RECENT PR00RES3 IN THEORETIC A.L PHYSICS. 215 



The precise character of the movement within the wire, is also 

 shown to be entirely irrelevant in this estimate of the current 

 strength. For " in the theory of electro-magnetism it is unnecessary 

 to adopt any such hypothesis as this [that the electric current consists 

 of matter flowing,] however probable or improbable it ratiy be as an 

 ulterior theory; and all that we could introduce as depending up- 

 on it is that, for a linear circuit of varying section or material, the 

 quantity is the same throughout the circuit, and that all finite 

 circuits possessing continuous currents are necessarily closed; two 

 facts which cannot be assumed a ■priori^ but which arc in reality 

 established by satisfactory experimental evidence.'"* 



C, the current strength here alluded to, is the product of the so 

 called inteiisitt] of the current, into the area of the cross-section of 

 the conductor. It maj' be measured of course by the work it w^ill 

 do in a definite time, either as electrolysis, heat, or other form of 

 work. Helmholtz' angular velocity of the vortex-filament in a 

 fluid, affords a means of forming a mental conception of intensity 

 of current, in electricity, by assimilating it to the rotatory energy 

 in a vortex-filament, which is far superior to any of the illustra- 

 tions ordinarily used: and this witnout in any way necessarily 

 implying that the electric current actually involves such rotating 

 elements, although this may really be. 



As a linear electro-magnet is completely specified when the form 

 of the closed curve of the current, and (), the strength, are given; 

 so also a vortex filament is completely specified when the form of 

 its axis and the product of its angular velocit}' into the area of its 

 cross section are given. 



In electro-magnetism we have iA=i'A' for the same circuit. In 

 vortex filaments qA=q' A' for the same filament; q being the an- 

 gular velocity; A, A,' areas of cross sections; ij'. current intensi- 

 ties. In electricity, magnets are known to circulate around cur- 

 rent-conducting wires, and wires reciprocally around magnets. In 

 fluids, vortex-filaments that are straight circulate around each other 

 and their mutual center of gravity; vortex filaments that are cir- 

 cular also revolve around each other, as is shown by the peculiar 

 action described above where the rings alternately pass through 

 each other, by contracting and accelerating their speed, and then wid- 

 ening and moving slower, while the one following contracts and 

 passf^s through in turn. 



* Eepnnt — p. 410 



