240 Mr. G. A\'. Walker on the 



It is next proved, somewhat doubtfully, that 



'be -dO ~ be ~^ be 

 be - be ~ ' 



and hence, i£ the couple due to the fibre is F^, we get 



F^=||'(V.-V0^V3-i(Vi + V,)|. . . (3) 



In the aboA'e process no exception can be taken to (1) and 

 (2) ; but in the remaining part of the proof the values of 

 the differential coefficients are calculated for ^ = 0. 



This is not valid. Formula (2) is onlj true provided the 

 quantities are reckoned for the displaced position. 



In what follows I shall assume perfect symmetry of the 

 arrangements. 



Let Cii = «o + ^r««^". 



where ao etc. are constants independent of e. 

 Then by symmetry we obtain 



Again, let 



c,,=h,+i'?Ke-, 



the condition of symmetry gives us 



C23 = ?>0 + 2r(-)"M". 



Further_, it is clear that Ci2 and C33 must be even functions 

 of e. Hence let us take 



C12 -^- C[s ~r .^1 Com^' 

 C33=4 + Sr^2,n^^"^ 



It is clear, since the zero of potential is arbitrary, that an 

 equal increase in each of the potentials must leave the force 

 unchanged. 



We thus get from formula (2) 



be '^ be '^be ~^ i 



^^22 0£23 bci2 _ /^ ' (A\ 



be ^ be '^ be ~^ I ^ ^ 



^£3:^ bcu bc2B _^ \ 



be '^^be '^ be ^^ 



