MOTION OF A BODY EXPOSED TO EATS OF HEAT AND LIGHT. 
717 
Discussion of Experiments. 
In order to imderstand fully the meaning of these experiments I shall take the most 
general case, and assume that forces act on the “ light-mill ” which are partly internal 
and partly external. I call internal forces all forces which act between the mill and its 
enclosure. We shall find that the experiments are not compatible with the existence 
of external forces. 
Let Xj be that part of the internal force and X 2 that part of the external force which is 
independent of the velocity of the “ light-mill.” It is found by experiment that, however 
small or large the whole force is, the mill always acquires a constant velocity. This velocity 
increases with the intensity of the force. In order to express this condition analytically, 
we must assume the existence of forces which increase as the velocity increases, and 
which always act in the opposite direction to X^X,,. I shall again take the most 
general case, and assume that these forces, which are functions of the velocity u, are 
partly internal and partly external. The internal force may be expressed by 
-*,/<»• 
That part of the external force which depends on the velocity may be expressed by 
-z 2 cp(u). 
The whole force which possibly can act on the light-mill can therefore always be 
expressed by 
Xj+X, — 7C x f{u) — * 2 <p(tt). 
The speed at which the mill will revolve uniformly will be determined by the equation 
X 1 +X 2 -z 1 f(u)-z 2 (Ji(u)=0. 
The force which acts on the enclosure is equal in amount, but opposite in direction, 
to the internal part of the whole force. (Any direct action of the light on the enclosure 
is left out of account.) 
The force on the enclosure is therefore expressed by 
-X.+zJiu). 
When u has become equal to the greatest possible speed corresponding to the whole 
force, this expression is proved by experiment to be zero, because then the vessel returns 
to the original position of rest. Hence also 
X 2 — z 2 <p(u)=0, 
which means that no external force acts on the “ light-mill,” as this equation is true for 
all intensities of light and therefore for all values of u. 
All the Forces acting on the Light-mill are internal. 
The accuracy of this statement naturally rests on the accuracy with which it can 
be ascertained that there is no force acting on the vessel when the speed of the mill has 
become uniform. It can be easily seen from what I have already said about the con- 
MDCCCLXXVI. 5 G 
