138 Count Rumford’s Enquiry concerning the Nature of Heat , 
simply by the difference of the times taken up in the cooling of 
the two vessels, without having regard to any other circum- 
stance. 
These times are, no doubt, inversely as the velocities of 
cooling ; but, as all the heat lost by the vessels, during the time 
of their cooling, did not pass off through their flat bottoms, and 
as the rays from the cold surface fell on the bottom only of the 
vessel which was suspended over it, without at all affecting its 
covered sides, the velocity with which the heat made its way 
through the covered sides of the vessels was the same in both ; 
consequently, more heat must have passed that way, and of 
course less through the bottom of the vessel, when the time of 
cooling was the longest, that is to say, in the vessel which was 
not placed over ice. 
As the cooling of these vessels is a complicated process, I will 
endeavour to elucidate the subject still farther. 
As the two conical vessels were of the same form and dimen- 
sions, and contained equal quantities of hot water, the quantities 
of heat they parted with, in being cooled the same number of 
degrees, must of course have been equal. 
Expressing that quantity by the algebraic symbol a , and put- 
ting x — the quantity of heat which passed off through the co- 
vered sides of the vessel which was suspended over ice, during 
the time it was cooling through the given interval of 10 degrees, 
and y — the quantity which passed off through the covered sides 
of the other vessel, during the time that vessel was cooling 
through the same interval ; the quantity of heat which passed off 
through the bottom of the vessel which was placed over ice, 
during the time it was cooling through the given interval, must 
