96 



Prof. Moseley on the Application of the Principle 



XP (y cos a — x cos /3) -f N, = "| 



2P \x cosy — z cos a) -f- N 2 = V 



£P (z cos fa — y cos y) + N 3 = 0. J 



7/, = 

 2* 2 = 

 "3= 



&c. = 0. 



(2.) 

 (3.) 



(4.) 



Cos 9 a t -f cos 2 /3, + cos 2 y x — 1 



Cos 9 a 2 + cos 9 /3, + cos 2 y 2 = 1 



Cos 9 a 3 + cos 2 /3 3 -f cos 9 y 3 = 1 

 &c. = 1. 



Differentiating with respect to x x y x z v x 2 y 2 z 2 , & c, > tne res i st ~ 

 ances of the system being considered functions of these quan- 

 tities both in respect to their magnitude and direction, we 

 obtain 



fdP . dP dP k D . t 1 > 



< -j- cosa§ t r+— cos a 83/ + -7- cosaSs — P sin a8a V = 



rf^cbi s |8ti+j? cos/38j/ + ^cos/382--Psin/38/3 j = o|(l'.) 



{^ cos r^ + ^ cosy8j/ + ^ cos y8z-Psiny8yj = o) 



"I j— ( j/ cos a— t r cos /3) 8 ,r + -7— (y cos a— .r cos (S) 83/ 



JP 

 4- 7— {y cos a— .r cos /3) 8z + P cos a 8^ 



— P cos/3 8#-Pj/sina$a-f P.r sin/3 8/3 j = 



E J r- (.rcosy — * cos a) 8.r+ v (#cosy — z cos a) 83/ 



<ZP 

 -j-j- (.rcosy — 2 cos a) 8 z -f P cos y8.r S(2'.) 



— P cos a 8 z— Pa: sin y8y+Pz sin«8a V =0 



x \ die ( z co *P-y cos y^ Zx+( dy ( * cos $~y cos i) s ^ 



+ ^- (« cos/3— 3/ cosy)8y + P cos/38z 

 -Pcos y8#— Pzsin /38/3-f P,*y siny8y| = 



