246 Mr. Meikle's improved Demonstration that Air expands 



art. 1. the pressure of air confined in an inextensible vessel 

 likewise varies as 448° + t*. 



4. If m denote the specific heat of air, or the quantity of 

 heat which would raise its temperatui'e one degree, under a 

 constant pressure, and n the specific heat of the same mass of 

 air if confined in an inextensible vessel, then m always ex- 

 ceeds n in a constant ratio. This is inferred from its being 

 ascertained through a great range of temperature and pres- 

 sure, that when the density of air suffers a minute and sud- 

 den change, m times such variation of density is to the whole 

 density as n times the accompanying variation of pressure 

 lo the whole pressure f. Or, g being the density and p the 

 pressure, 



, , ndp m dp 

 mdg : Q :: 7idp : p: and ^ = ~. 



. P ? . L 



5. The last equation evidently expresses the relation be- 

 tween the fluxions of the logarithms of the pressure and den- 

 sity of air, when the quantity of heat in it is constant. The 

 fluent is 7^ log p = m log § + C. If p' and g' be put for the 

 initial values of p and g, we have C = n log p'—m log §', and 



nlog^ = ^n log -^; or (-^) = {^) 



which is the relation between the pressure and density of air, 

 when the quantity of heat in it is invariable. 



Now, to apply these principles to determine the scale of 

 temperature for air: Let ABC be a curve, such that whilst 



* Strictly speaking, art. 2 and 3, especially in so explicit a form, are 

 not essential to the final result ; but they serve to trace more readily, in 

 known terms, the relation between the common scale and the one we are 

 investigating. The whole force of the reasoning depends upon the law of 

 Boyle, and the constancy of the ratio of m to n as defined in art. 4. 



■f The first experiments of this sort seem to have been made in 1813 

 by MM. Clement and Desormes, in their researches after the absolute 

 zero. But it was the illustrious Laplace who, several years after, showed 

 their use for computing the ratio of )n to n. At his suggestion, those able 

 chemists MM. Gay-Lussac and Welter undertook a much more extensive 

 series of experiments, throughout which the ratio of m to n was found to 

 be constant. However, from employing a needlessly abstruse mode of in- 

 vestigation, the French mathematicians entirely lost sight of the more im- 

 portant consequences necessarily resulting from the conslnnct/ of that ratio; 

 and, among others, that the quantities m and n must themselves be constant. 

 This, I presume, was first demonstrated in the Edinb. Phil. Journ. for 

 September 1826, and afterward more at length in the Quart. Journ. of 

 Science for March 1829, 



In the Edinb. Phil. Journ. for March 1827, 1 described an apparatus for 

 such experiments. I have since had another one constructed, of which 

 I intend soon to give some account. From many experiments, I have 

 little doubt that the true ratio of ?« to n is that of 4 to 3, 



the 



