concerning the Constitution of Matter. 



195 



Substituting these values in (8), and again using (5) and (6), 

 we obtain 



/=— aiX — a 2 Y — a 3 Z + G) 1 (a 2 f— a 3 7?) + G> 2 (a 3 f — a^ + y) 

 Similarly + ®b(«i* -««£-£)■ 



and +®3 (£i*7 -&? + *), 



^ (9) 



A = - 7 X X - 7 2 Y - y 3 Z + ft)i(7 2 ? - 7s 7 ? + £) + ®«(73f — yi?— «) 



* + <w 3 (7i 7 ? — 72?). 



If these values are substituted in (4) , we obtain immediatel y 

 a complete expression for the energy due to the motion of the 



strain-fig are j and this expression involves only X, Y, Z, 

 o) 1; (o 2 , co 3, and quantities which remain constant throughout 

 the motion. We may therefore apply the principle of moving 

 axes to find the components F, Q, H of effective force on the 

 strain-figure ; thus 



™_ d bT bT BT 



dt ^X dY BZ 



which by means of (4) and (9) becomes 

 F=(ll)X+.(12)Y+(3i)Z 



- (12> 3 X - (22> S Y - (23> 3 Z 

 + (31)a> 2 X + (23)a> 2 Y + (33)co 2 Z 

 + {(3l7 7 )-(12?) + (/31 r )}a) 1 + {(ll?)-(31?) + (7l«)}© 2 



+ {(12f)-(ll^) + (al/3)}a;3 



+ {(3l?)-(33|) + (73 a )}a) 2 2 + {(127;)-(22|)-(a2^)}a) 3 2 



+ {2(23?)-(120-(3l7 7 ) + ( a 3/3)-( r 2«)}a) 2 a> 3 

 + { (22?) - (23i?) + (£2y) }»,(», + {(33r,) - (23£) + OS&y)}*^, (10) 

 with similar values for G and H ; where we write 

 jjj(V + ^ 2 + 7i 2 ) df^Mfs (11), to, 

 j5J («»•, + Aft + w») #4»«*C= (23) = (32), to., 

 JjJ (« 2 « 3 + && + 727s)? d? A? #= (23?) = (32& to, 

 §J G8.7-7U8) <Z? A| «*S = (/3l7) = - (7l/8), to. j 



>» (11) 



