Mr. E. J. Lowe on a remarJcable Solar PJKjenomenon. 437 



I feel some doubt as to another portion of Mr. Jerrard's ar- 

 gument. At all events I think it would be very desirable to 

 show clearly the solvibility of the equation by which W is to 

 be determined. It is true that one of its roots appears to be 

 a known and rational function of another of them, and that an 

 equation among whose roots such a relation exists is supposed 

 to be capable of solution by means of the process of Abel. 

 But doubts — and doubts apparently well-founded — have arisen 

 respecting the universality of that theorem. It is not my 

 object to discuss them here ; but I would refer the reader to 

 the learned paper on the Calculus of Functions in the Ency- 

 clopedia Metropolitana^ where, at pp. 327, 328, art. (90.), and 

 at pp. 381, 382, arts. (302.) and (303.) of vol. ii. of the Pure 

 Sciences, he will find remarks upon this question ; and I 

 would also call attention to the respective notes to arts. (90.) 

 and (303.) just adverted to. There, the nature of the difficulty 

 which militates against the generality of the theorem — a diffi- 

 culty which, in the instance of functions of a degree so low as 

 the third, is only obviated by our having complete solution of 

 a cubic — is clearly exhibited. 



Standing on the frontiers which separate solvible equations 

 from those as yet unsolved, the biquadratic partakes of the 

 nature of both. It resembles the one inasmuch as it is capable 

 of finite algebraic solution; the other, in its incapability of 

 finite algebraic solution in terms of irreducible biquadratic 

 surds. The latter characteristic might perhaps be of ser- 

 vice in the discussion of equations of the fifth degree, and 

 in the manner which I suggested in my First Series of Notes 

 on the Theory of Algebraic Equations, published in vol. xlvi. 

 of the Mechanics' Magazine. The reader is referred to p. 125 

 of that volume, and to the condition mentioned at a subsequent 

 page (180) of it. 



2 Church -Yard Court, Temple, 

 November 1, 1849. 



LTII. Remarkable Solar PJiocnomenon seen at the Villa, 

 Beeston near Nottingham, October 22, 1 849. By Edward 

 Joseph Lowe, Esq., F.Il.A.S.* 



/^N the above day a strange spectacle presented itself about 

 ^-^ the sun. The morning had been misty, and had cleared 

 up about 22^^; but being engaged with some papers I did 

 not look at the sun until 0^ 10™, when a remarkable phae- 

 nomenon was immediately discovered: it resembled a huge 



* Cominunicated by the Author. 



