46 PROCEEDINGS OF THE CANADIAN INSTITUTE. 
sun was 4 7(433)? (10)° (5280)? 5,500,000 foot-pounds per second, or 
(10)* foot-pounds per annum. It therefore follows that if the theory 
of the origin of solar heat under examination were the true one, the: 
energy of the sun would be completely exhausted in 3,680 years, 
while we know that the quantity of heat radiated from the sun has. 
been practically as great as at present for millions of years. The 
theory of combustion or chemical combination, therefore, falls to the 
ground, and it is now generally supposed that the perennial fountain 
whence flow the vast energies of the solar system. is the potential 
energy of gravitation which is converted into kinetic energy by its: 
mass moving towards the centre of inertia of the solar system, and 
thence into heat by a mechanism indicated by the physical constitu- 
tion of the fiery ruler of the day. 
The following investigation will show that this now generally 
accepted hypothesis predicates a cause known to be a vera causa 
amply capable of producing the results it is supposed to explain, and 
that therefore it is not inconsistent with the axiom that the cause 
must be equal to the effect. 
Let p represent the density at distance 7 from the centre of a 
spherical mass, supposed equally dense at equal distances from the 
centre. The elemental mass, therefore, between the spherical surfaces 
whose radiiare r andr + dr,isp4ardr., 
Taking proper units of force, &c, and remembering the theorem 
that the attraction of a spherical shell on an internal particle vanishes, 
it follows that the force acting on this elemental mass is measured by _ 
the quantity— 
4nzprdrft4zpr dr. 
a 
assuming of course the Newtonian law of gravitation. The work 
done by this elemental mass moving through an infinitesimal de, will 
consequently be— 
4zprdrf *4zprdrde. 
2 
1 
Integrating with respect to dr we get as the total work done— 
Ei { dnp ur. flan pr dr. | ar. 
a formula which will be found to be of considerable use in solving 
certain important classes of problems, 
