Chase.] -^98 [July 21, 



the absence of any aullioritatlve information on the subject, we may rea- 

 sonably conjecture that it signifies French (or Royal) America, and, if this 

 be so, the only characteristic needed to make this coin pre-eminent in 

 interest among all American colonial pieces, that, namely, of having on 

 its face a distinct mention of our Continent, is supplied. 



In concluding this paper, of which tlie subject, and the treatment of the 

 subject, will, it is hoped, not be found beneath the notice of the American 

 Philosophical Society, the writer may be permitted to observe that the fact of 

 its being presented in this our year of Jubilee, and at the moment whence, a 

 century ago, our first grand " annorum series " began to proceed, is entirely 

 accidental, resulting from the casual acquisition, at this time, of the speci- 

 men which accompanies it. There seems, however, to be an eminent pro- 

 priety in calling to mind, on the present most interesting occasion, and 

 also connecting with tangible objects of curiosity, however slight, the 

 American history of the great ally who rendered such essential aid to the 

 insurgent colonies during their doubtful struggle. In regard to matters 

 like this, perhaps not likely to be remembered with sufficient tenacity, 

 medals and coins perform an important service ; while, to take a broader 

 view, through their distinct marking of decisive epochs, they contribute to 

 enable us, in the words of a writer of the illustrious nation referred to, 

 '^vivre de la grande vie dessieclea" — to live in the great life of the Centu- 

 ries. 



On some Fundam ntal Propositions of Central Force.* 



By Pliny Eakle Chase, LL.D., 

 Professor op Philosophy in Haverford College. 



{Read before the American Philosophical Society, Jitly 21, 1876.) 



All cyclical motions which are produced by the action of a central force 

 are, necessarily, of an oscillatory character. They may, therefore, be mathe- 

 matically represented by suitable modifications of simple pendulum equa- 

 tions, as Fourier has well shown. f The first attempt at a general discussion 

 of such motions seems to have been made in 1827, by Dr. Henry James 

 Anderson, Professor of Mathematics and Astronomy in Columbia College, 

 whose paperj may be found in the third volume of the second series of the 



♦Whenever I speak of "central force," In the present paper, I refer to force 

 varying Inversely as the square of the distance. 



+ Sce, also, puporsby David Uittcnhouse, Trans. Soc. Phil. Am., iil; Jos. Clay 

 lb., v; Owen Nulty (suggested by Hittcnliouse's), lb. [2] 1; James Dean, and N. 

 Bowditch, Trans. A. A. S., ill; Robert Adrain, Trans. S. P. A., [2] i; Eugenius 

 Nulty, lb. [2]1l. 



X "On the motion of Solidson Surfaces, in the two Ilypotlicses of perfect Slid- 

 ing and perfect Rolling, with a particular e.xamination of their small Oscilla- 

 tory Motions." Op. cit. p. 315. 



