E N 



Ex. 2. If bodies revolve in the conic sections the force tending to the 



focus, F = = 5, where L = lat. rect. 

 L>y* 



Cor, The space through which a body P must fall, the force at P con- 



p y 



tinuing uniform, to acquire the velocity in the curve = . If the 

 curve be a circle, space . 



3. Of the linear velocity of bodies revolving in trajectories round a cen- 

 tre offeree. 



Here V - ^/F~xJPV, or = . 



And velocity (V) in any point of a curve : velocity (c) of a body re- 



volving in a circle at the same distance :: ^P V : ^p v \\ tj ^ y ' 



js. 



Ex. 1. In an ellipse (the centre of force being in the centre), V = <p| 



x c D. Also v : v : : c D : c p. 



Ex. 2. In conic sections, having the centre of force in the focus, v V 

 J- X g^r; or, by substitution, we have in the parabola V = 



i n eiijpge an a hyperbola, V = <s/ilZS 

 A. C. b r 



Ex. 3. In the conic sections (force iu the focus) V : v '.'. VHP VA C. 

 In the parabola, this ratio becomes that of VT : 1 ; in ellipse, that of 

 V T : 1 ; in the hyperbola, that of VT 4. : I. 



Ex. 4. In the ellipse velocity at any distance S P : velocity at the mean 

 distance :: VTfP : VsT- 



4. Of the angular velocities of bodies revolving in trajectories. 



Let a = area described dat. temp, y distance, then 



Angular velocity varies as j~. 

 Ex. 1. In the conic sections (force in the focw*} angular velocity varies 



50 



