1819.] and on the Laws of the Communication of Heat. 837 
being equal, this velocity changes in a remarkable degree with 
the temperature of the fluid which surrounds the body. 
It is needless, therefore, to enter into any discussion on this 
subject ; for, admitting that the laws of which we have just 
spoken represent the results of experience within the limits in 
which they have been determined, it is certain, from all that 
precedes, that when we extend them beyond these limits, we 
arrive at results very different from the truth. 
We may, by considerations analogous to those which we have 
used above, determine in what manner the law of total cooling 
changes for the same body with the nature and density of the 
ases. 
The total velocity of cooling is expressed by 
m(ai—1l)tnt? 
If we consider another gas, or the same gas, at a different 
density, the velocity of cooling will be for the same body 
m(ai—l)4+ rt 
for the coefficient » is the only part of the expression which 
changes in this case. ; 
On comparing these two expressions, we find that their ratio 
becomes equal to unity, whether we make ¢ = 0, or t =o, 
Hence the total velocities of cooling in different gases approach 
equality at very high and very low temperatures ; while in the 
intermediate part of the scale these velocities may be very 
different. This result is sufficient to show the inaccuracy of the 
processes which Mr. Dalton and Mr. Leslie employed to compare 
the losses of heat due to different gases ; for these processes are 
founded on the supposition that the total velocities of cooling in 
the different gases preserve the same ratio at all temperatures. 
But from a very singular circumstance, upon which it is need- 
less to insist, the particular temperature at which they operated 
renders the error very small, and they were far from ascribing it 
to their mode of calculation. Accordingly their determinations, 
as we have said before, are very near the truth, provided they be 
restrained to the circumstances in which they have been made. 
The necessity of estimating separately the influence of each of 
the causes which modify the progress of the cooling of a body 
not having allowed us to bring together the different laws to 
which we have come, we conceive that a summary recapitula- 
tion will be so much the more useful, because we shall have it in 
our power to re-establish the natural order which the description 
of experiments and the discussion of the results have often 
obliged us to interrupt. 
Distinguishing, as we have done, the losses of heat due 
separately to the contact of fluids and to radiation, we soon 
erceive that each of these two effects is subject to particular 
aws. These laws ought to express the relations which exist 
between the temperature of the body and the velocity of its 
Y 
Vou. XIII. N° V. 
