RSWTOH. 



distance; prove that, in whatever position the particle be placed 

 at starting, the time of describing a given angle about the centre 

 roe will be the same. 



1340. An endless string, on which runs a small smooth bead, 

 incloses a fixed elliptic lamina whose perimeter is less than the 

 length of the string; the bead is projected so as to keep the string 

 in a state of tension ; prove that it will move with constant 

 \vl.H-ity, and that the tension of the string will vary inversely a> 

 the rectangle under the local distances. 



1341. A parabola is described with constant velocity under 

 the action of two equal forces, one of which tends to the focus ; 



that either force varies inversely as the focal distance. 



1342. A particle is describing an ellipse about a centre of 

 force /xr~*, at a certain point /* receives a small increment 8/x, 

 and the eccentricity is unaltered ; prove that the point is one 

 extremity of the minor axis, and that the m;ij >r axis 'la is dimin- 



ished bv ! 

 ^ 



1343. A particle is describing an ellipse about a centre of 

 force /xr~ 8 , and at a certain point ft is .suddenly inn-rased by 8/x ; 



the following equations for determining the corresponding 

 alterations in the major axis 2a, the eccentricity e, and the longi 

 tude of the apse -BJ, 



r8a efo r 8/x 



a(2a-r) ~ 1-e' a -r ~~ 8iiT(0-r) ~ " p. ' 

 r, beinx >-ordinates of the point at which the ch 



' place. 



1344. In an elliptic orbit about the focus, when the particle 

 is at a distance / fi m >rco, the direction <>f n, 



Mcnly turnrd through a small angle 8/3; prove that the 

 consequent alteration in the longitude of the apsr 



2a being th . of the major axis, and e the eccentricity. 



