The Rev. J. M. Heath on the Variation of Temperature in Gases. 347 



substance was invariably left, that would not crystallize after ex- 

 posure to the air for months. Mannitan, or some similar body, 

 may be one of the products. 



Dextro-glucose made from honey gave mannite when treated 

 in the same way, having exactly the same melting-point as ordi- 

 nary mannite. In treating milk-sugar with dilute sulphuric acid, 

 changing into gallactose and hydrogenizing, dulcitewas not iso- 

 lated ; but I have not specially studied the reaction. 



L. On the Theory of the Variation of Temperature in Gases 

 in consequence of Changes in their Density and Pressure. By 

 the Rev. J. M. Heath*. 



IF v is the volume of a unit of weight of a gas, p its pressure, 

 and t its temperature, then the equation of Mariotte and 

 Gay-Lussac may be thus written : — pv — k(l +ut), or =A + B/, 

 and its differential d(pv) = ~Bdt. From these equations we learn 

 that every change in the temperature of the gas must cause, or 

 be caused by, a corresponding change in the magnitude jot; which 

 depends upon^ and v only. 



Now d(pv) = pdv + vdp, which is therefore equal to ~Bdt. 

 But the theory which has been propounded for the last twenty- 

 five years, and is all but universally received as established 

 beyond all doubt, is that one of these two terms only, viz. pdv, 

 is alone connected, whether as cause or as effect, with variation 

 in the temperature. It is held that whenever the gas, being 

 under the pressure^, is expanded or contracted by the quantity 

 dv, there is a certain loss or gain in the quantity of heat, and a 

 corresponding variation, therefore, in the temperature. 



This doctrine is reconcilable with the older one only so long 

 as the causes which they respectively assign for the same effect, 

 viz. a variation of temperature, are the same — that is, so long- 

 as pdv — d(pv) . Rut d(pv) =])dv + vdp. This identity can there- 

 fore only exist so long as vdp=^Q, or so long as p is a constant. 



This fact, that the modern doctrine is true as long as p is 

 invariable, is perhaps the explanation of the facility with which 

 it has been almost universally admitted. For the experiment 

 by which the value of the mechanical equivalent of heat was 

 supposed to be determined from the expansion of gas by heat, 

 was made upon a gas kept under a constant pressure. An in- 

 variable weight P was raised by the additions made to the heat 

 in a gas; but a portion of the heat so added, proportional to 

 the product of P into the height through which it had been 

 raised, did not appear to have contributed at all to the altera- 



* Communicated by the Author. 



