96 POPULAR LECTURES AND ADDRESSES. 



have, as it were, two unknown quantities and 

 two equations ; and the elimination of one of 

 the unknown quantities from the two equations 

 gives us the other explicitly. The two are 

 mixed up in a somewhat embarrassing way in 

 the primitive definitions, but when we disentangle 

 them we arrive at the simple result, which I 

 shall state presently, of independent definitions 

 of the unit of mass and the unit of force, 

 each in terms of units of length and time chosen 

 arbitrarily. 



Though the units of force and mass thus defined, 

 are essentially implied in all the regular formulas 

 of physical astronomy, from those most elementary 

 ones, which appear in the treatment of the 

 undisturbed elliptic motion, according to Newton's 

 inferences from Kepler's laws, up to the most 

 elaborate working out of the lunar, planetary, and 

 cometary theories, and of the precession and nuta- 

 tion of the earth's axis ; it has not been usual 

 for physical astronomers to found any systematic 

 numerical reckoning upon them, nor even, to 

 choose arbitrarily and definitively any particular 



