Mr. II. A. Rowland on Magnetic Distribution. 271 



and the vertical ordinates are values of Q' e . The full line 

 gives the observed distribution, and the dotted line that accord- 

 ing- to the formula. 



The formula gives the distribution very nearly for all points 

 except those near the end. The formula indicates that Q' e de- 

 creases continually toward the end ; but by experiment we see 

 that it increases near this point. On first seeing this, I thought 

 that it was due to some residual magnetism in the bar ; but after 

 repeating the experiment several times with proper care, I soon 

 found that this was always the case. I give the following ex- 

 planation of it : — In the formulae we have assumed W, the re- 

 sistance of the medium, to be a constant; now this resistance 

 includes that of the lines of force as they pass from the rod 

 through the medium and thus back to the other end of the rod ; 

 and of this whole quantity the part which affects the relative 

 distribution at any part of the rod most is that of the medium 

 immediately surrounding that part ; and so the parts near the 

 end have the advantage over those further back, inasmuch as the 

 lines can pass forward as well as outward into the medium. 

 The same thing takes place in the case of the distribution of 

 electricity, where the " density " is inversely proportional to the 

 resistance which the lines of inductive force experience from the 

 medium ; and here we find that the (< density " is greatest on 

 the projections of the body, showing that the resistance to the 

 lines of induction is less in such situations, and by analogy 

 showing that this must also be the case for lines of magnetic 

 force. But this effect is not very great in cylinders until quite 

 near the end ; for Coulomb, in a long electrified cylinder, has 

 found the density at one diameter back from the end only 1*25 

 times that at the centre ; and so there is probably a long distance 

 in the centre where the density is sensibly constant. Hence we 

 may suppose that our second hypothesis, that R' is a constant, 

 will be approximately correct for all parts of a bar except the 

 ends, though of course this will vary to some extent with the 

 distribution of the lines in the medium ; at least the change 

 in R' will be gradual except near the end, and so may be par- 

 tially allowed for by giving a mean value to r. 



Hence we see that could the formula be so changed as to in- 

 clude both the variation of R and of R', it would probably agree 

 with the three Tables given. 



To study the effect of variation in the permeability more care- 

 fully, we can proceed in another manner, and use the formula!; 

 only to get the value of r at different parts of the rods. 



No matter how r may vary, equations (2) and (3) will apply 

 to a very small distance I along the rod; and as the origin of 

 coordinates may be at any point on the rod, if Q' and Q' e are 



