APPENDIX. 441 



whose radius is the radius vector at the given point of 

 the curve, there is no error, and indeed he obtains his 

 result in the same way as Newton does, nor could it well 

 be obtained otherwise. His XVth proposition equally 

 coincides with the equation to the centripetal force de 

 duced from the Vlth proposition of Book I. of the Prin- 

 cipia ; and the resolving the forces into two, one of which 

 is in the direction of the radius vector, is according to that 

 proposition.* By harmonical motion he means motion 

 whereby equal curves are described by the radius vector 

 in equal times; of which he gives no demonstration. 

 Though we may be surprised with several other coinci 

 dences, it must be remembered that Leibnitz had the 

 great benefit of Huygens theorems on centrifugal forces ; 

 and if it be alleged that he threw his propositions into the 

 form of dealing with centrifugal forces, the circumstance 

 just adverted to will account for it without the suspicion 

 that he did so to distinguish his investigations from those 

 of the Principia. Still less have we a right to suggest that 

 the attempt at reducing the whole within the scope of the 

 hypothesis of vortices was made to conceal his knowledge 

 of the Principia. It without doubt originated in the 

 favour still entertained generally in that day for the Car 

 tesian philosophy, of which not only Huygens was a zealous 

 supporter f&amp;gt; but Euler himself a disciple, half a century 

 later.! 



Upon the whole, we may affirm that the internal evi 

 dence is insufficient to support the charge. 



* The exact agreement of his XVth prop, without equation ~ - r _i* =, 



at d t\ 



centripetal force, 6 being the angle of the radius vector with the axis, is 

 to be noted among other coincidences. 



f Letter to Leibnitz against the principle of gravitation, 1690. 



J Mem. Acad. Paris, on the Tides, 1740. 



It should seem that M. Biot has, though with some hesitation, arrived 

 at the same conclusion, from several passages of his most learned and valu 

 able papers in the Journal des Savatits, 1852$ a paper which deserves to be 



