Prof. Young's Method of proving the Lata of Gravitation. 333 



for instance, the discharge of a Leyden jar. The curious facts 

 observed by Professor Graham, respecting the power of even 

 smaller quantities of the same and other gases to arrest the 

 slow oxidation of phosphorus, are also favourable to the 

 doctrine that the interfering gases act solely by virtue of their 

 superior attractions for oxygen. 



LX V. Simple Method of proving the Lata of Gravitation. 

 By J. R. Young, Esq-^ Professor of Mathematics in Belfast 

 College. * 



'X'HE following is a concise mode of establishing the law of 

 gravitation, with the aid of only the most obvious dyna- 

 mical principles. Its novelty, and remarkable simplicity, may 

 perhaps entitle it to a place in the Philosophical Magazine. 



Let R be the radius of curvature at any point of the pla- 

 netary orbit, r the distance of the planet from the sun, p the 

 semiparameter, and P the perpendicular from the centre of 

 force upon the tangent through the extremity of r. 



By a known property of the conic sections, if from the foot 

 of the normal, N, a perpendicular be drawn to the radius 

 vector, the part intercepted between this perpendicular and 

 the curve will be equal to the semiparameter. Hence by si- 

 milar triangles we shall have 



^ _ N_ 



P - p' 

 Now from the usual expression for the radius of curvature 

 we have 



R = A = N -^. 



p- P3 



Moreover, by the resolution of forces, 



N / _ jr\ _ force of gravit ation 



p \ P/ normal force ^ '' 



But from the well-known theorem of Huygens, the normal 



force is expressed by -^ ; and it is an obvious deduction from 



the first law of Kepler that the velocity varies inversely as 

 the perpendicular upon the tangent. (PnHCif/jea, sect. 2. prop.l. 

 cor. 1.) Hence 



Normal force = -^ = p, j^ = ^y, (2.) 



Consequently (1.) 



* Communicated by the Author, 



