392 



ferential equation itself which you have obtained. For the equation 



kc = -=-5 shows that two submarine wires will be similar, provided 

 dt ckr 



the squares of the lengths x, measured to similarly situated points, 

 and therefore of course those of the whole lengths /, vary as the times 

 divided by ck ; or the time of any electrical operation is proportional 

 to hd*. 



" The equation kc -r = ~r^ hv gives h x l~ s for the additional 

 condition of similarity of leakage." 



The accompanying set of curves represents the strength of the 

 current through the instrument at the remote end of a wire as it 

 gradually rises, or gradually rises and falls, after the end operated 

 on is put in connexion with one pole of a battery, and either kept 

 so permanently, or detached and put in connexion with the ground 

 after various short intervals of time. 



The abscissas, measured on OX, represent the time reckoned 

 from the first application of the battery, and the ordinates, mea- 

 sured parallel to OY, the strength of the current. 



kcl- /4 \ 

 The time corresponding to a is equal to - log f - 1, if / be the 



length of the wire in feet, k its "resistance" per foot, in electro- 

 statical units, and c its electro-statical capacity per foot (which is 



equal to - 57, if I be the electro-statical inductive power of the 



gutta percha, probably about 2, and R, R' the radii of its outer and 

 inner surfaces). The principal curve (I.) represents the rise of the 

 current in the remote instrument, when the end, operated on is kept 

 permanently in connexion with the battery. It so nearly coincides 

 with the line of abscissas at first as to indicate no sensible current 

 until the interval of time corresponding to a has elapsed ; although, 

 strictly speaking, the effect at the remote end is instantaneous (i.e. 

 according to data limited as regards knowledge of electricity, to such 

 as those assumed in hydrodynamics when water is treated as if in- 

 compressible, or the velocity of sound in it considered infinitely great, 

 which requires instantaneous effects to be propagated through the 

 whole mass of the water, on a disturbance being made in any part 



