150 Mr. E. H. M. Bosanquet on 



Force, to emphasize the analogy with electromotive force. 

 Intensity is the same as Magnetic Induction, or lines of force 

 per unit area, and is represented by t$. 



We will first consider what I have called the linear range ; 

 that is to say, the case of cylinders whose length does not 

 exceed ten times their radius, including thin disks. 



We suppose the steel to have a difference of magnetic 

 potential imbedded in it per unit of length, corresponding to 

 the values observed. 



4?rM 



Potential per unit length = - 2- = P 7 , 



& IX area 



and 



Potential of length x — Y'x> 



Now within the linear range t$ = B^ say, where B' is the 

 coefficient given at (1), 



.'. Magnetic resistance = m 



and is constant within the linear range. 



Further, by (1) the value of W is 



I 



4ttM 



.'. Magnetic resistance = l ® = , 4<7rM ° , 



i 



which is the same as the value of F (2). 



It is at once apparent that this must be so. For the resist- 

 ance is the altitude of a cylinder which would have the same 

 resistance as the actual distribution; and in the case of the disk 

 this is the same as the distance between the points of appli- 

 cation of the resultants of the lines of force. 



Hence the magnetic resistance throughout the linear range 

 is constant: it is nearly three fourths of the radius in A and B, 

 and about two thirds of the radius in C. This is nearly 

 equal to the resistance at one end of an open organ-pipe. If 

 we could arrive at this independently by an extension of 

 reasoning such as that employed in connexion with the open 

 ends of organ-pipes, we could found the whole theory upon it. 

 As it is, the admission of this law throws some light on the 

 laws of the linear range. 



For let P' be the potential per unit length, and p the 



