NEWTON S PRINCIPIA. 153 



only laws which preserve the proportions between the force 

 and the distance, the same for the attraction of the particles 

 of bodies, and for the attraction of the masses in which 

 those particles may be distributed the only laws which 

 make the attraction of bodies the same with that of their 

 mass placed in the centre of gravity. Now these two 

 laws regulate the actions of bodies gravitating towards 

 each other, the one being the law 7 of gravitation beyond 

 the surface of attracting bodies, the other, the law of gra 

 vitation between the surface and the centre. Thus, then, 

 there is every reason to believe that this law pervades 

 the material world universally, acting in precisely the 

 same manner at the smallest and at the greatest distances, 

 alike regulating the action of the smallest particles of 

 matter, and the mightiest masses in which it exists. This 

 action, too, is everywhere mutual ; it is always in direct 

 proportion to the masses of the attracted and attracting 

 bodies at equal distances; where the masses are equal, 

 it is inversely as the squares of the distances beyond the 

 bodies, and within the bodies, as the distances from the 

 centre; and where the masses and distances vary, it is 

 as the masses divided by the squares of the distances in 

 the one case, and as the masses multiplied by the dis 

 tances in the other. This law then pervades and governs 

 the whole system. 



The discoveries which astronomers have made since 

 the death of Newton, upon the more remote parts of the 

 universe, by the help of improvements in optical instru 

 ments, have further illustrated the general prevalence of 

 the law of gravitation. The double fixed stars, many 

 of which had long been known to astronomers, and which 

 were believed to retain at all times their relative posi 

 tions, have now been found to vary in their distances 

 from each other, and to move with a velocity sometimes 



