PRESENT PROBLEMS 89 



situation has changed in various ways. The discovery of radioactive 

 matter in wide diffusion in the earth's crust has reopened the whole 

 question of underground temperature as related to the age of the 

 earth and its past history. Nevertheless, if the nebular theory in 

 any form, or any similar theory, represents the process of evolution 

 of the solar system, a large amount of heat due to gravitational 

 contraction must have resulted, and must have been disposed of by 

 radiation. 



During several years I have been giving attention to the condi- 

 tions of evolution of a gaseous nebula. The equations of equilibrium 

 for such a mass have been developed. 1 A cosmical mass of gas was 

 assumed, satisfying everywhere the Boyle-Gay-Lussac law, capable 

 therefore of expanding, of being compressed, and of transmitting 

 pressure, and having a centre towards which it gravitates. 



Such a mass of gas is a simple heat-engine. The piston face is any 

 spherical concentric surface. The load on the piston is the weight 

 of superposed layers, external to the piston face. The radially in- 

 wardly directed pressure is exactly that required to balance the 

 outward pressure of the inclosed mass. As radiation and contraction 

 proceed, the load on the piston increases, in a perfectly definite way, 

 due to increase in weight of each element of mass as it approaches 

 the gravitating centre. Whatever may be the nature of the gas, as 

 determined by the numerical value of the Boyle-Gay-Lussac con- 

 stant, at some time in its history contraction will have proceeded 

 until some fixed or definite mass shall have been compressed within 

 a fixed volume of definite radius. The equations show that the 

 pressure at the surface of this mass, that is to say, the load on the 

 piston, will then be entirely independent of the nature of the gas. 



The difference between gases will only be show^n in the time re- 

 quired for them to reach this assumed stage in their gravitational 

 history. A gas which permits the heat of compression within the 

 piston face to escape most quickly into the refrigerator external 

 to the nebula will reach this stage most quickly. When this has 

 been done, pressures and densities at the piston face are wholly inde- 

 pendent of the nature of the gas. The total work of compression done 

 on the mass within the piston face up to this time is also independent 

 of the nature of the gas. But the temperatures at the piston face 

 will be inversely as the numerical value of the Boyle-Gay-Lussac 

 constant. 



It is evident, therefore, that the law of contraction cannot be 

 indeterminate as in the case where the load is imposed by the hand 

 of man. There is, therefore, in addition to the Boyle-Gay-Lussac 

 law, another definite relation between any two of the three variables 

 involved in that law. The application of well-known equations of 

 1 Transactions, Academy of Science of St. Louis, xin, no. 3; xiv, no. 4. 



