162 Count Rumford’s Enquiry concerning the Nature of Heat , 
smallness, of the confined space (of a room, for instance) in 
which a hot body is placed, to cool. 
To simplify this investigation, we will suppose this confined 
space to be a hollow sphere of ice, 9 feet in diameter, at the 
temperature of freezing water ; and the hot body to be a solid 
sphere of metal, 2 inches in diameter, at the temperature of 
boiling water, placed in the centre of it ; and we will suppose 
farther, that this hollow sphere is void of air, and that the cool- 
ing of the hot body is effected solely by the frigorific rays from 
the ice. 
The question to be determined is, in what manner the cooling 
of the hot body would be affected, by increasing the diameter of 
this hollow sphere of ice ? 
Let us suppose its diameter to be increased to 18 feet. Its in- 
ternal surface will then be to the surface of a sphere 9 feet in 
diameter, as the square of 18 to the square of 9, that is to say, 
as 324 to 81, or as 4 to 1. And, as the quantity of frigorific 
rays emitted are, cceteris paribus, as the surface from which they 
proceed, the quantity of rays emitted by the internal surface of 
the larger sphere, will be to the quantity emitted by the internal 
surface of the smaller, as 4 to 1. 
But the intensities of these rays, at the common centre of 
these spheres, (where the hot body is placed,) being as the 
squares of the distances from the radiating points, inversely, the 
intensity of the rays from the internal surface of the smaller 
sphere, must be to the intensity of the rays from the internal 
surface of the larger sphere, as 4 to 1, at the common centre of 
those spheres. 
Now, as the time of the cooling of the hot body will depend 
