66 SOUTHERN CALIFORNIA ACADEMY OF SCIENCES 
only the periodie comets but also the planet Mercury. No such 
effects have developed. 
Helmholtz’s theory of the mechanical origin of solar heart— 
his contraction theory announced in 1853—fully accounts for 
the Sun’s heat. Recall that the inward pull of gravity at the 
Sun’s surface is nearly twenty-eight times eravity at the 
Earth’s surface. Abundant evidence furnished by the spectro- 
scope, and the Sun’s known low density not much greater than 
that of water force the conclusion that the Sun is a vast sphere 
of commingling gases, among which many of our known va- 
porized terrestrial elements have been unmistakably indenti- 
fied. 
As the Sun contracts by its own powerful gravitation, the 
potential energy lost by gradual inward motion is replaced by 
equivalent heat energy. Every particle in the whole stupen- 
dous mass moving’ inward, contributes to the Sun’s inconeeiva- 
ble aggregate of heat. Helmholtz computed that an annual 
contraction of two hundred feet in the Sun’s diameter is suffi- 
cient to produce the heat it radiates. More accurate recent 
measurements of the amount of heat radiated, indicate a great- 
er contraction—a lessening of the Sun’s diameter by three 
hundred feet annually. This even, is so slight a change in that 
diameter of near a million miles that in seven thousand years 
will not appreciably alter the Sun’s apparent breadth. Our 
present most exact heliometers could not then detect the 
change—a change in the Sun’s angular breadth in seven thous- 
and years of less than a single second! But as the Sun is a 
gaseous mass, its expanding force just counterbalanced by its 
gravitating foree, it can contract only as its expanding foree 
lessens by loss of heat radiated. Will it not then cool as it 
contracts? Not necessarily, for Lane’s law, discovered about 
1870, asserts the paradox that a globe of gas contracts by its 
own gravity and grows hotter, as necessary results of its loss 
of heat by radiation. 
To illustrate: 
Let v—volume of a globe of gas; p=its surface gravity, or 
pressure; and ¢—its absolute temperature. When from loss of 
heat by radiation its radius contracts one-half, let v’, 7’, 2’ repre- 
sent respectively its changed volume, pressure, and temperature. 
Since volumes compare as their radii cubed, and surfaces as 
radii squared, v’ will equal % v, and the surface of v’ will = 4% 
the surface of v. Since surface gravity increases as the square 
of the radius diminishes, the inward pull or pressure on the sur- 
face of v’ will—4 times what it was on the surface of v; and as 
