COMMUNICATION OF HEAT BETWEEN A SUEFACE AND A GAS. 
727 
Now, from the description of Mr. Ckookes’s instruments which he has published, it 
appears that they, like the one which I possess, arrive at a constant velocity depending 
on the intensity of the light. Hence it may be fairly inferred that in them the motion 
of the wheel is restrained by the same resistance as in mine ; and that this resistance, 
as I have just shown, is not the resistance of the pivot. 
(2) The limited velocity of these mills is therefore exactly what would be caused by 
the friction of the air, just as in the clock : but there is another conceivable cause of 
the limit ; and this is, that the force which causes the motion diminishes with the velo- 
city. Fortunately, however, there is another test by which the resistance may he 
examined, a test altogether independent of the action of light or heat. This is the 
rate at which the mill comes to rest when the light is turned off. If the pivot were 
the only source of resistance the time required for the mill to come to rest would be as 
the speed; that is to say, if it required 15 seconds for the mill to come to rest when 
making 10 revolutions per minute, it would require 150 seconds to come to rest from 
100 turns per minute. In fact, however, my mill, which requires 15 seconds to come 
to rest from 10 revolutions, does not take 30 to come to rest from 100 revolutions. 
In these experiments the wheel was set in motion by turning the envelope, and not by 
the aid of light or heat. We have, therefore, conclusive evidence that the resistance 
is not merely that of the pivot (which, in fact, is so small as to be inappreciable) ; and 
the only other resistance of which we know * is that of the air. But this is not all. 
The behaviour of the mill furnishes us with the exact law of the resistance ; and this 
is identical with the law of the resistance of air in a highly rarefied condition, a law 
distinctly special in its character. 
The resistance which bodies experience in moving through the atmosphere at consi- 
derable velocities is proportional to the square of the velocity ; but if the velocity is 
very small, less than one tenth of a foot per second, then, as Prof. Stokes has shown, 
the resistance is nearly proportional to the velocity. Now, so far as this latter resistance 
goes, Prof. Maxwell has shown the singular fact that, although it depends on the 
nature, it is independent of the density of the air or gas. A body moving at a very 
small velocity would therefore experience the same resistance whether moving outside 
or within the receiver of an air-pump in which the air was highly rarefied, the only 
difference being that the speed for which the resistance continues proportional to the 
velocity is higher in proportion as the tension of the air is reduced. 
If, therefore, the vanes of the light-mill were moving in air as dense as the atmosphere 
they would experience a resistance increasing with this speed according to a law varying 
from the velocity at low speed to the square of the velocity at high speeds ; but since 
they move in an exceedingly rare medium, the resistance which it offers is more nearly 
proportional to the velocity throughout, and only at the highest speeds can there be any 
appreciable deviation from this law. 
* Ethereal friction, if it exists at all, must he too small to produce any appreciable effect, and it is not 
probable that it would follow the same law as air. 
5 H 2 
