434 ]\Ir. G. B. JeiTard on solving Equations of any degree. 



In the second member of this equation p' denotes the pressure 

 of the air through the second spiral, which would be the atmo- 

 spheric pressure, or excessively near it, if, as in Joule's third 

 experiment mentioned above (described by the author in p. 378 

 of -the volume* containing his paper), the air leaving the second 

 spiral be measured by means of a pneumatic trough : p denotes 

 the pressui'e in the first spiral, which ought to be constant, and 

 must be carefully measured ; v! denotes the volume of air which 

 leaves the apparatus in any time ; and H denotes the quantity 

 of heat emitted in the same time. The experiment might be 

 continued for any length of time, and each one of these four 

 quantities might be determined with great accuracy, so that pro- 

 bably very accurate direct results of observations might be ob- 

 tained. If so, no way of experimenting could be better adapted 

 than this to the determination of Carnot's function, for different 

 temperatures, in terms of Joule's mechanical equivalent of 

 heat. 



LXVIII. On the possibility of solving Equations of any degree 

 however elevated. By G. B. Jerrard, Esq. 



[Continued from vol. iii. p. 460.] 



§5. 



I DO not think it necessary, after what has been already said, 

 to state explicitly the objection to AbeFs inference ; but I 

 cannot dismiss the subject without referring the reader to an 

 admirable disquisition on equations the roots of which have a 

 given relation among themselves in the Memoires de Mathe- 

 matiques of M. Libri. 



We might now return to the general equation of the mih. 

 degree. Before, however, resuming the inquiry with which we 

 set out, I purpose to show how to complete the method, given 

 in my "Mathematical Researches, of transforming equations by 

 means of symmetric functions. This method, which cannot be 

 explained in few words, will form the subject of a separate paper. 



Long Stratton, Norfolk, 

 August 27, 1852. 



Erratum in vol. iii. p. 457, line 37- 

 For will admit read will, when the roots are unequal, admit. The case of 

 jj. eqval roots is not considered by Abel. 



* Phil. Mag. vol. xxvi. 



