and th^ Laws regarding the Nature of Heat. 7 



manent gases, and of vapours at their maximum density ; as 

 besides possessing the greatest interest, our superior knowledge 

 of these recommends them as best suited to the calculus. It 

 will, however, be easy to see how the maxim may be applied to 

 other cases also. 



Let a certain quantity oi permanent gas, say a unit of weight, 

 be given. To determine its present condition, three quantities 

 are necessary ; the pressure under which it exists, its volume^ 

 and its temperature. These quantities stand to each other in a 

 relation of mutual dependence, which, by a union of the laws of 

 Mariotte and Gay-Lussac*, is expressed in the following equation: 



|?i;=R(« + 0, (I.) 



where p, v, and t express the pressure, volume, and temperature 

 of the gas in its present state, a a constant equal for all gases, 



and R also a constant, which is fully expressed thus, ^^ ^ , where 



Poy ^oj ^^d ^0 express contemporaneous values of the above three 

 quantities for any other condition of the gas. This last constant 

 is therefore different for different gases, being inversely propor- 

 tional to the specific weight of each. 



It must be remarked, that Regnault has recently proved, by a 

 series of very careful experiments, that this law is not in all 

 strictness correct. The deviations, however, for the permanent 

 gases are very small, and exhibit themselves principally in those 

 cases where the gas admits of condensation. From this it would 

 seem to follow, that the more distant, as regards pressure and 

 temperature, a gas is from its point of condensatioij, the more 

 correct will be the law. Its accuracy for permanent gases in 

 their common state is so great, that it may be regarded as per- 

 fect ; for every gas a limit may be imagined, up to which the 

 law is also perfectly true ; and in the following pages, where the 

 permanent gases are treated as such, we shall assume the exist- 

 ence of this ideal condition. 



The value - for atmospheric air is found by the experiments 



both of Magnus and Regnault to be =0-003665, the tempera- 

 ture being expressed by the centesimal scale reckoned from the 

 freezing-point upwards. The gases, however, as already men- 

 tioned, not following strictly the law of M. and G., we do not 



always obtain the same value for - when the experiment is re- 

 peated under different circumstances. The number given above 

 is true for the case when the air is taken at a temperature of (f 

 under the pressure of one atmosphere, heated to a temperature 



* This shall be expressed in future briefly thus — the law of M. and C^. j 

 and the law of Mariotte alone thus — the law of M. 



