194 Prof. E. Bouty's Studies on Magnetism. 



o 



Tnese factors reduce to 2\- g and Aa 2 respectively for very 



high values of X. 



On the other hand, the ordinate y of a curve may always be 

 regarded as the product of the angular coefficient of the tangent 

 at the point considered, into the difference of the abscissa 2\ and 

 the abscissa at the origin of the tangent. From these principles 

 the magnetic moment of the needle considered is represented by 

 the product of the two factors 



2 e^-e-P* " 



A^[l"(^x) 2 ] 



(8) 



2 



These factors, like the preceding, reduce to 2\-— -5 and A a 2 



for very high values of X. Hence it is that we have before em- 

 ployed the asymptote for determining the polar distance of long 

 needles ; but this cannot be extended to the tangents, as I at 

 first expected, since the expressions (8) differ from expressions 



2 

 (6) and (7) by the variable factor 1 + -^ _ px . The method 



which has served us for the determination of the magnetic mo- 

 ments cannot, therefore, enlighten us on the independent varia- 

 tion of the two factors on which they depend. 



3. Breaking of non-saturated Needles perpendicular to the axis. 



A. Regular needles. — 'When a needle is magnetized regularly 

 without being saturated, a sufficient length of its extremities can 

 be removed, and then the middle portion can be treated like that 

 thus taken from a saturated needle. 



A characteristic curve is obtained tangent to the axis of w at the 

 origin, and presenting an asymptote the curve of which converges 

 rapidly. The semiabscissa at the origin of this asymptote is the 

 distance of the poles of long rupture-needles (obtained by break- 

 ing) from their extremities*. This distance is therefore constant 

 in rupture-needles as in saturated needles. Moreover two cases 

 are to be distinguished : — 



I. When the needles are thin (0*175 to 0*551 millim. dia- 

 meter) the distance of the poles from the extremities of rupture- 

 needles depends only on the diameter, and is the same as in satu- 

 * Demonstration the same as for saturated needles. 



