J. H. Lane on the Theoretical Temperature of the Sun. 59 
it were composed of some known gas such as hydrogen, or “i 
osing it to be composed of such a a of gases as Wo 
represented by common air. e hydrogen will, of ¢ ieee 
give us the lowest temperature of ‘all known substances, under 
the general hypothesis. 
The question was resolved, and,the results were communica- 
ted in graphical and numerical form in May or June last to two 
or three scientific friends, but their publication has been delayed 
by an unavoidable absence of several months from home. 
Premising that the unit of density shall correspond to a unit 
of mass in the cube of the unit of length, the unit of force to 
the force of terrestrial gravity in the unit of mass, and the unit ~ 
of pressure or elasticity in the gas to the unit of force on a 
spc equal to the square of the unit of len h: 
r=the distance of an element of the sun’s mass from the 
sun’s center, 
t=the temperature of the elemen 
o¢=its atmospheric subtangent, referred to the force of 
gravity at the earth’s surface, or height of the column 
of homogeneous gas, whose terrestrial gravitating force 
would equal - “earboe 
e=its density, or mass of its unit volume, 
=force of Serica’ gravity in its unit volume, 
9ot=its elasticity, or elastic force per unit surface, 
#=the earth’s radius, 
M=the earth’s mass, 
m=the mass of the part of the sun’s st contained in 
the concentric sphere whose radius is 
M 2 
er 2 o¢t= the subtangent of the gas under its ne gravitat- 
ing force in the sun. 
The condition of equilibrium between the gravitating force 
of a thin horizontal layer of gas whose thickness is dr, and 0 
difference of elastic force between its lower and upper surfac 
is expressed by the equation, 
d-gat= —— ar. 
ke er pt © 
Under the hypothesis that the law of Mariotte and the law 
of Poisson prevail throughout the whole mass, and that this 
mass is in convective equilibrium, we have 
o=a constant, (1) 
ae 
4 representing the value of ¢ in the part of the mass where the 
density is a 
The theoretical difficulties which, if the supply of solar heat 
* k represen! ts the ratio of the a heat of a d ssure 
its specific heat under constant vo. ee ” 
