Royal Society. 149 



For since, in accordance with what has been already stated, 

 we are permitted to assume 



[/WP [/(OP [/(' 3 )1 5 L/W] 6 =k, • • • ftj 



K being a root of an Abelian equation, (ej) will take the form 



\/jL = L-{-\uv (e lt e 2 ) 



8. We might, indeed, without considering at all the ground of 

 M. Hermite's argument, have inferred, from the very enunciation 

 of the result at which he had arrived, that an error must some- 

 where have crept into his processes. How, in effect, can we 

 reconcile such a result with the possibility of solving binomial 

 equations of the fifth degree, not to speak of any other class of 

 solvable equations of that degree into the expressions for whose 

 roots irreducible radicals of the form \/z enter ? But I thought 

 that it was due to a mathematician so eminent to trace his error 

 to its source. Trusting implicitly in the theory of Lagrange, 

 M. Hermite was led, as we have seen, to suppose that in the 

 equation (e 1} e 9 ) the function designated by \/TL would be gene- 

 rally expressible in rational terms of K. What a confirmation is 

 here of the truth of the solution given in my ' Essay ' ! 



December 1861. 



XXI. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 79. ] 



April 18, 1861. — Major-General Sabine, E.A., Treasurer and Vice- 

 President, in the Chair. 



nPIIE following communication was read: — 



■*■ "On the Effect produced on the Deviation of the Compass by 

 the Length and Arrangement of the Compass Needles ; and on a 

 New Mode of correcting the Quadrantal Deviation." By Archibald 

 Smith, Esq., M.A., F.ll.S. ; and Frederick John Evans, Esq., R.N. 



When the length of the compass needle may be neglected com- 

 pared with the distance of the iron which acts on a ship's compass, 

 the deviation is accurately expressed by the formula 



sin 2=A cos o + B sin £' + C cos £' + D sin (£+£')+E cos (£+£') ; 

 in which £ is the azimuth of the ship's head measured eastward from 

 the correct magnetic north ; 



£' is the same azimuth, but measured from the direction of the 

 disturbed needle ; 



<) = £—£' is the easterly deviation of the needle; 



A, D, E are coefficients depending on the distribution of the soft 

 iron of the ship. 



