ON THE MATHEMATICAL THEORY OF FLUIDS. 231 



that the density is a function of the heat of combination, with- 

 out allowing that the loss of tenipei-ature is exactly equal to the 

 heat that enters into combination in the latent form. His rea- 

 soning is in fact conducted on the supposition that the loss of 

 temperature is equal to the heat of combination, diminished by 

 heat from extraneous bodies. To ascertain the function that 

 the density is of the latent heat, he avails himself of a well-known 

 experiment, first made by MM. Clement and Desormes, and re- 

 peated afterwards by MM. Gay-Lussac and Welter, which de- 

 termined the ratio of the specific heat of air submitted to a 

 constant pressure to its specific heat when retained in a con- 

 stant volume. This ratio Gay-Lussac found to be nearly of con- 

 stant value between the temperatures — 20° and 40° of the cen- 

 tigrade thermometer, and between the pressures 0'"*144 and 

 l'^'46. By assuming it to be constant, Mr. Ivory arrives at the 

 function he is seeking for, and further, supposing the heat from 

 extraneous sources to vanish, i. e. by returning to theDaltonian 

 hypothesis, he is conducted to a very simple relation between the 

 pressure and the density expressed algebraically by the equation 

 p = p*", where j} is the pressure relative to a unit of pressure, p 

 the density relative to a unit of density, and m the ratio just 

 spoken of. This same eqviation M. Poisson had previously ob- 

 tained* by means of the same experimental results, but without 

 the consideration of latent heat, as I shall afterwards have oc- 

 casion to mention. As the efifect of heat in determining the at- 

 mospheric density and pressure is taken into account in this 

 equation, if it be a true equation, it will be that additional one 

 which is required for the complete solution of problems, such as 

 the barometric measurement of heights. It is, therefore, im- 

 portant to inquire whether the equation p = p'" expresses the 

 law of nature. By pursuing the investigation, on the supposition 

 that the total heat of a mass of air is made up of the latent heat, 

 the heat of temperature, and extraneous heat, and joining to ex 

 pressions previously obtained for ]j and p, the usual differential 

 equation dp = — g pd z relative to the pressure, density, and al- 

 titude (z), Mr. Ivory arrives at an equation (Phil. Mag., vol. Ixvi. 

 p. 242) by which the hypothesis of Dalton may be put to the 

 test. He finds that there are an unlimited number of supposi- 

 tions all equally leading to an equation of the form p = p'", m 

 being different for each, and all indicating diffei'ent atmospheres, 

 which possess the common property of decreasing in tempera- 

 ture, at a rate proportional to the increase of altitude. If w = 1, 

 and consequently/; = p, the decrement of temperature is infi- 



* Connuhsance des Terns for 1826, published in 1823. 



