XV. Experimental researches in electro-magnetism and magneto-electricity

Abstract

According to the experiments of Professors Cumming and Barlow, the conducting power of a wire for voltaic electricity varies directly as its diameter, and inversely as the square root of its length. My own previous experiments on this subject, with all the conductors I then tried, led to the same result. According to the experiments of M. Becquerel, the conducting power varies directly as the square of the diameter or area of the section, and inversely as the length. M. Pouillet, from an extensive series of experiments, arrived at the conclusion that the conducting power was exactly proportional to the section of the wire, and inversely proportional to the length, increased by a constant quantity. Such discordant results, in establishing a fundamental law in electromagnetism, obviously require a more careful examination than has yet been bestowed on them. Before we admit the accuracy of the conclusions, we must first examine the accuracy of the galvanometer employed, and the different modes of using it. The mode employed by Professors Cumming, Barlow, and Pouillet, was to observe the deflections of a compass needle placed over the conducting wire, and calculate the forces by assuming that the tangents of deflection were proportional to the deflecting forces. Now, when the conductor is indefinitely long, the wire very fine, the needle placed very near it, and the arcs of deflection small, the results obtained will not be very far from the truth. These conditions approach to the assumptions from which the mathematical law is deduced. But when the wire placed below the needle is short, when the diameter is considerable, and when the arcs of deflection rise to sixty, seventy, or eighty degrees, the results calculated in this way will be found to deviate very far from the truth. When the wire is formed into a short rectangular coil, as in the common galvanometer, no numerical results can be obtained from its indications; for all the conditions assumed in the mathematical investigation are here completely violated. A single experiment will prove the truth of this assertion. Having placed four copper wires, about four inches long, parallel to one another, on a divided circle, I soldered the ends to those of four other wires about ten feet long, these wires being connected with an elementary battery, composed of two parallel plates of zinc and copper, each containing four square inches. The plates were immersed in diluted acid and the degree of deflection observed. An elementary battery, composed of two parallel plates, each one inch square, and having a single copper wire of the same diameter and length soldered to each, was connected with the ends of the four short wires, the battery immersed in the same acid, and the deflections observed. The tangents of these deflections, reckoning from the middle of the wires, were very nearly in the ratio of one to two, whereas the quantities of electricity were very nearly as one to four. When my torsion galvanometer (which is founded on no assumption,) was employed, the degrees of torsion were found to be nearly as one to four.