383 



note communicated as an addition to a paper in the last June Num- 

 ber of the Philosophical Magazine, and I believe at present in the 

 Editor's hands for publication, I proved that the value of c is 



- t , if I denote the specific inductive capacity of the gutta 



21 4 



percha, and R, R' the radii of its inner and outer cylindrical surfaces. 



" Let k denote the galvanic resistance of the wire in absolute elec- 

 tro-statical measure (see a paper ' On the application of the Principle 

 of Mechanical Effect to the Measurement of Electromotive Forces 

 and Galvanic Resistances,' Phil. Mag. Dec. 1851). 



" Let y denote the strength at the time t, of the current (also in 

 electro-statical measure) at a point P of the wire at a distance x from 

 one end which may be called O. Let v denote the potential at the 

 same point P, at the time t. 



" The potential at the outside of the gutta percha may be taken as 

 at each instant rigorously zero (the resistance of the water, if the 

 wire be extended as in a submarine telegraph, being certainly inca- 

 pable of preventing the inductive action from being completed in- 

 stantaneously round each point of the wire. If the wire be closely 

 coiled, the resistance of the water may possibly produce sensible 

 effects). 



" Hence, at the time t, the quantity of electricity on a length dx of 

 the wire at P will be vcdx. 



" The quantity that leaves it in the time dt will be 



dt d -Zdx. 

 dx 



" Hence we must have 



dv dy , 



X ~dl ' ~dx 



"But the electromotive force, in electro-static units, at the point P, is 



_dv, 

 dx 

 and therefore at each instant 



7 dv /r> \ 



" Eliminating y from (1) by means of this, we have 

 , dv d^v 





f n \ 



(3) - 



