18 i". 



ptinadi] 



}". '/. : 'ng r>n the parti< '. 



,llcl to throe rectangular ; IUHYC of the 



: of tin- o.t in 



etion normal to tin- su I the 

 particle is sit; did not, ;,t decoi: 



forces, ono in t :il and our at ri 



normal, of which the 1 ild set the p 



of the angles which the. resulta: 



A". )". /. mak< I with the axes arc propnriionnl to A". )", /, 



respectively; and if /',./'. j/ t -) = be the (Mpiati.n to the 



oaines of the angles which the normal to the 



point (j*, y, z] makes with the axes, u 



Analytical (Ir..inctry of tliree dimensions proportional to 



i W c i f !! 



- , and -r respectively. Hence for equilibrium we 



must have 



V Y 



If these relations are satisfied, the resultant force is di. 

 along the normal; hence, if we suppose the particle incapable 



vin;_r the surface, the above conditions will ! 

 to ensure its equilibrium; but if the particle be merely p 

 on a surface, it will be further nee, A'. )'. '/. -hould 



act so that their resultant may press the parti-- H f/n> 



xanijilc. if the j.artic.le lie placed on the outside 

 of a sphere, the resultant of A', V, and /, must a- h the 



centre of the 



required to determine the act; . the. 



or tne surface exerts on in the preceding 



cases. Denote it by 11. and let 7, ft. 7 be the angles 



H with the axes. :id the forces A", 



itain the particle in equilibrium, we L \rt. k J7, 



sa + A' = 



