BiCKERTON. — Causes tending to alter Eccentricity of Planetary Orbits. 151 



I have now to notice gaseous resistance and interchange of molecules, 

 whose action will be found chiefly to diminish aphelion distance. The fol- 

 lowmg problem demonstrates decrease of aphelion distance by a resistance 

 at perihelion. 



Problem. 2. Suppose a planet to be at that part of its orbit nearest to 

 the sun, and, when in that position, suppose a retarding force to act upon 

 it, — required to trace the effect of this upon the orbit of the planet. 



Let Px represent a tangent to perihelion, and ^^a, ab, be be components 

 in direction ^J7i, passed over m three successive infinitesimals of time. Let 

 a a, b f^, c y represent the total fall towards the sun in the same intervals. 

 Then p a fi -y, represents the orbit. Now let the velocity in the direction 

 }]x be diminished by the retarding force, and let the spaces pa', a'b', b'c' 

 represent the components in the direction px in the same infinitesimals of 

 time. The components toAvards the sun remaining the same draw aa' /3/3' 

 yy' parallel to px, then a' ft' y are points in the new orbit. 



This curve lies entirely within the other. Thus, by a retardation at 

 perihelion, aphelion distance is dimmished, as shown in fig. 5. If this 

 retardation is great enough, the orbit may become a circle or an ellipse 

 with foci reversed, as shown in fig. 5. The general action of gaseous re- 

 sistance is to convert the energy of the system into heat by gradually draw- 

 ing the planet into the sun, or to the centre of attraction. It is maximum 

 at perihelion, for there the density of the nebula is greater than at any other 

 part of the orbit. Molecular exchange results from the varying densities of 

 the different parts of the system. The planets are cooler than the central 

 parts of the nebula, and will most likely be denser than the matter surround- 

 ing them in their path, and have sufficient attractive power to collect the 

 heavy molecules in their vicinity. The temperature of the surface of the 

 planet will be raised to an unknown extent by its immersion in the nebula 

 and its progress towards perihelion. Its light molecules have their velocity 

 so ulcreased as to escape the planet, while the heavier molecules of the 

 vicinity, with their lower velocity (though equal temperature), will be 

 attracted, picked up, and become permanently part of the planet. A 

 greater proportion of heavy molecules will be found towards perihelion, for 

 at the centre of the nebula will probably be its greatest density, and the 

 original expansion of the central mass into a nebula will result in the more 

 rapid outward escape of the light molecules compared with the heavy, in 

 obedience to the laws of gaseous diffusion. Thus the accretion of molecules 

 to the planet wiU be maximum at perihelion distance. Its effect will be to 

 retard the motion of the planet, as, in order to give its own velocity to a 

 molecule, it will impart some of its energy. The escape of the light mole- 

 cules will not affect the planet's orbit. We find therefore that gaseous re- 



