NEWTOX. 281 



1349. A lamina moves in its own plane, so that two points, 

 fixed in the lamina, describe straight lines with equal accelera- 

 tions; prove that the acceleration of the centre of instantaneous 

 rotation is constant in direction, and that the acceleration of any 

 point fixed in the lamina is constant in direction. 



13-jO. Two points fixed in a lamina move along two straight 

 lines fixed in space, and the velocity of one of the points is uni- 

 form ; prove that every point in the lamina moves so that its 

 acceleration is constant in direction and varies inversely as the 

 of the distance of the point from a fixed straight line. 



1351. Two ellipses are described about a common attractive 

 force in their centre; the axes of the two are coincident in direc- 

 tion, and the sum of the axes of one is equal to the difference of 

 the axes of the other ; prove that if the describing particles be at 

 corresponding extremities of the major axes at the same moment 

 and he moving in opposite directions, the line joining them will be 

 of constant length during the motion and will revolve with uni- 

 form angular velocity. 



1. ,.>2. A lamina moves in such a manner that two straight 



i in the lamina pass through two points fixed in qp*06j 



prove that the motion of the lamina may be completely r -j.lv- 



Rented by Mi|]><i-mg a circle fixed in the lamina to roll with 



nal contact on a circle of half its radius fixed in -pace. 



l.".">.. A triangular lamina ABC moves BO that the point A 

 lies on a straight line be fixed in space, and the side BC passes 

 h .i ji..int a fixed in space, ami tin- triangles ABC, abc are 

 iMjual and similar : ]>r..ve that the motion of the lamina may be 

 completely represented by >upp.singa parabola lixcd in the lamina 

 to roll on an equal parabola fixed in 



1. T\v.i | .articles describe curves under the action <>f 

 ve forces, and the radius vector of either is always 

 parallel and pn>p<,rt imial to tlie velocity ->f the other; prove that 

 the curves will be similar ellipses described about t ret. 



