Chap. XXL] THE HEAVENS. 267 



action of the forces of astral gravitation mentioned 

 in the foregoing Proposition. 



' Because vis-hiertias is the gravitation of the 

 universe, of which the sun's direct force of gravita- 

 tion is a part and astral gravitation the remainder ; 



Therefore the decrease of the solar force is the 

 increase of the astral force ; and therefore at some 

 greater or lesser distance from the sun the opposing 

 forces are equal. ^ 



* We have said that, setting aside planetary influences, the 

 earth in its orhit round the sun is held between the opposing forces 

 of astral and solar gravitation. But, in fact, the astral gravitation 

 which at any given point of the earth's orbit is acting in opposition 

 to the sun, is at the opposite point of the orbit acting in conjunction 

 with the sun, its force being there diminished in the inverse 

 pi'oportion to that in which the square of the distance at which 

 it is acting is increased. Therefore, the astral gravitation acting 

 in opposition to solar gravitation, is at any point of the earth's 

 orbit equal to the force of solar gravitation, together with the 

 force of astral gravitation which, by acting across the orbit of the 

 earth, acts in conjunction with the sun. From which it follows, 

 that the force of solar gravitation is equal to the amount by which 

 the force of astral gravitation is diminished by the increase of its 

 distance in acting across the orbit of the earth. Now, if we take 

 into consideration only the mean distance of that part of the 

 universe which the telescope has revealed to us — even taking that 

 distance as the mean distance from which astral gravitation acts 

 upon the solar system — even then, the difference in the force 

 acting in the same direction at two opposite points of the earth's 

 oi'bit causes an inexpressibly slight difference in the relation of 

 those forces to each other : and since this difference is equal to 

 the power of solar gravitation, this latter is, therefore, when 

 compai'ed with that of astral gravitation, insignificant beyond the 

 power of mathematical expression. The comparison is as that of 

 day with the entire duration of time, or as that of a mile with the 



