GENERALIZATION OF PRINCIPLES 75 



and stated, more truly, that, supposing no resist- 

 ance, it would be " an eccentric ellipsoid," that is, a 

 figure resembling an ellipse. But though he had 

 made out the approximate form of the curve, in 

 some unexplained way, we have no reason to believe 

 that he possessed any means of determining the 

 mathematical properties of the curve described in 

 such a case. The perpetual composition of a cen- 

 tral force with the previous motion of the body, 

 could not be successfully treated without the con- 

 sideration of the Doctrine of Limits, or something 

 equivalent to that doctrine. The first example 

 which we have of the right solution of such a pro- 

 blem occurs, so far as I know, in the Theorems of 

 Huyghens concerning Circular Motion, which were 

 published, without demonstration, at the end of his 

 Horologium Oscillatorium, in 1673. It was there 

 asserted that when equal bodies describe circles, if 

 the times are equal, the centrifugal forces will be 

 as the diameters of the circles ; if the velocities are 

 equal, the forces will be reciprocally as the diame- 

 ters, and so on. In order to arrive at these pro- 

 positions, Huyghens must, virtually at least, have 

 applied the Second Law of Motion to the limiting 

 elements of the curve, according to the way in which 

 Newton, a few years later, gave the demonstration 

 of the theorems of Huyghens in the Principia. 



The growing persuasion that the motions of the 

 heavenly bodies about the sun might be explained 

 by the action of central forces, gave a peculiar 



