AND MODERN PIIYSICa 1C3 



surfaces is unity, then the surfaces will be close 

 t together at points at which the pressure changes 

 rapidly ; where the variation of pressure is slow, the 

 distance between two consecutive surfaces will be 

 considerable. 



If, then, in any case of motion, wo can draw the 

 pressure surfaces, and the tubes of flow, we can de- 

 termine the motion of the fluid completely. Now, 

 tho same mathematical expressions which appear in 

 the hydro-dynamical theory occur also in tho theory 

 of electricity, tho meaning only of the symbols is 

 changed. For velocity of fluid we have to write 

 electrical force. For difference of fluid pressure we 

 substitute work done, or difference of electrical 

 potential or pressure. 



Tho surfaces and tubes, drawn as tho solution 

 of any hydro-dynamical problem, give us also tho 

 solution of an electrical problem ; tho tubes of flow are 

 Faraday's tubes of force, or tubes of induction, tho 

 surfaces of constant pressure are surfaces of equal 

 electrical potential. Induction may tuko place in 

 curved lines just as tho tubes of flow may bo bent and 

 curved ; tho analogy between the two is a complete 

 one. 



But, as Maxwell shows, tho analogy reaches further 

 fttill. An electric current flowing along a wire had 

 been recognised as having many properties similar to 

 those of a current of liquid in a tube. When a steady 

 current is passing through any solid conductor, there 

 are formed in tho conductor tubes of electrical flow 

 and surfaces of constant pressure. These tubes and 

 surfaces are the same as those formed by the flow of 



K 1> 



