GRAVITATION VERSUS INERTIA 29 



is really a gravitational unit, or balancing entity, un- 

 der the control of a distant external attraction, then 

 the velocities and distances of the planets should con- 

 form to the lever principle, should they not? And 

 suppose I am able to show that THE LAWS OP KEPLER ARE 



MERELY THE EXPRESSION OF THOSE OF THE LEVER CARRIED 



THROUGH THE ENTIRE 360, what more remains to be 

 proved ? 



Let R be the longer arm of the lever and r the 

 shorter. Then by rule, 



R 2 : r 2 :: (2?R) 2 : (2?r) 2 

 But in the case of the lever, a weight r at the R end 

 will counterbalance a weight R at the r end; or, ex- 

 pressed in terms of arc, any weight at R need travel 

 only r degrees to counterbalance an equal weight 

 through R degrees of the smaller circle; or, again, ex- 

 pressed in terms of units of time required to complete 

 the full circuits, any weight at the R end can take R 

 time units while the same weight at the shorter end 

 must perform its journey in r units. 



Taking now the last two terms of our proportion 

 and correcting them so as to express the time, in place 

 of the linear, length of the respective circumferences, 

 and simultaneously multiplying the first two terms in 

 the same order and manner, to preserve the propor- 

 tion, we obtain the expression, 



R 3 : r 3 :: (Rx2?R) 2 : (rx2?r) 2 

 "The cubes of the distances are proportional to the 

 square* of the periodic times" Q. E. D. 



I therefore claim to have proved: That all the 

 planetary revolutional (as distinguished from rota- 

 tional) motions of our solar system, and presumably of 

 all planetary systems, are not inertial in their nature 



