OUTLINES OF NATURAL PHILOSOPHY. 



position, tS at the force of gravity is inversely 

 the square of the distance. 



5. Since, by the Moon's inequalities, the 

 ratio of the Sun's disturbing force to the force 

 with which the Moon gravitates to the Earth 

 becomes known ; if the ratio of the former, to 

 the whole force retaining the Earth in its or- 

 bit, could be found, the ratio of this last to the 

 force of the Earth on the Moon would also be 

 found, and from thence the ratio of the distance 

 of the Moon to the distance of the Sun from 

 the Earth. 



The latter ratio would be given, because if F and f 

 are the forces that retain the Earth and the Moon 

 in their orbits ; if a and r are the radii of those 

 orbits, P and p the periodic times, 



F : F' : : : ; 



and so if the ratio of F to F' be given, P and p 

 being also given, the ratio of a to r is found. 



In this way the Sun's distance might be found from 

 his own force to disturb the Moon, the idea of 

 which appears first to have occurred to Dr MA- 

 THEW STEWART. The principal difficulty is to 

 find the ratio of the disturbing force of the 

 jSun to the force which the Sun exerts on the 

 Earth. If the expression of that force was carried 



no 



