248 MR. DAVIES ON TERRESTRIAL MAGNETISM. 



In conclusion of the present paper I shall, though I have not been able to decom- 

 pose the equation which results from {77-) and (78.) into factors, yet hazard the con- 

 jecture of its being even in its literal form capable of such a resolution ; so that the 

 component equations are, when viewed simultaneously, the one essentially imaginary 

 with the values which render the other real. Of course these must be into factors of 

 even degrees, — probably two of the fourth and one of the second. Several instances 

 of this kind are well known to geometers ; a very remarkable one of which is the 

 expression given by M.Bret for the determination of the foci of a line of the second 

 order, in Gergonne's Annales des Math4matiques, tom. viii. I offer it, however, only 

 as a conjecture, which future researches may show, after all, to be too hastily made. 



Royal Military Academy, Woolwich, 

 December 16, 1834. 



