60 Royal Society :-— 
reduced to a harmonic law, with an amplitude falling in equal pro- 
portions during equal intervals of time. Unless the electric opera- 
tions fulfil a certain condition, this ulterior distribution is according 
to the simple harmonic law (that is, is proportional to the sine of the 
distance from either extremity, the whole length being reckoned as 
180°). The condition which I propose to fulfil is, that the coefficient 
of the simple harmonic term in the expression for the electrical 
potential shall vanish. Then, according to Fourier, the distribution 
will very much more quickly wear into one following a double har- 
monic law (that is, the sine of the distance from one extremity, the 
whole length being reckoned as 360°). In this state of electrifica- 
tion the two halves of the wire on each side of its middle point, 
being symmetrically and oppositely electrified, will discharge into 
one another, as well as into the earth at their remote extremities ; 
each will be like a single wire of half-length, with the simple har- 
monic distribution ; and the wire will, on the whole, be discharged 
as fast as a wire of half the length, or four times as fast as a wire of 
the whole length, after an ordinary electrification. There is con- 
siderable latitude as to the mode of operating so as to fulfil this con- 
dition, but the theoretical investigation is readily available for finding 
the best way of fulfilling it in practice. The result, as I have tested 
by actual calculation of the electric pulse at the remote end, is most 
satisfactory. ‘The calculations, and curves exhibiting the electric 
pulse in a variety of cases, will, I trust, very soon be laid before the 
Royal Society. 
The time and law of operations being once fixed upon, a mecha- 
nical contrivance of the simplest kind will give the means of direct- 
ing a regulated galvanic battery to perform it with exactness, and to 
any stated degree (positive or negative) of strength. Complete 
plans of all details I have ready to describe when wanted, and shall 
very soon be able to state exactly the battery power required for a 
cable of stated dimensions. 
2. Plan of observation for receiving a message.—The instrument 
which I propose is Helmholtz’s galvanometer, with or without modi- 
fication. The time of vibration of the suspended magnet, and the 
efficiency of the copper damper, will be so arranged, that during the 
electric pulse the suspended magnet will turn from its position of 
equilibrium into a position of maximum deflection, and will fall back 
to rest in its position of equilibrium. The possibility of fulfilling 
these conditions is obvious from the form of the curve I have found 
to represent the electric pulse. The observer will watch through a 
telescope the image of a scale reflected from the polished side of the 
magnet, or from a small mirror carried by the magnet, and he will 
note the letter or number which each maximum deflection brings into 
the middle of his field of view. 
3. Code of letter-signals.—The most obvious way of completing 
a telegraphic system on the plans which have been described, is to 
have the twenty-six letters of the alphabet written on the scale of 
which the image in the suspended mirror is observed, and to arrange 
thirteen positive and thirteen negative strengths of electric operation, 
