40 FROM NEBULA TO NEBULA 



its own fall, and the Laplacian conception of a nebula 

 "existing of itself ", "incandescent by assumption ", 

 "rotating of its own accord ", and centrifugalizing and 

 ordering its parts by no more substantial a power than 

 the scientific imagination to which should our judgment 

 incline us? But we do not need to rely solely upon de- 

 ductive reasoning as a support for our new conviction, 

 for the best and surest of proof, namely, an exact con- 

 cordance between theory, observation and mathematical 

 demonstration, is forthcoming. The problem here pre- 

 sented itself to me in this guise : If it be true that the 

 gyrations of the planets around the sun are indeed pure 

 and simple evolutions of equilibrism, then should not the 

 laws governing their velocities, distances and periodic 

 times coincide with the known laws of the ordinary lever 

 or balance-arm revolving in a horizontal plane! To this 

 preliminary question the answer was promptly ascer- 

 tained to be in the negative. But, came this new reflec- 

 tion, our hypothesis is not that of Newton, to wit, that the 

 plane of the ecliptic is stationary, but that the planets 

 and the sun are falling. Do, then, their velocities, 

 distances and periodic times conform to the laws of bal- 

 anced weights revolving horizontally and falling at the 

 same time? Here the answer was found to be triumph- 

 antly in the affirmative. 



The mathematics involved in this demonstration is 

 of the simplest and easily within the capacity of the high- 

 school graduate to understand and verify for himself. 

 As " by-products ' ' it yields: (1) a new demonstration of 

 the law of gravitation, (2) a demonstration of the law of 

 areas, (3) a direct formula for the ratio of times to dis- 

 tances, and (4) a direct formula for the planetary veloci- 

 ties. In addition to these important results, the first 

 law of Kepler, namely that the planets revolve in closed 

 ellipses, is shown to be fundamentally false, although his 

 second and third laws, which heretofore have been recog- 

 nized as purely empirical, are substantially corroborated. 



Now, the one peculiarity that distinguishes the 

 velocities of falling bodies from most others with which 



