S!99 



the advantage of the method of deflection recently proposed 

 by Professor Lauiont, in which \p = 90°, or the deflecting bar 

 perpendicular to the suspended bar. 



In the ordinary method, ./- = 90° — u ; and, the moment 

 of the force exerted by the earth being xM'sinw, where x de- 

 notes the horizontal component of the earth's magnetic force, 

 the equation of equiUbrium is 



2m S 1 /.^Ma oMa' . ,- . o Ma'N I > 

 tanuzz — ^—3 + [2— — 3-~ + \5sm^u-4 ) —^l . 



X (. D^ \ U M' m' / d'' > 



The angle of deflection, u, being small, the term involving 

 the square of its sine may be neglected, in comparison with 

 the others ; and the equation assumes the form already ad- 

 verted to, namely, 



tan« = -3(^H--,j; 

 in which we have made, for abridgment, 



X MM 



In order to apply this result, we must know, at least ap- 

 proximately, the law of magnetic distribution, or the function 

 of »• by which m is represented. Almost the only knowledge 

 which we possess on this subject is that derived from the 

 researches of Coulomb. From these researches M. Biot has 

 inferred, that the quantity of free magnetism, in each point 

 of a bar magnetized by the method of double touch, may be 

 represented by the formula 



fx being a quantity independent of the length of the magnet, 

 and A a function of yu and I. M. Biot has further shown, that 

 when the length of the magnet is small, the relation between 

 tn and r is approximately expressed by the simple formula 



_ ,r 

 m =: »» T- ; 



