Mr. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 



231 



rolling movement, and which may be considered, for simplicity, as forming a plain curve. Moreover, 

 since the greater and smaller axes of this curve will not 

 diifer much in magnitude, we may suppose it approxi- 

 mately to be an ellipse. Let its semi-major axis AC 

 = a, and BC = b; CP=r, CY= p, CV being vertical, 

 and therefore perpendicular to the horizontal tangent 

 at P, the point of contact. The horizontal force of 

 the current {R') will be approximately equal to that 

 on a sphere whose radius = a, and its direction will 

 pass nearly through C, which will also approximately 

 coincide with the centre of gravity of the body. Hence 

 when the body is in equilibrium in the position above 

 represented, we shall have 



R'p = (p- pi)gU\/r^-p''; 



or. 



R' ^{p-p,)gU\/-^-l; 



and in order that R' may be just sufficient to make the body roll over, this equation must hold 



when the angle PCY k a maximum, i.e. when - is a minimum. Now 



r 



vhich 



and 



gives 



Also 



and 



R' ■=\-K(i?. —p\ nearly. 



as determined by experiment on the resistance on a sphere. 

 Hence the above equation becomes 



(a + h)(a- b) 



2g \p, I 



'!• f ^ - 1 J (a - 6) nearly ; 



