SOLIDS <>\ SURFACES. I .'7 



ded into two dissertations; treating of the oscillations of a 

 heterogeneous vertical circle rolling I'nsi without and (hen 

 with friction upon another vertical circle of support 1 *. The 

 entire paper is a favourable specimen of the characteristic 

 perspicuity of Euler, and contains the solution of the problem 

 of the small pendular motions of the body, comprised in two 

 eiiuations expressing in finite terms the coexisting oscillations 

 of the centre of gravity around the centre of the rolling cir- 

 cle, and of this centre around the centre of the circle of sup- 

 port. The integrations are effected by an application of rules 

 which Euler had himself laid down forty years before 30 in 

 discussing the coexisting oscillations of a jointed pendulum or 

 -trin-- of weights, a problem of which John Bernoulli had 

 previously proposed and resolved the simplest case, namely, 

 that in which all the weights cross the vertical at the same 

 instant of time". Eider's solution of tin- general problem of 

 the jointed pendulum stands precisely in the same relation to 

 Bernoulli's that D'Alembert's essay on the vibrations of a 

 tense string does to the original paper of Brook Taylor, and 

 must be regarded as constituting an era not only in mechani- 

 cal but equally «> in analytical science. The singular laws 

 of coexisting oscillations which Daniel Bernoulli had already 



motu penduli c n cyliodricum fulcra date i nbentem 



mobilis, remota frictione Dissertatio prior. Acta lead. Petrop. 1780, p. I 



De motu penduli, ! frictionis ratione. Dissertatio altera, p. 164. This 



if the numerous posthumous memoirs of Euler. No?a 



l, Tom. VI. 1 7 7.:. The friction is here supposed to prevent all sliding. A 



ligation require: don of a friction proportioned to the 



ili'; basis of a dissertation of Euler's (inserted in the Ni 



V 1 1 foi i 71 3, the year in which he died . — De tu globi hi li rogenii Buper piano 



horizontal^ ejusque motu .i fricl e impedito. Iirthis paper the axis of rotation is 



to I horizon and in triable in direction. For :i i r recent investiga- 



n in the ca e of a boi m forward 



and on a horizontal plane, see Bulletin doa Sciences Math. Tome 



VI. II .>'•. p. 161. This paper proceeds on the same principles as those which 



form the groundwork of Eul ly— De effectu frictionis in motu volulorio. 



Petrop. 1781. p. 131 — 1 h . 



'• De oscillationibus fili flexilis quotcunque pondusculia onusti. Com. . 



1741. 

 ' De pendulo luxate luctione ail {>< -ii. 1 1 1 Ui m simplex iaocbronum. 



J4.i1. Bernoulli Opera, Tom. IV. p. t02. 



\ OL. ill. — 4 o 



