Mr. G. B. Jerrard on solving Equations of any degree. 457 



All these facts, and many others which could be adduced, seem 

 to render it highly probable, if not to prove, that the peculiar 

 sparks and shocks occasioned by voltaic series are caused by an 

 agent of a different nature from that which produces ordinary 

 electrical phsenomena. And further, reasons in my opinion suf- 

 ficient, have been assigned for doubting the force of the evidence 

 derived from the so-called immediate charge of a Ley den battery 

 by a voltaic series, as proving the vast quantity of electricity 

 which constitutes the voltaic current, and the identity of the 

 agent in all electrical and voltaic phenomena. 

 [To be continued.] 



LXIV. On the possibility of solving Equations of any degree how- 

 ever elevated. By G. B. Jerrard, Esq* 



§1. 



THERE is little difficulty in the theory of the solution of 

 equations beyond those of the fifth degree. By following 

 a method analogous to the one which, in No. 45 of my " Reflec- 

 tions on the Resolution of Algebraic Equations of the Fifth De- 

 gree t," brought us to a class of equations solved by Abel, we 

 should always in our progress find ourselves conducted to a cor- 

 responding class of solvable equations of degrees more and more 

 elevated. Various other methods, all leading to the same con- 

 clusion, might here be readily pointed out. But I am constrained, 

 in the first place, to turn my attention to the particular classes 

 of equations just alluded to, in order to consider an objection 

 which, by some eminent mathematicians of the present day, is 

 supposed to affect the validity of the method of solution given 

 by Abel. 



§2. 



Passing to the 3rd section of Abel's Memoire sur une classe 

 particuliere d' Equations resolubles algebriquement% (for it is 

 against the process contained in this part of his memoir that the 

 objection is mainly directed), we there find that illustrious ma- 

 thematician maintaining that every equation of the /ith degree, 

 <f>x = 0, the roots of which may be expressed by 



x v 6x v 6*x v . . fl'-'ari, 



wherein 6x x designates a rational function of a?„ will admit of 

 being solved algebraically. 



* Communicated by the Author. 



t See this Journal for June 1846, vol. xxvi. p. 5/3. 



j Crell'8 Journal, vol. iv. 



