_ Ing equation (I.), as appears from the Table of the values o 

HEAT PRODUCED BY THE COMPRESSION OF A GAS. 291 
is not constant for all temperatures, unless Carnot’s function for different tem- 
peratures vary inversely as 1+ Ez, and that it is not the simple mechanical equi- 
valent of the heat, as it was unwarrantably* assumed by Mayer to be, unless 
this function have precisely the expression 
pad. a ° ; 2 : ¢ : (1.) 
This formula was suggested to me by Mr Jove, in a letter dated December 9th, 
1848, as probably a true expression for yu, being required to reconcile the expres- 
sion derived from Carnot’s theory (which I had communicated to him), for the 
heat evolved in terms of the work spent in the compression of a gas, with the 
hypothesis that the latter of these is exactly the mechanical equivalent of the 
former, which he had adopted in consequence of its being, at least approximately, 
verified by his own experiments. This, which will be called Maver’s hypothesis, 
from its having been first assumed by Mayer, is also assumed by Ciausius 
without any reason from experiment; and an expression for 1 the same as the 
preceding, is consequently adopted by him as the foundation of his mathematical 
deductions from elementary reasoning regarding the motive power of heat. The 
preceding formulze show that if it be true at a particular temperature for any one 
fluid fulfilling the gaseous laws, it must be true for every such fluid at the same 
temperature. 
6. Of the various experimental researches which might be suggested as suit- 
able for testing MAyeEr’s hypothesis, it appears, from the preceding formula, that 
any which would give data for the determination of the values of uw through a 
wide range of temperatures, would, with a single accurate determination of J, 
afford a complete test. Thus an experimental determination of the density of 
saturated steam for temperatures from 0° to 230° cent., would complete the data, 
of which a part have been so accurately determined by Recnautt, for the calcu- 
lation of the values of 4 between those wide limits, and would contribute more, 
perhaps, than any set of experimental researches that could at present be pro- 
posed, to advance the mechanical theory of heat. 
7. The values of py, given in Table I. of my Account of Carnor’s Theory, 
which were calculated from REGNavLT’s observations on steam, with the assump- 
tion of mae (the maximum density of water being unity) for the density of satu- 
rated steam at 100° cent., and of the gaseous laws for calculating it by means 
of Recnavt’s observed pressures, at other temperatures, are far from verify- 
f ee given in 
the preceding paper, ) 51; or as the following comparative Table shows :— 
* In violation of Carnor’s important principle, that thermal agency and mechanical effect, or 
mechanical agency and thermal effect, cannot be regarded in the simple relation of cause and effect, 
when any other effect, such as the alteration of the density of a body, is finally concerned. 
