Gravitational Matter through Infinite Space. 169 



This shows that the average normal component force over the 

 surface S is infinitely great, if p is finite and r is infinitely 

 great, which suffices to prove § 11. 

 § 14. For example, let 



r = 150. 10«. 206. 10 6 = 3"09 . 10 16 kilometres. . (5). 



This is the distance at which a star must be to have parallax 

 one one-thousandth of a second ; because the mean distance of 

 the earth from the sun is one-hundred-and-fifty-million kilo- 

 metres, and there are two-hundred-and-six-thousand seconds 

 of angle in the radian. Let us try whether there can be as 

 much matter as a thousand-million times the sun's mass, or, 

 as we shall say for brevity, a thousand-million suns, within a 

 spherical surface of that radius (5). The sum's mass is 

 324,000 times the earth's mass ; and therefore our quantity 

 of matter on trial is 3' 24 . 10 14 times the earth's mass. 

 Hence if we denote by g terrestrial gravity at the earth's 

 surface, we have by (4) 



Q = 3-24. 10»(|g~JJ 6 )^ = l-37 . 10-».£ . (6). 



Hence if the radial force were equal over the whole spherical 

 surface, its amount would be 1*37 . 10~ n of terrestrial 

 surface-gravity; and every body on or near that surface 

 would experience an acceleration toward the centre equal 

 to 



1*37 . 10~ 13 kilometres per second per second . (7), 



because g is approximately 1000 centimetres per second 

 per second, or '01 kilometre per second per second. ]f the 

 normal force is not uniform, bodies on or near the spherical 

 surface will experience centreward acceleration, some at 

 more than that rate, some less. At exactly that rate, the 

 velocity acquired per year (thirty- one and a half million 

 seconds) would be 4*32 . 10 -6 kilometres per second. With 

 the same rate of acceleration through five million years the 

 velocity would amount to 21*6 kilometres per second, if the 

 body started from rest at our spherical surface ; and the 

 space moved through in five million years would be *17 . 10 16 

 kilometres, which is only -055 of r (5). This is so small 

 that the force would vary very little, unless through the 

 accident of near approach to some other body. With the 

 same acceleration constant through twenty-five million years 

 the velocity would amount to 108 kilometres per second ; 

 but the space moved through in twenty-five million years 

 would be 4*25 . 10 16 kilometres, or more lhan the radius r, 

 which shows that the rate of acceleration could not bo 



