144 Mr. H. A. Rowland on Magnetic Permeability, 



apply only to endless solenoids, and to those which are very long 

 compared with their diameter. The unit of number of lines of 

 force I have taken as the number in one square metre of a unit 

 field measured perpendicular to their direction. As my data 

 for reducing my results to these units, I have taken the hori- 

 zontal force of the earth's magnetism at Troy as 1*641, and the 

 total force as 6*27. 



The total force, which will most seriously affect my results, 

 is well known to be nearly constant at any one place for long 

 periods of time. 



From the analogy of a magnet to a voltaic battery immersed 



in water I have obtained the following, on the assumption that 



fi is constant, and that the resistance to the lines of force passing 



out into the medium is the same at every point of the bar. 



Let R = resistance to lines of force of one metre of length of 



bar. 



IV = resistance of medium along 1 metre of length of 



bar. 

 Q' = lines of force in bar at any point. 

 Q e = lines of force passing from bar along small dis- 

 tance I. 

 e = base of Napierian system of logarithms. 

 x = distance from one end of helix. 

 b = total length of helix. 

 s' = resistance at end of helix of the rest of bar and 



medium. 

 M= magnetizing- force of helix. 

 We then obtain 



MI 1— A 



ry- erb - 1 M M 1-A , . _, fh . 



(Ae>-»-l)(v/UR' + r 2RAe'-*-l (e +1 e e " 

 in which 



=vi 



and 



A = \/Rg+s' , 



for near the centre of an infinitely long bar, where x>0 and 



* Formulae giving the same distribution as this have been obtained by 

 Biot and also by Green. See Biot's Traiie de Physique, vol. iv. p. 669, 

 and * Essay on the Application of Mathematical Analysis to the Theories 

 of Electricity and Magnetism/ by Green, 17th section. 



