lM EXAMPLES. 



18. tides of a thin hemi- ' attract with 



a force = /u. (distance). bell repel 



with a force =/* (distance). The rims ,f their l.ases coincide, 



and their vertices are turned in opposite dir ihcNV that 



will rest in the common axis produced at a distance. 



from the vertex of the sphere = length of tin axis of the cone, 



ieal angle of the cone being 2 tan" 1 1. 



in. Shew that if the attraction vary inversely as the 

 tance an indefinitely thin plane ring exerts no force on a 

 particle in the plane of the ring within its inner circum- 

 ference. 



[This and the following example depend on the integral 



* + c* 2ac cos 6 ' 

 for which see Integral Calculus, Chapter IV.] 



20. Shew that if the attraction vary inversely as t he dis- 

 tance an indefinitely thin plane ring attracts a particle in the, 

 plane of the ring beyond its outer circumference in the 

 same manner as if the mass of the ring were col 



its centre. 



21. If a straight line be the attracting body, shew that 

 the lines of force are hyperbolas and the , f ,,/ui- 



m spheroids. (Cambridge and Dublin M<itlinatical 

 Journal, Vol. III. p. 94.) 



__. From the proposition established in Art. L'l 1. d 

 that established in Art. 239. (Cambridge and Dublin M<itl- 

 matical Journal, Vol. V. p. 215.) 



