454 H. A. Rowland—sStudies on Magnetic Distribution. 
The horizontal line in the figure represents values of L, 
and the vertical ordinates are values cf Q’e. e 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 continully 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 formule we have assumed R’, the re- 
sistance of the medium, to be a constant; now this resistance 
edium: 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 1:20 
_times that at the center, and so there is probably a long distance 
in the center 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’ wil radual except near the end, and so may be par- 
tially allowed for by giving a mean value to 7. : 
ence we see that could the formula be so changed as to 10- 
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 
the formule 
. 
_ fully, we can proceed in another manner, an 
only to get the value of r at different parts of the rods. 
No matter how r may vary, equations (2) and (8) will apply 
to a very small distance / slong the rod; and as the origin of 
ordinates may be at any point on the rod, if Q’ and Q’e are 
