408 Mr, Htrapathon the Causes, Xmws, and principal [June, 



mena. A full development of these things, and the inferences 

 which might be drawn from them, would swell the memoir con- 

 siderably oeyond the limits of an ordinary communication. 



I come now to the law of gravitation or attraction.* If a par- 

 ticle of matter were put in the centre of such a fluid medium as 

 we have supposed in the fifth postulatum, and if by its agitations 

 propagated every way about, and duly counterbalanced at the 

 limits of space, it kept the minute parts of this fluid medium in 

 continual motion, then would a spherical atom be urged towards 



the central particle by a force which is as — ^, in which a repre- 

 sents the intensity of the central agitation, m the magnitude of 

 the impelled atom, and x the distance of the centres of the two 

 Dodies. 



When the attracted atom is not a sphere,t its law of gravita- 

 tion becomes more complex ; and in a general way is not to be 

 obtained in algebraic terms ; for it is dependant not only on the 

 intensity of the central agitation, the magnitude of the attracted 

 atom, and its distance from the central one, but likewise on its 

 figure and position. In all cases, however, when the attracted 

 atom is exceedingly small and at any sensible distance, or when 

 it is at a distance sufliciently oreat to render the influence of its 

 magnitude insensible, its gravitating force will be as its magni- 

 tude and the intensity of the central agitation directly, and the 

 square of its distance inversely. Consequently, if instead of 

 a single central particle, there were a great number distributed 

 so as to form a uniform sphere, and in such a manner that the 

 agitations of each may take eflect, the force of the impulsion on 

 the solitary atom, Principia, prop. 74, lib. 1, would be as 



- — ; in which m is the mass of the attracted atom, A the agitat- 



• That no one may have to charge me with a desire of making innovations, I have 

 retained the terms attraction, centripetal force, &c. though from the cause of the phae- 

 uomena, as laid down in this memoir, probably impulsion, adpulsive force, &c. or some 

 other words having a nearer affinity to the primitive cause, would be preferable. 



•f- The simplest case after a sphere is, perhaps, that of a cylinder, having the centre 

 of agitation in its axis produced. Let B C be a cylinder, 

 £ F its axis, and A the centre of aj;itation. Draw A C, A D, 

 and in A F take A G, A H, respectively equal to A C, AD; 

 join C G, and complete the parallelogram I C. Then will the 

 grantating force of the whole cylinder towards A be as the rec- 

 tangle of the agitation at A, and the distance H I. But if the 

 semidiameter E D be vastly small, compared to A E, the gra- 

 vitation is as the agitation at A, and themagnitude of the cylin- 

 der directly, and the rectangle A E, A F, inversely. Therefore, 

 if E F be likewise very small in comparison of A E, the gravi- 

 tation is directly as the agitation at A, and the magnitude of the 

 cylinder, and inversely as the square of its distance from A. 



M'hen the impelled body is a parallelopipedon, its gravitation 

 iM as the logarithm of a function of its dimensions and distance 



from the central particle, raised to a power equal to the intensity of agitation. And 

 when it is so small, or at such a distance from the centre, that its dimensions are insen- 

 sible in respect of that distance, its gravitation is proportional to its magnitude and the 

 inteuityof the agitation directly, and the square of the distance inversely, .j : <ij i .i 



