PROGRESS OF MAGNETIC THEORY. 59 



magnetism appears only towards the extremities of 

 the body, as it would do if the fluids could permeate 

 the body freely. We shall have exactly the same 

 result, as to sensible magnetic force, on the one 

 supposition and on the other, as Coulomb showed 7 . 



The theory, thus freed from manifest incongrui- 

 ties, was to be reduced to calculation, and com- 

 pared with theory; this was done in Coulomb's 

 Seventh Memoir 8 . The difficulties of calculation in 

 this, as in the electric problem, could not be entirely 

 surmounted by the analysis of Coulomb; but by 

 various artifices, he obtained theoretically the rela- 

 tive amount of magnetism at several points of a 

 needle 9 , and the proposition that the directive force 

 of the earth on similar needles saturated with mag- 

 netism, was as the cube of their dimensions ; con- 

 clusions which agreed with experiment. 



The agreement thus obtained was sufficient to 

 give a great probability to the theory; but an 

 improvement of the methods of calculation, and a 

 repetition of experiments, was, in this as in other 

 cases, desirable, as a confirmation of the labours of 

 the original theorist. These requisites, in the course 

 of time, were supplied. The researches of Laplace 

 and Legendre on the figure of the earth had (as we 

 have already stated,) introduced some very peculiar 

 analytical artifices, applicable to the attractions of 

 spheroids ; and these methods were employed by M. 

 Biot in 1811, to show that on an elliptical spheroid, 



7 Mem. A. P. p. 492. s A. P. 1789. 9 p. 485. 



