282 AT. x OP A MOi'M A 



Also the attraction of the sphere, by An. J 1 -'. 



therefore the attraction of the spheroid on the particle 



lie same manner it might be shewn that tin 1 attractions 

 of a homogeneous prolate spheroid of small cxeentricity on 

 particles at the pole and equator are respectively 



j)c and 3 

 2c being the axis of revolution of the spheroid, and 



219. One more example may be given. It i 

 useful to compare the attraction exerted by the Eartli on a 



rticle at the top of a mountain with the attraction ex. 

 the Earth on the same particle at the ordinary level of the 

 Earth's surface. The investigation is given by ]'< -: 



///'<///*, Tom. I. pp. 492 496). Let r denote t!. 

 radius, x tlie height of the mountain, y the attraction of the 

 Karth on a particle of a unit of mass at the ordinary lc\ 

 the Earth's surface. If there were no mountain the at traction 

 of the Earth on the particle at a distance x from its surface 



would be g-. r- t : we have then to add to this expression 



the attraction exerted by the mountain itself. Suppose the 

 mountain to be of uniform density p, and consider it to be 

 cylindrical in shape, and the particle to be at the centre of its 

 upper surface ; then by Art. 208 the resultant attraction is 



where b is the radius of the cylinder. If b is so large in com- 

 parison with x that the square of r can be neglected, this 



