3d. By making _x = 0_, we find _y_ to be infinite and negative. Now, these are the properties of the logarithmic curve, which furnish an explanation of the case in hand. Assuming that the _x_’s represent the quantities of electricity, and the _y_’s the lengths of the wires, we perceive at once, that those parts of the curve which we have to consider, lie wholly in the fourth quadrant, where the abscissas are positive and the ordinates negative. When, therefore, the battery current passes without the intervention of any obstructing wire, its value is equal to unity. But, as successive lengths of wire are continually added, the quantities of electricity passing, undergo a diminution, at first rapid, and then more and more slow. And it is not until the wire becomes infinitely long that it ceases to conduct at all; for the ordinate _y_, when _x = 0_, is an asymptote to the curve. In point of practice, therefore, when a certain limit is reached, the diminution of the intensity of the forces becomes _very small_, whilst the increase in the lengths of the wire is vastly great. It is, therefore, possible to conceive a wire to be a million times as long as another, and yet, the two shall transmit quantities of electricity not perceptibly different, when measured by a delicate galvanometer. But, under these circumstances, if the long wire be coiled, so as to act as a multiplier, its influence on the needle will be inexpressibly greater than the one so much shorter than it. Further, from this we gather that for telegraphic despatches, with a battery of given electromotoric power, when a certain distance is reached, the diminution of effect for an increased distance becomes inappreciable. THE GALVANOMETER OR GALVANOSCOPE.