198 COSM1CAL ARRANGEMENTS. 



and of any of the planets ; and hence, cannot 

 make any calculation, founded on such a com- 

 parison. Newton has endeavoured to show how 

 small the resistance of the medium must be, if it 

 exist.* The result of his calculation is, that if 

 we take the density of the medium to be that 

 which our air will have at 200 miles from the 

 earth's surface, supposing the law of diminution 

 of density to go on unaltered, and if we suppose 

 Jupiter to move in such a medium, he would in a 

 million years lose less than a millionth part of his 

 velocity. If a planet, revolving about the sun, 

 were to lose any portion of its velocity by the 

 effect of resistance, it would be drawn propor- 

 tionally nearer the sun, the tendency towards the 

 centre being no longer sufficiently counteracted 

 by that centrifugal force which arises from the 

 body's velocity. And if the resistance were to 

 continue to act, the body would be drawn per- 

 petually nearer and nearer to the centre, and 

 would describe its revolutionsquicker and quicker, 

 till at last it would reach the central body, and 

 the system would cease to be a system. 



This result is true, however small be the velo- 

 city lost by resistance ; the only difference being, 

 that when the resistance is small, the time re- 

 quisite to extinguish the whole motion will be 

 proportionally longer. In all cases the times 



* Principia, b. iii. prop. x. 



