Mr. Lane on Electric Conduction in —_ 241 
would increase by increments forming in equ 
vals of time, a descending geometrical. ssion,* of which 
the common ratio would be determined yy the section and con- 
ducting power of the wire. If this is" “so, the induction of cur- 
rents on themselves will no more interfere with the application 
of the law of conduction to the case of discharges through the 
telegraphic wires, than through the shorter conductors in ordi- 
nary experiments, and we may presume therefore that the effect 
of this induction is not appreciable in telegraphic discharges. 
21. If in the register of Morse’s telegraph the wire in the coil 
of the electro-magnet be supposed always to occupy the same 
space, and to be of constant weight, then according to Lenz’s 
law the maximum effect on the electro-magnet ought to be ob- 
tained when the length and section of the wire of the coil are 
such as to make its resistance to conduction equal to that of the 
wire between the stations; and if this adjustment of the register 
to the distance of the stations could always be made, the inten- 
sity of battery required to work it ought to be, not as the dis- 
tance itself, but as the square root of that distance. If it be 
found that the inductive reaction of the electro-magnet on the 
current prevents the latter from reaching its maximum during the 
period of discharge, the advantageous length of the wire of the 
coil would be less and its section greater than as determined by 
the above rule. It would still remain true, however, according to 
theory, that if the intensity of the battery varies as the square 
root of the distance, and the resistance to conduction of the wire 
of the coil have a constant ratio to that of the wire between the 
stations, the space of time in which the current will attain any 
given fractional part of its maximum, and the magnetic — 
developed in that time, a fai be the same. 
Yale College, January, 1846. 
ua ‘ suecessive inter- 
* This is strictly affirmed only with respect to a conductor in the form of a thin 
hollow cylinder. The law of increase in such a se eige may be shown by the 
logarithmic curve aa’. If time be represented by m a 
tion along the line é#/, and if ¢ represent the point of ‘eg oe mati 
time at which the current begins, the space tt' aa’ may ; 
represent the quantity of the current at a poi int of time * : 
represented by t/. In a solid conductor this law must be a little modified, the in- 
crease of current being at first more and afterwards less rapid at the surface than 
in the central parts. But this does not affect the truth of the othier facts stated. 
Szeconp Sgrizs, Vol. I, No. 2,—March, 1846. pt 
