AMPLER. 



7. Find tho loons of .1 point snrli tliat its result:- 

 tion on a fixed straight line may always pass through a 

 point in the straight line. Result. 



8. Find tin 1 , attraction of a segment of a paraboloid ol 

 volution, bounded by a plane perpendicular to : 

 particle at the focus. 



cf ~\- CL 

 Result. 47r/xzlog -, where x is the distance of the 



bounding plane from the vertex. 



9. Round the circumference of a circle n equal centres of 

 force are ranged symmetrically ; each force is rcpnl.-ive and 

 varies inversely as the w th power of the distance. A particle 

 is placed in the plane of the circle very near it- c.-ntrc; 

 shew that approximately the resultant force on it tends to the 

 centre of the circle and varies as the distance of the particle 

 from the centre, except when m = l. 



10. Eight centres of force, resident in the 



cube, attract, according to the same law and with the same 

 absolute intensity, a particle placed very near the 

 the cube; shew that their resultant attraction passes tin 

 the centre of the cube, unless the law of force be that of the 

 inverse square of the distance. 



11. If the law of force in the preceding example be that 

 of the inverse square of the distance find the approximate 

 value of the attraction on a particle placed very near the 

 centre. 



Result. Take the centre of the cube as origin and t he- 

 parallel to the edges of the cube ; then if y, y. z be the co- 

 ordinates of the particle the attraction parallel to the axis of a; 

 is approximately 



towards the origin ng the length of an edge. 



12. The attraction of a uniform rod of indefinite length on 

 an external particle varies as (distance)' 1 of the point from the 



