PROGRESS OF MAGNETIC THEORY. 23 



tive amount of magnetism at several points of a needle, 9 and the 

 proposition that the directive force of the earth on similar needles satu- 

 rated with magnetism, was as the cube of their dimensions ; conclusions 

 which agreed with experiment. 



The agreement thus obtained was sufficient to give a great probabi- 

 lity 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 labors of the original theorist. These requi- 

 sites, 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, the thickness of 

 the fluid in the direction of the radius would be as the distance from 

 the centre. 10 But the subject w r as taken up in a more complete man- 

 ner in 1824 by M. Poisson, who obtained general expressions for the 

 attractions or repulsions of a body of any form whatever, magnetized 

 by influence, upon a given point ; and in the case of spherical bodies 

 was able completely to solve the equations which determine these 

 forces. 11 



Previously to these theoretical investigations, Mr. Barlow had made 

 a series of experiments on the effect of an iron sphere upon a compass 

 needle ; and had obtained empirical formulas for the amount of the 

 deviation of the needle, according to its dependence upon the position 

 and magnitude of the sphere. He afterwards deduced the same for- 

 mula? from a theory w r hich was, in fact, identical with that of Coulomb, 

 but which he considered as different, in that it supposed the magnetic 

 fluids to be entirely collected at the surface of the sphere. He had 

 indeed found, by experiment, that the surface was the only part in 

 which there was any sensible magnetism; and that a thin shell of iron 

 would produce the same effect as a solid ball of the same diameter. 



But this Avas, in fact, a most complete verification of Coulomb's 

 theory. For though that theory did not suppose the magnetism to be 

 collected solely at the surface, as Mr. Barlow found it, it followed from 

 the theory, that the sensible magnetic intensity assumed the same dis- 

 tribution (namely, a surface distribution,) as if the fluids could per- 

 meate the whole body, instead of the " magnetic elements" only. Cou- 

 lomb, indeed, had not expressly noticed the result, that the sensible 



' p. 435. 10 Bull dcs Sc. Xo. li. " A. P. for 1S21 and 2, published 1S26. 



