KYNAMI S, r.LKMKNTARY. 



1317. A particle is projected so as to move on a parabolic 



is vertical and vertex upwards; prove that the 

 ire on the curve in any position is proportional to the cur- 

 vature. 



1318. Two heavy particles, connected by a fine string passing 

 through a small fixed ring, describe horizontal circles in equal 

 times; prove that the circles must lie in the same horizontal 

 plane. 



1319. A particle P is attached by two strings to fixed points 

 A, B in the same horizontal line, and is projected so as just to 

 describe a vertical circle; PB is cut when the particle is in its 

 lowest position, and P proceeds to describe a horizontal circle ; 

 prove that 



cos 2 ALB, :, 

 o 



and that, if the tension of PA be unaltered, the angle APE is a 

 ri^ht angle. 



1 -20. Two given weights are attached at given points of a 

 fine string, which is attached to a fixed point, and the system 

 revolves with uniform angular velocity about the vertical through 



tin- fixed point in a state of relative equilibrium; determine the 

 inclinations of the two parts <>f the string to the vertical. 



1 "-!. A parabola is placed with its 'axis In.ri/.ontal and plane 

 vertical, and a heavy smooth particle is projected upwards fioin 

 the vertex so as to move on the concave side of (lie curve ; prove 



. ertical space described before leaving the curve 

 thirds of tin- greatest height attained. If 20 be the angle described 

 about the focus before leaving the curve 



/' b'-ini: ' Ity of pn.jertion and \,i the 



latn> reetum ; abo the lutus rectum 



4a tan"0. 



181 



