EECENT PROGRESS IN" THEORETICAL PHYSICS. 211 



A, B, and C, represent the intensities of the magnetization, along 

 the thren co-ordinate axes; and 



?, m, n, are the direction-cosines with reference to these axes, o£ 

 a normal to the surface. 



6 is often called, as was said beiore, the surface-density of the 

 magnetic matter; and 



9 = interior-density of magnetic matter; — 9 is also 



d A d B d C\ 

 'd^'^'d^'^'dij "^ ^' 



when the magnetization is soJenoidal. 



Now, since A, B, C, are the components of the magnetization of the 

 magnet, if we take a quantity T such that 



ax ay dz ' 



then, also, as was said before, I may be called the potential of mag- 

 netization, and it is evident that when the magnetization is sole- 

 noidal, we shall here also have the condition 



dx^ ^ dif ^ dz 2 



as in the case given above, [Equation (M)], of the velocity potetdial 

 of fluid flow. 



Hence the velocities u, v, w, in the case of fluid flow in incompres- 

 sible fluids, are the analogues of the electric and magnetic 

 forces in free space, and of the components of magnetization in the 

 case of solenoidal magnets. At least, all three sets of quantities 

 are subject to the same analytical conditions. I the Potential of 

 Magnetization gives, 



dn_ dn_ _^ ^ 



~dx2 ^ dy^ ' (^z2' = ^- 



Q, the Velocity Potential of an incompressible fluid, gives 



dQ , d'Q , dW 



— ^+ — — + — — == 



dx' dy^ dz^ ^• 



V, the electric potential gives 



d-V . d^V . d'^V 

 + — - + — == 



dx"^ dy^ dz"^ 



In magnetic and electric distributions, the rate at which V varies 

 along a line, determines the electric or magnetic force in free space 

 along that line. 



