38 HENRY A. EOWLAND 



of magnetism is the same as that of the flow of heat in a solid, as the 

 static induction of electricity, and as the flow of a frictionless incom- 

 pressible liquid through a porous solid. It is evident that to these 

 analogies we may add that of the conduction of electricity. 7 We readily 

 see that the reason of the treatment being the same in each case is that 

 the elementary law of each is similar to Ohm's law. Mr. Webb 8 has 

 shown that this law is useful in electrostatics; and I hope, in a sequel 

 to this paper, to apply it to the distribution of magnetism: I give two 

 equations derived in this way further on. 



The absolute units to which I have reduced my results are those in 

 which the metre, gramme, and second are the fundamental units. The 

 unit of magnetizing-force of helix I have taken as that of one turn 

 of wire carrying the unit current per metre of length of helix, and is 

 4?r times the unit magnetic field. This is convenient in practice, and 

 also because in the mathematical solution of problems in electrodynam- 

 ics the magnetizing-force of a solenoid naturally comes out in this unit. 

 The magnetizing-force of any helix is reduced to this unit by multiply- 

 ing the strength of current in absolute units by the number of coils in 

 the helix per metre of length. These remarks apply only to endless 

 solenoids, and to those which are very long compared with their diam- 

 eter. 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 horizontal 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 // 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. 

 E' = resistance of medium along 1 metre of length of bar. 

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

 Q f = lines of force passing from bar along small distance I. 

 e =base of Napierian system of logarithms. 

 x = distance from one end of helix. 



1 Maxwell's 'Treatise on Electricity and Magnetism,' arts. 243, 244 and 245. 

 s "Application of Ohm's Law to Problems in Electrostatics," Phil. Mag. S. 4, vol. 

 xxxv, p. 325 (188). 



