and on Astronomical Refractions. 4 3 5 



If d be the temperature as indicated by a thermometer, there can 

 be little doubt that V is capable of being expressed in a series 

 proceeding according to positive powers of 5, so that 



F = a + 6 S + c S^ + &c. 



a, h, c, &c., have a certain signification in Taylor's theorem, but 

 without being able to determine their values, a priori, or to obtain 

 any relations between them, they may be treated as constants. If 

 the latent heat be constant, which is probable, and if the effect 

 indicated by the thermometer is proportional to the sensible heat, 



c = bQ, V = a + bQ. 



It must, however, be left to experiment to decide how many 

 terms are to be taken into account for any given substance, within 

 any given range of the thermometric scale, and in order to satisfy 

 the results of observation within any given quantity. The other 

 suppositions upon which my theory is founded are those of Laplace, 

 viz. that the quantity called y by M. Poisson is constant for the 

 same substance at different temperatures, and that the equation 



}_ 



is the solution of a certain differential equation. See Mec. Cel., 

 vol. V. p. 108. Poisson, Mec, vol. ii. p. 640. 



The theorems which are given by M. Poisson in the second vo- 

 lume of the Mecaniqiie, and which are also to be found in the 

 works of Pouillet and Navier, rest upon the condition that the ab- 

 solute heat is constant, v/hile the sensible heat varies. This is the 

 most restricted hypothesis which can be made upon the nature of 

 heat, and it does not satisfy the observations. In this Treatise I 

 have gone a step further, by supposing the absolute heat to vary 

 with the sensible heat, or to be represented by an expression 

 of the form a + 6 9, (or what is the same, V=C+D{\+a^). 

 See p. 2.) S being the temperature reckoned from some fixed point, 

 a and b constants. This includes implicitly the other hypothesis, 

 which if true, in determining a and b by means of observations, 

 the constant b should come out zero. This in the case of steam 

 is certainly not the case, nor is it so in any case which I have 

 examined. 



The experiments of Dulong and Arago upon steam at high 

 temperatures, those of Southern and Dalton, and those of Dr. Ure, 

 furnish data by which the supposition I have adopted and the for- 

 mulge which flow from it can be scrutinized ; and if the expres- 

 sions which result from it fail to represent those observations, we 

 have at least arrived at this conclusion, that the condition of the 

 invariability of the quantity called y by M. Poisson does not ob- 



