254 Prof. C. Niven on the Theory of an 



"d 2 ^2, d 2 ^3j where 



^ (d 1 d 2 \ x0 (d 2 t d 2 \ i (d? d 2 \ na . 



The acceleration in any other definite direction is obviously 

 d'^W 1 , where ot 1 is the component rotation in that direction. 

 Consequently the component accelerations along the original 



axes are 



where 



B 2 ^l, "d 2/ &2> B 2 ^3> 



^2 d 2 , , d 2 , d 2 , 



+ 2/, 





(17) 



some quadratic function of -y-> ^-? ^-« 



doc dy dz 



Adding these terms to the equations (10), the equations of 

 motion of the solid now become 





c^-2c 





1 dx 

 d 2 w_ 9 odvr l 

 dt ~ ^ 



^-2a?^P+B 



dz 

 1 dx 



(18) 



I shall return to the solution of these in art. (12), and in the 

 mean time proceed to the discussion of the 



Terms of Class (I., IV.). 

 10. There is no reason a priori why the group m\ , ta^, vr should 

 not appear in the expression for the energy of the solid ; for 

 they correspond to a real strain of it. This species of strain 

 may be easily analyzed geometrically, and has some interest- 

 ing properties, especially in an isotropic homogeneous solid. 

 Let us pass, however, to the expression for the energy depend- 

 ing on these terms, which must be of the form 



f v { OT ;(N n A + N 12 B+ ... + N 16 F) + <(N 21 A+ ... +N*F) 



+ w ;(N 31 A+... + N 36 F)}. 

 d 2 d 



The value of 



di- 



(*„*+,..+* 



which corresponds to it is clearly 



(P \ , . /« (P . . M cP \ , 



d4V' + ( N -£ + - + 



