Prof. E. Bouty's Studies on Magnetism. 

 Table V. — Power of the Poles. 



193 



d. 



C 



d 2 ' 



B. 



r. 



millim. 









0175 



58719 



+3094 



0055 



0-282 



51-558 



-4-067 



0073 



0-368 



55 531 



-0094 



0002 



551 



56695 



+ 1070 



0019 



In short, experiment confirms in a very remarkable manner 

 the various laws contained in Green's formula, except in the case 

 of excessively short needles. It follows that, with the exception 

 mentioned, the distribution of free magnetism in the needles is 

 also represented by the formula given for it by Green, of which 

 our formula is a consequence*. The quantity of free magnetism 

 in a section perpendicular to the axis, of thickness dx t situated 

 at a distance x from the middle, is, according to that formula, 



Aa*/3 



e& x —e~P x 



(5) 



\ being half the length of the needle. This formula is equiva- 

 lent to Biotas, and faithfully represents the results of Coulomb's 

 experiments. 



Poles of short needles. — The magnetic moment of a needle can 

 always be considered as the product of two factors, one of which 

 represents the distance of the poles, the other the quantity of 

 magnetism of each of them. According to Green's formula, the 

 distance of the poles is 



2 e^-e-^ 



-o > ( 6 ) 



D = 



1- 



e 0* + c -0A 



and the other factor 



* -*>(*- ;*£=*)■ 



(7) 



* The pole is defined as the projection of the centre of gravity of the 

 curve of distribution 



a i^ x — e~P* 

 r=Aa 2 /3— 



eP^-\-e~ P* 



on the magnetic axis of the needle. The distance D of the two poles has 

 been calculated according to this definition. 



Phil. Mag. S. 4. Vol. 49. No. 324. March 1875. O 



