STATICS. 2G7 



wards, one extremity being at the vertex and the other at the 

 cusp; prove that 



^ 3 



1 -SO. A heavy uniform chain fastened at two points rests in 

 the form of a parabola under the action of two forces, one (A) 

 parallel to the axis and constant, and the other (F) tending from 

 the focus ; prove that 



<f> being the angle which the tangent at any point makes with the 

 tangent at the vertex, and m a constant. 



1281. Find the law of repulsive force tending from a focus 

 under which an endless uniform chain can be kept in equilibrium 

 in the form of an ellipse; and, if there be two such forces, one in 

 each focus and equal at equal distances, prove that the tension at 

 any point varies inversely as the conjugate diameter. 



1282. A uniform chain rests in the form of a cycloid whose 

 is vertical under the action of gravity and a certain normal 



force, and the tension at the vertex vanishes; prove that the 

 tension at any point is proportional to the vertical height above 

 the vertex, and that the normal force at any point is 



is the angle which the normal makes with the vertical. 



1283. A heavy chain of variable density, suspended from two 

 tt, hangs in the form of a curve whose intrinsic equation is 

 =/(<), the lowest point being origin; prove that the density 

 lit any point will vary inversely as oos* </*' (<). 



- i. A string is kept in equilibrium in the form of a closed 



l'\- the action of a r-|.ul-i\,- force tending from a fixed 



ity at each point is proportional to the tension; 



