196 Dr. C. Y. Burton on a Theory 



Again, if L, M, N are the effective couples, 



T d ST *3T ^BT 3T BT 

 At B<»i BY 3X o« 2 B« 3 



= {(12?)-(31^)-(i31 7 )}X+K237?)-(22r) + (/32 7 )}Y 



+ {(33»,)-(23£) + ( / 33 y )}Z 

 + (23) Y 2 - (23) Z 2 + { (33) - (22)} YZ - (12)ZX + (31)XY 

 + {(12?)-(lft) + ( a l/3)} ft . 2 X+{(31f)-(lir)-(7l«)}o) 3 X 

 + {(33i 7 )-(230+O37)} a , 1 Y+{(22?)-(23,)-(y32 7 )}6) 1 Z 

 + {(22f)-(33f) + (31^-(12i ? )+(73«) + («2/3)}( <02 Y- , 3 Z) 

 + {2(23f)-(120-(31,) + («3/3)-(72*)}( > 3 Y+ 6 ) 2 Z) 

 + { (22?) + (33^ 2 ) -2(23^)- (£2 7 ?) + (/33y V ) \k 

 + {(23» ) + (81?0 - (88ft) - (12g») - (y2«D + foS-*) 



-0837|) + (/81 7 ?)}ffl 2 

 + {(1217(0 + (23ft) - (22??) - (3ft 2 ) - («2/8J) + («3/ft) 



-(/81 w ) + 082 7 f)}« 3 



+ { («3/8£) - («l/3?) + (yl«,) - ( 7 2«£) + ipj) \ (ui-cof) 

 + {«2/3£> - («l/ft) + (<y3«£> - ( 7 1«?) + (/3 2 ) - ( 7 2 )}*> 2 «>3 

 + {(33ft) + (12? 2 )-(23?|)-(31^) + ( 7 2«?)-( 7 3«,) 



+ ( y 83 7 ?)-( / 81 7 ?)}o) 3 <» 1 

 + {(12^ + (23ft)-(22g)-(3ft 2 )-(«2/30 + («3/ft) 



-Wri + fflyto}*!"* • • (12) 



with similar values for M and N, where, in addition to (11), 

 we have 



£ijK« 2 + A/5 2 + W2h?^^^=(12^?) Ac, "J 



jJj(A7-7i«^^^^(/31 7 ?) Ac., V (13) 



ffi/9y«*«sG9y)Ao. J 



Mr. Gr. H. Bryan has pointed out to me that the equations 

 of motion (10) and (12) are of exactly the same form as those 

 of a solid immersed in a perfect liquid. 



5. If U is the force-function of the impressed forces, we 

 shall have of course 



F _3U P _BU H _BU 

 BX' ^~BY' BZ ' 



