266 Radiation in the Solar System. [June 16, 



above the freezing point on the average. This leads us to the conclu- 

 sion that it is not higher than four-fifths the highest possible value, 

 the reduction being due to inward conduction. 



The temperature of a small body, dimensions of the order of 1 cm. 

 or less, but still so large that it absorbs radiation, is shown to be nearly 

 uniform, and at the distance of the earth from the sun about 300 abs. 



Under otherwise similar conditions temperatures must vary inversely 

 as the square root of the distance from the sun. Thus Mars, if an 

 earth-like planet, has a temperature nowhere above 253 abs., and if a 

 moon-like planet, the upper limit to the temperature of the hottest part 

 is about 270. 



PART II. Radiation Pressure. 



The ratio of radiation pressure due to sunlight to solar gravitation 

 increases, as is well known, as the receiving body diminishes in size. 

 But if the radiating body also diminishes in size this ratio increases. 

 It is shown that if two equal and fully radiating spheres of the tem- 

 perature and density of the sun are radiating to each other in a 

 zero enclosure, at a distance large compared with their radii, then the 

 radiation push balances the gravitation pull when the radius of each is 

 335 metres. If the temperature of two equal bodies is 300 abs. and 

 their density 1, the radius for a balance between the two forces is 

 19*62 cm. If the density is that of the earth, 5 -5, the balance occurs 

 with a radius 3'4 cm. If the temperatures of the two are different, 

 the radiation pressures are different and it is possible to imagine two 

 bodies, which will both tend to move in the same direction, one chasing 

 the other, under the combined action of radiation and gravitation. 



The effect of Doppler's principle will be to limit the velocity attained 

 in such a chase. The Doppler effect on a moving radiator is then 

 examined and an expression is found for the increase in pressure on the 

 front, and the decrease in pressure on the back of a radiating sphere of 

 uniform temperature moving through a medium at rest. It is propor- 

 tional to the velocity at a given temperature. The equation to the 

 orbit of such a body moving round the sun is found, and it is shown 

 that meteoric dust within the orbit of the earth will be swept into the 

 sun in a time comparable with historical times, while bodies of the order 

 of 1 cm. radius will be drawn in in a time comparable with geological 

 periods. 



