268 Mr. J. Parker on the Theory of Magnetism and 



f =?=! = p=x'(r.p,*), • • • (6) 



where %' is always positive. 



Now let the air be mapped out by equipotential surfaces 

 and lines of force, just as in electrostatics, and imagine a 

 small right circular cylinder described in the air with its ends 

 at right angles to the axis and the radius of its normal section 

 very small in comparison with the length of the axis. Then, 

 by taking the axis of the cylinder tangential to an equi- 

 potential surface, it is easily seen that the pressure and density 

 of the air have constant values all over the same equipotential 

 surface. If the axis coincide with a line of force, and we 

 suppose ourselves to travel in the direction of the force, we 

 obtain, since the force exerted at any point by the neigh- 

 bouring molecules is zero, 



dp=I- r -ds=V— -r-ds, 

 as p Q as 



or, if we assume the simple law of gases, p = ~Rp0, where R is 

 a constant for the same gas, 



„pdF 



dp = I 1 — -— - ds, 

 r p Q ds 



or 







dp 



_ 1'dF 



ds. 







P 



p Q ds 





Integrating 



this 



equation, we get 









log£- 2 = 

 8 P. 



If 2 1 



d¥. 



—rds 



as 



Now it is usually assumed that for the feebly magnetic 



substances, the positive quantity ^ is practically constant, 



and its value is written k. We have then, in a homogeneous 



dY 

 soft body (liquid or solid), A=&X=— &— , &c. &c, so that 



if p be the volume-density of the magnetism in the interior 

 of the body, 



" \dx dy dz ) 

 Hence, since V 2 V= — 4tt/o, we have 



p(l+47T&) = 0, 



and therefore p = 0, or the body is magnetically equivalent to 

 a layer of magnetism on the surface. 



