Proceedings of the British Association. 87 



vations, the magnetic direction and intensity, in high southern latitudes, 

 between the meridians of New Holland and Cape Horn. 



The successful result of the exertions of the Committee, and the ad- 

 mirable Report drawn out by the Royal Society, for the guidance and 

 instruction of the officers engaged in the expedition, and which we so 

 lately published (Athen. Nos. 616, 617), have so far anticipated the in- 

 terest which would otherwise have attached to this paper, that we are 

 reluctantly compelled, in the present crowded state of our columns, to 

 pass it over. 



' On certain Points in the Wave-Theory, as connected with Elliptic 

 Polarization, &c.' by Prof. Powell. — The object of this communication is 

 to lay before the Section a general statement of some material condi- 

 tions which involve in a common relation the theory of dispersion, of 

 the wave-surface, and of elliptic polarization. These have been the 

 subject of some difference of opinion, and are still involved in consi- 

 derable difficulty and apparent contradiction ; a brief and clear state- 

 ment of those points may, perhaps, tend to their better elucidation and 

 ultimate solution. All the investigations set out from these equations 

 of motion : — 



H , (j,( r ) a£ 



i — 2 



\ + \f,( r ) A*[A*A£+A2/Ar,+A.*A£] 



d\ r <p(r) At} 



(A) 1 1* - 2 \ +Xt(r) A*[ ] 



[ «fta ^t +#•)£*[ ] 



By certain developements of A£ A>j A£, these forms involve as 

 factors of products such as 



2 ty(»-)A*Ay] Sfc. 



If these sums are =o, the expressions are brought into forms in 

 which they are directly integrable, and we have for solutions :— 



s = 2 [a sin (nt — kp) 



V = 2 [fi s in (nt—kp) 



t — 2 [y sin (nt—kp) 

 which are shown to involve such a relation between n and k, as gives the 

 formula for the dispersion. 



This condition, which I call (B), reduces the equation (A) to the 

 form — 



f d 2 £ 



(O ^ =2 {^)+^)^AS} 



| &c. = &c. 



^ &c. == &c. 



And it corresponds to the supposition that the molecules are so arranged 

 with respect to the axes x y z, that the sums with opposite signs destroy 



