90 PHYSICS OF MATTER 



thermodynamics led to the result that the density at any such piston 

 face was directly proportional to the nth power of the pressure. 

 The value of n is found to be 0.908 for all gases like oxygen, hydrogen, 

 nitrogen, and air. The operation is, therefore, one lying between iso- 

 thermal and isentropic compression, and near to the former. The 

 specific heat of gravitational compression is therefore negative. The 

 unit mass of gas at any point rises in temperature during compres- 

 sion, and for a rise of temperature of 1C., it gives off by radiation 

 a definite amount of heat. 



If, now, such a nebula be supposed to extend to an infinite distance 

 from the gravitating centre, the mass of the nebula will be infinite. 

 Pressure, density, and temperature then all become zero at an infinite 

 distance. Suppose such a nebula to have reached such a stage in its 

 contraction that the mass of our solar system, 1.99X 10 33 grammes, 

 is internal to Neptune's orbit, then it turns out that the pressure there 

 will be about what it is in Crookes tube, 1.74X 10~ 7 atmospheres. The 

 density will be far less than in a Crookes tube, viz.: 1.40X 10~ 12 

 c. G. s. The temperature for a hydrogen nebula will be 3000C., and 

 for other gases it will be higher in inverse ratio as the value of the 

 Boyle-Gay-Lussac constant. 



If the mass of the nebula be made finite, the conditions become 

 still more interesting. Let the condition be imposed that the mass of 

 the nebula is that of our solar system, and that it has so contracted 

 that Neptune's mass only is external to Neptune's orbit. Then the 

 temperature at Neptune's place drops to about 1900C., for hydrogen, 1 

 and both pressure and temperature become very much less than 

 before. P 1.49 X 10~ 10 ; d 1.93 X 10~ 15 . The thickness of the spherical 

 shell which would contain Neptune's mass is about a million miles 

 (1.65X 10~ u cm.). At the external surface of this nebula, the con- 

 dition imposed makes P, d, and T zero, as the equations show. 

 Nevertheless, a large fraction of Neptune's mass would be gaseous 

 and far above its critical temperature. It seems to me impossible to 

 think of a nebula having such properties generating by any reason- 

 able rotation a system of planetary bodies. With Neptune's mass 

 on the surface of such a nebula consisting of matter having a density 

 and pressure less than a thousandth of these values in a Crookes 

 tube vacuum, how could we conceive of this matter being gathered 

 into a single planet? 



A much more reasonable hypothesis is one discussed by G. H. 

 Darwin in 1889, in the Philosophical Transactions of the Royal 

 Society. 2 Darwin discussed the properties of a swarm of solid 

 meteoric masses, and gives very strong proof of the proposition that 



1 In a nebula of mixed gases, each gas will, of course, have its own temperature, 

 as is well understood. 



2 On the " Mechanical Conditions of a Swarm of Meteorites," and on "Theories 

 of Cosmogony," Phil. Trans. 1889. 



