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may be drawn, which, with the two former systems of surfaces, 

 divides the medium into cells, in each of which the same amount of 

 work is done in overcoming resistance. It is then shown that if the 

 fluid be supposed to emanate from certain centres, and to be absorbed 

 at others, the position of these centres can be found when the pres- 

 sure at any point is known ; and that when the centres are known, 

 the distribution of pressures may be found. Methods are then given 

 by which the motion of the fluid out of one medium into another, 

 the resistance of which is different, may be conceived and calculated, 

 and the theory of motion in a medium in which the resistance is 

 different in different directions is stated. 



The mathematical ideas obtained from the fluid are then applied 

 to various parts of electrical science. It is shown that the expres- 

 sion for the electrical potential at any point is identical with that of 

 the pressure in the fluid, provided that "sources" of fluid are put 

 instead of positive electrical "matter," and centres of absorption or 

 " sinks" for negative " matter." 



The theory of Faraday with respect to the effect of dielectrics in 

 modifying electric induction, is illustrated by the case of different 

 media having different conducting power ; and it is shown, that, in 

 order to calculate the effects by the ordinary formulae of attractions, 

 we must alter in a certain proportion the quantities of electricity 

 within the dielectric, and conceive an imaginary distribution of elec- 

 tricity over the surface which separates it from the surrounding 

 medium. 



The theory of magnets and of the phenomena of paramagnetic 

 and diamagnetic bodies is expressed with reference to the " lines of 

 inductive magnetic action;" and elementary proofs of the tendency 

 of paramagnetic bodies toward places of stronger magnetic action, 

 and of diamagnetic bodies toward places of weaker action, are given. 

 This distinction of paramagnetic and diamagnetic is not here used 

 absolutely, but indicates a greater or less conductivity for the lines 

 of inductive action than that of the surrounding medium. 



The magnetic phenomena of crystals are then examined, and 

 referred to unequal magnetic conductivity in different directions ; 

 and the case of a crystalline sphere in a uniform field of force is 

 worked out. 



The laws of electric conduction, as laid down by Ohm, are shown 

 to agree with those of the imaginary fluid, and definitions of quan- 

 tity and intensity are given, which will apply to magnetism as well 

 as galvanism. 



The theory of the attractions of closed circuits, as established by 

 Ampere, is shown to lead to the following results : — 



1. The total intensity of the magnetizing force estimated along 

 any closed curve embracing the circuit is a measure of the quantity 

 of the current. 



2. The quantity of the current, multiplied by the quantity of in- 

 ductive magnetic action, from whatever source, which passes through 

 it, gives what may be called the potential of the circuit. The ten- 

 dency of the resultant forces is to increase this potential. 



