438 Mr. Lubbock on the Heat of Vapours 



CONTENTS. 



General Expressions.' — On the Pressure of Steam. — On the Steam 

 Engine. — On the Vapours of j^ther. Alcohol, Petroleum, and Oil of 

 Turpentine. — On the Conditions of the Atmosphere and on the Calcula- 

 tion of Heights by the Barometer. — On Astronomical Refractions. 



GENERAL EXPRESSIONS. 



Let V be the quantity of absolute heat, considered as a function 

 of the sensible heat or temperature 9, 



dV _ d Vd g cLF d_^ 



d9~dgd9 '^ dj) d6 



p = k g (1 + a 9). 



g being the density, p the pressure, k and « constants, 



d g cc g 



dT ~ ~ 1 + ocS 



dp a p 



d¥ ~ 1 + a 9 



dV ag dV ap 



~ d7 (1 + « 9) "^ dp (1 + « 9~) 



dV dV ^ 



^Tg^y^'dj^^''- 



If y be considered as a constant quantity the integral of this 

 partial differential equation is 



^-^- = funct". F*. 

 ? 

 The simplest form which can be assigned to this function of Fis 

 sjuch that 1 



A and B being constants. 



* So far the reasoning is identical with that contained in the Mecanique of M. Poisson; 

 but M. Poisson proceeds further upon the limited supposition of V being constant. 



if 



