefficients of which have been determined empirically by 

 three experimental data for each fluid. For proofs of the extreme 

 closeness with which the formulse thus obtained agree with ex- 

 periment, I refer to the Journal in which they first appeared. 



In the Philosophical Magazine for December 185 1 is given a 

 table of the coefficients for water, alcohol, ether, turpentine, 

 petroleum, and mercury, in the direct equation, and also in the 



inverse formula 



V_ /g-logP ^_^ , , . (XV.) 



by which the temperature of vapour at saturation may be calcu- 

 lated from the pressure. 



For turpentme, petroleum, and mercury, the formula consists 

 of two terms only, 



logP = a-^, (XVI.) 



the small range of the experiments rendering the determination 

 of 7 impossible. 



Section I. — Of the Mutual Conversion of Heat and Expansive 

 Power, 

 1 . The quantity of heat in a given mass of matter, according 

 to the hypothesis of molecular vortices, as well as every other 

 hypothesis which ascribes the phsenomeua of heat to motion, is 

 measured by the mechanical power to which that motion is 

 equivalent, that being a quantity the total amount of which in a 

 given system of bodies cannot be altered by their mutual actions, 

 although its distribution and form may be altered. This is ex- 

 pressed in equation XII. of the Introduction, where the quantity 



v^ 

 of heat in unity of weight, Q, is represented by the height ^ , 



from which a body must fall in order to acquire the velocity of 

 the molecular oscillations. This height, being multiplied by the 

 weight of a body, gives the mechanical power to which the 

 oscillations constituting its heat are equivalent. The real specific 

 heat of unity of weight, as given in equation XIII. of the In- 

 troduction, ^Q 3y{. 



(It 2Cn/i.' 



