A great irregularity is seen between the 10th and 12th miles, which is due, undoubtedly, to a deficiency of accuracy in the weighing apparatus. I take pleasure in sending you the following calculation of the law of the conducting power of wires, for which I am indebted to my friend Prof. Draper, of the New York City University. _On the Law of the Conducting Power of Wires. By John W. Draper, M. D. &c. &c._] It has been objected, that if the conducting power of wires, for electricity was inversely as their length, and directly as their section, the transmission of telegraphic signals, through long wires, could not be carried into effect, and even the galvanic multiplier, which consists, essentially, of a wire making several convolutions round a needle, could have no existence. This last objection was first brought forward by Prof. Ritchie, of the University of London, as an absolute proof, that the law referred to is incorrect. There is, however, an exceedingly simple method of proving that signals may be despatched through very long wires, and that the galvanic multiplier, so far from controverting the law in question, depends for its very existence upon it. Assuming the truth of the law of Lenz, the _quantities_ of electricity which can be urged by a constant electromotoric source through a series of wires, the lengths of which constitute an arithmetical ratio, will always be in a geometrical ratio. Now the curve whose ordinates and abscissas bear this relation to each other, is the logarithmic curve whose equation is _aʸ_ = _x_. 1st. If we suppose the base of the system, which the curve under discussion represents, be greater than unity, the values of _y_ taken between _x = 0_, and _x = 1_, must be all negative. 2d. By taking _y = 0_, we find that the curve will intersect the axis of the _x_’s, at a distance from the origin, equal to unity.