NEWTON S PRINCIPIA. 155 



sesquiplicate proportion of the periodic times and mean 

 distances is observed *, from whence the conclusion would 

 of necessity follow, that the centripetal force followed 

 the rule of the inverse square of the distance, and that 

 gravitation such as we know it in our part of the uni 

 verse, likewise prevails in these barely visible regions. 

 Thus additional confirmation accrues to the first great 

 deduction drawn from the theorems respecting attraction 

 in the Principia. 



But other interesting corollaries are also to be deduced 

 from these propositions. They enable us to ascertain, 

 for example, the attractions, the masses, and the figures 

 of the heavenly bodies. Sir Isaac Newton boldly and 

 happily applied them to determine these important par 

 ticulars, apparently so far removed beyond the reach of 

 the human faculties. 



1. The weights of bodies at the surface of the different 

 planets were thus easily determined. The law by which 

 the attractive force of spherical bodies decreases as the 

 square of the distance increases, whether those bodies be 

 homogeneous or not, provided their densities vary in the 

 same proportion, and the other law regulating the pro 

 portion between the periodic times and the distances of 

 the planets, enabled him to compute the attraction of 

 each planet, for equal bodies at given distances from their 

 centres, by comparing the observed distances and periodic 

 times of each ; and he was thus also enabled, by knowing 

 their diameters, to ascertain the weights of bodies at their 

 surfaces. He found in this manner, that the same body 

 which at the surface of the Earth weighs 435 pounds, at 



* It may even seem that already the observed axes of those remote orbits, 

 when compared with their periodic times, approach the sesquiplicate ratio- 

 Thus one has its axis 7&quot; 9, and time 58 years ; and another its axis 3()&quot; - 8, 

 and time 452 years. 



