132 THE PRESSUEE DTTE TO RADIATION". 



THE APPLICATION OF RADIATION PRESSURE TO COMETARY THEORY. 



In the experiments described in the foregoing paper the close agree- 

 ment of theory with experiment warrants the rigid application of the 

 radiation-pressure theor}^ in the explanation of cosmical phenomena. 



In any balancing of radiation pressure against gravitation in comets 

 the size of particles is the determining factor. The repulsion due to 

 radiation pressure depends upon the intensity of the rays, the al^sorb- 

 ing and reflecting power of the surface, and the cross section of the 

 body exposed. Gravitational attraction depends only upon mass, 

 or the product of volume and density. It will be seen, therefore, that 

 for spheres of a given substance the weight at a lixed distance from 

 the sun will vary with the cube of the radius, while radiation pressure 

 will depend upon the radius squared. The ratio of pressure to weight 

 will thus be inversely as the radius. This relation holds down to the 

 point where the particles become so small that they begin to lose in 

 absorbing and reflecting power through diffraction. 



The intensity' of the solar radiation and gravitation diminish with 

 distance in accordance with the .same law, so that the ratio of pressure 

 to weight is a constant for the same body at all distances from the ,sun. 



For spheres of the same size, and the same absorbing and reflecting 

 power, the ratio of pressure to gravitation is inversely as the density. 

 The variation of this ratio, as it depends upon size and density, hae* 

 been used by Lebedew" and Arrhenius'' in the computation of the 

 repulsion upon the finely divided matter of comets' tails, but the lim- 

 iting value of the ratio for diminishing spheres of the same density 

 due to diffraction first appears in Schwarzschild's paper. ^ 



Cornet hr<ids. — In the heads of comets the phenomena are most com- 

 plicated and ditficult of explanation, yet it seems worth while to try 

 to gather together a few of the separate causes which may be at work 

 in producing this intricate structure. 



The heat received from the sun })y the nucleus of a comet may be 

 spent in three ways: (1) In raising the temperature of the nucleus. 

 As the nucleus is of relatively small mass and probably of low heat 

 conductivity no verv considerable quantity of heat is required for this 

 purpose. (2) Heat may l)e, and doubtless is, used in the vaporization 

 of volatile hydrocarbons and other substances in the nucleus. (3) Large 

 quantities of heat are lost from the nucleus by radiation. 



The porous structure of meteorites points to a similar structure in 

 cometary nuclei. The jets from the nucleus outward to the envelope 

 of the head may l)e formed by the heating of the vaporizal)le materials 



«Wied. Ann., 45, 292, 1892; also Astrophysical Journal, 14, 155, 1902. 

 6Lehrl)iu'h der kosmischen Physik, p. 150, Leipzig, 1903. 



cSitzungsl)erichte der niath.-phys. Classe der k. b. Akademie der Wissenschaften 

 zu Miinchen, 31, 293, 1901. 



