and of Chemical Forces. 9 



Tq and pressure Pqj P, D, t the actual pressure, density, and 

 absolute temperature, and a and b two constants*. 



The numerical value of the absolute temperature of melting 

 ice is of much importance in researches on heat. It is usual to 

 employ an approximate value deduced from the coefficient of 

 expansion of air, such as 491° Fahr. or 273° Cent. ; but on com- 

 paring a series of such approximate values (which are all too 

 small) deduced from Regnault^s experiments on air and carbonic 

 acid at progressively diminishing pressures, it appears that as 

 the density diminishes, those values tend towards 



274°'6 Cent. =494°-28 Fahr. ; 



which is the true absolute temperature of melting ice, correct (as 

 I believe) to a small fraction of a degree. 



I may add, that the cooling effect of cohesion in carbonic acid 

 gas, as calculated from the formulse I have given, varies directly 

 as the difference between the initial and final densities^ and in- 

 versely as the following function of the absolute temperature : — 



2a_ 6 

 ^ t' 



So that at a certain temperature it disappears, and a heating 

 effect commences, which with increase of temperature gradually 

 becomes insensible. The law for atmospheric air is much more 

 complicated. 



I beg you will excuse the great length of this letter, which 

 has arisen from my anxiety to explain to you fully my reasons 

 for recommending carbonic acid as a subject for experiments on 

 the thermal effects of currents, and for adopting the value I have 

 mentioned for the absolute temperature of melting ice. 



Until further experiments are made, I think that for practical 

 purposes we may neglect the constant k. 



I am, yours very truly, 



/. P. Joule, Esq. W. J. Macquorn Rankine. 



Dec. 24. — On completing the reduction of the experiments 

 referred to above, I have found the results, especially where 

 large quantities of air were employed, to agree better than I at 

 first anticipated. They seem to indicate that the value of k is 

 somewhere about 2° Centigrade. — W. J. M. R. 



* The details of this and similar formulae are contained in the 21st, 25th, 

 and 26th Articles of a paper " On the Centrifugal Theory of Elasticity/' 

 Philosophical Magazine, December 1851. 



