1826.] Mr, Meikle on the Law of Temperature. 



367 



inconsistencies in the opinions which are entertained by most of 

 the principal authorities of the present day, regarding the law of 

 temperature. The subject is one of great difficulty, and those 

 who have given it sufficient attention are aware, that there is 

 abundant room for falling into mistakes. In such researches, 

 as is well known, it is no easy task to avoid confounding varia- 

 tions in the quantity of heat with the variations on our common 

 scales of temperature ; and it is curious that though new terms 

 have been coined for the express purpose of overcoming this 

 source of fallacy, those who were thus accoutred have not 

 thereby been protected from their former mistakes ; from which 

 it would appear, that the difficulty was owing to something else 

 than a want of words ; and that the nature of things was not, 

 in this instance at least, changed by a new name. 



In the paper referred to, I have attempted both to point out 

 some of the chief misconceptions which exist on this subject, 

 and also to show what law of temperature is alone consistent 

 with admitted principles. No new hypothesis is introduced. 

 But from reconsidering the subject, I find that the law of tem- 

 perature admits of being investigated in a somewhat simpler 

 form, so as entirely to avoid the differential equation, and the 

 determination of the requisite form of its integral, which led 

 those great mathematicians who have preceded me in this 

 inquiry so far astray. 



Let t be the temperature, or rather 

 the indication on the common scale of 

 an air thermometer, p the pressure, and 

 g the density of a mass of air ; then a 

 and b being constants, we have from the 

 law of Boyle, 



p = bg(l +at) ,., (A) 



Now it is obvious, that the specific 

 heat of air under a constant pressure 

 will be to its specific heat under a con- 

 stant volume, in the inverse ratio of the 



variations of temperature produced in these two different cases 

 by equal variations in the quantities of heat ; so that the follow- 

 ing expressions respectively contain all the variables which enter 

 into these specific heats, relatively to the ordinary graduation, 

 viz. 



1 



d~7 



a g ,1 1 



— ^ and it: = T- 



+ at* d't dp 



a p 



1 + at 



• The specific heats are — x Pand-T^ x 1°. But rf o the differential of the 

 at at 



quantity of heat, being constant, and the same in both terms, is here omitted, as also 

 the constant linear degree of the common scale, 



