of the Gases by increase of Temperature. 275 



^=•13913, and -='3730, 



a 2 a 



m= 277*464, 



a 2 =5111'2, and = 71-492. 



Applying these to find the remaining values of y by the equation 

 of the hyperbola, we have 



y =100 



?/! = 137-533, 



?/ 2 =139-176, 



2/ 3 =170-584, 



2/ 4 =197-628, 



y 5 = 213-700, 



2/ 6 =217-613, 



and we see that the ordinates of the hyperbola furnish volumes 

 as near to M. Regnault's experimental results as can be expected. 



The value of - = -3730 is trig, tangent of the angle which 



the asymptote makes with the axis of oc, and is the extreme 

 value of a, which we see is not the same as for other gases, 

 which M. Regnault expected* might be the case in the limit for 

 very high temperatures, or in the state of extreme dilatation. 



By differentiating the equation of the hyperbola to the centre 

 as origin, or 



we have 



dy = b 1 



/jifj 



and when a/=±a } then ~ = infinity; and this must be at the 



point of liquefaction of the gas, which, when known under a 

 given pressure, will give an important datum, and probably much 

 more accurate than can be found from the discussion of experi- 

 ments like the preceding. When #= infinity, we have ~ = -, 



ax a 



which equals a in Gay-Lussac's law. The law of Amontons 

 being expressed in the form p^/cp(l-\-ut°) } must be received 

 as the true law within the limits of accuracy which can be attri- 

 buted to the laws of Boyle and Gay-Lussac, of which it is com- 

 pounded, but it is not an absolutely exact law for any gas. 



* Relation des Experiences, &c, vol. i. p. 120. 



