number which denotes how many times its resistance is greater than that of a copper wire of equal dimensions. Representing by s the specific resistance of a metal, the absolute resistance w of a wire with a length and a radius r, is Specific resistance is what Riess terms electrical retarding force; hitherto the reciprocal value of specific resistance has been indicated by the term capacity for conduction. But in practice it seems advisable to use the numerical value of specific resistance instead of capacity for conduction. The values found by Buff for specific resistance of silver, copper, and German silver, given above, deserve entire confidence, because they were determined with great care, and by, what is important, a simple and direct method, which is susceptible of the greatest accuracy. The silver was prepared specially for this object in the chemical laboratory at Giessen. The copper was prepared with great care by the galvanic process, but was not entirely free from iron, as analysis showed that it contained 0.02 per cent. of that metal. The first quality of commercial copper contained 0.22 per cent. of iron; the second quality, besides a trace of iron, 0.2 per cent. of lead, and 0.26 per cent. of nickel. In the following table the resistances of different metals, as determined by E. Becquerel, (Ann. de chimie et de phys. 3 serie XVII, 242; Pog. Ann. LXX, 243,) are compared with those found by Riess, the specific resistance of copper being taken as unity: The method by which Becquerel obtained these numbers is essentially as follows: His galvanometer, which he terms a differential galvanometer, is formed of two equal but separate wires placed side by side, each three metres long. The ends of the two coils of the multiplier are now so joined to the electro-motor that the current takes opposite directions in them, so that only the difference of strength of the two currents comes into play. In one of the closing conductors the rheostat is inserted, by means of which the resistance in both circuits can be made perfectly equal, so that the galvanometer needle remains at zero. Now, if in the other circuit we insert the wire to be determined, then to retain the needle at zero, the resistance of an equivalent number of rheostat coils must be added to the existing resistance. In this way the resistance of the wire is first expressed in rheostat coils. It is easily seen that this method is practically the same as that by Wheatstone's differential resistance-measurer, which, however, has the great advantage that with it any ordinary galvanometer can be used, while Becquerel's method requires one of peculiar construction. The silver which Becquerel used in his experiments was reduced from the chloride, and the copper was precipitated electro-chemically and melted. The numbers of the last column are computed from experiments which Frick and myself made conjointly by Wheatstone's method. The copper was from galvanic precipitation. Most of the experiments gave for silver a resistance very near to that of copper, while Riess and Lenz before him found it considerably less. This great difference cannot depend upon the want of purity in the silver, for that would increase rather than diminish the resistance. According to the measurements of Lenz (Pog. Ann. XLIV, 345) the resistance of Antimony is.............11.23 .21.45 .38.47 § 30. Dependence of the resistance of metals on temperature.-Lenz has investigated the influence of change of temperature on the conductive capacity of metals. His reports may be found in Poggendorff's Annalen, Bd. XXXIV, p. 418, and Bd. XLV, p. 105. extract from the last-named paper the following results: We It is very evident from this table how great the influence of heat is on the conductive capacity of metals, and also how unequal this influence is in the different metals. For instance, at 100° the last five metals have entirely changed their respective positions in the order o conductive capacity: lead has become the worst conducting metal; platinum has gone above iron; brass conducts better than tin, which, at 0°, is above it. At 200° the series is relatively the same as at 100°, though here copper and gold have become nearly equal; so that gold, at a yet higher temperature, must be a better conductor than copper. In reference to the method by which Lenz arrived at the above results, we have a few remarks to make. The current which he used was magneto-electrical, in the closing circuit of which a multiplier was inserted alternately with and without the wire to be determined. This wire was coiled spirally, yet so that the single coils did not touch, and it was plunged in an oil bath, kept at a constant temperature by a spirit-lamp. The conductive capacity of the wire was now determined for a series (mostly 10 to 15) of different temperatures of the oil bath, and then by means of the different relative values of the conductive capacity g and the temperature t, the probable values of the constant factors of the equation, g=a+bt + ct2, were found. In this manner the following equations for computing the conductive capacity of different metals were obtained: g= 136.25 0.4984 t +.0.000804 9= 79.79 g= 30.84 ... ... 29.33 0.1703 0.000244 t2 g= 17.74 0.0837 -- ... g= 14.62 0.0608 ... g= 0.000061 0.000150 € 0.000107 These formulas, by which the above table was computed, accord very well with the observations. E. Becquerel has also investigated the relation of the conductive capacity of metals to temperature. A Fig. 21. The method by which Becquerel maintained his wires at a high temperature is as follows: The metallic wire to be used in the experiments is wound on a glass tube C D, Fig. 21, one centimetre in diameter and five or six centimetres in length, so that the single coils do not touch each other. If the wire should be more than one layer, it must be covered with silk, and then the second layer of coils wound on the tube. To prevent the coils from unrollA ing, they are fastened with silk. Both ends of the wire are now fastened to the lower ends of the thick copper rods a b, whose resistance may be disregarded. One of the rods, namely, a, is fastened to the upper end of the glass tube CD; the other, b, passes down into the tube. The coil, with its wrappings, is now placed in a test tube filled with oil. The two rods a and b pass through two small openings made in the cork A A', which holds CD in the middle of the oil. A thermometer with a long bulb serves for taking the temperature of the oil. T The oil was heated by immersing the test tube in a water bath; hence Becquerel's measurements did not exceed the boiling point of water. Becquerel infers from his observations that the decrease of conductive capacity is proportional to the increase of temperature. Consequently, the resistance of a metal increases by an equal amount for each degree of temperature. The following table indicates the amount of increase of resistance for one degree expressed in fractions of the resistance at zero. From this Becquerel computed a table for the conductive capacity of these metals at 0° and 100°, in which, however, the conductive. capacity of silver at 0° is made equal to 100; to compare these data with those of Lenz, I have re-computed the table, making copper = 100. It is evident that there is not the least accordance here with the results of Lenz, either in regard to the conductive capacity of the metal at 0°, or in regard to the decrease of the same with increasing temperatures. If the law found by Becquerel were correct, the factors of in the equations on the last page should be zero, and the factors of t multiplied by 100 should be equal to the differences of the above table. Finally, Müller, of Halle, has investigated this subject (Pog. Ann. LXXIII, 434) with the view of showing that a relation exists between the increase of the specific resistance to conduction, and the increase of specific heat. He assumed the measurements of Lenz with reference to resistance; for verifying those numbers he instituted a series of experiments himself with iron wire, the results of which accorded well with those of Lenz. The increase which the resistance of zinc and mercury underwent at increasing temperatures, and which Lenz had not determined, Müller found to be very nearly proportional to the increase of temperature. With reference to specific heat at different temperatures, Müller adopted the determinations of Dulong and Petit, with the assumption that the increase of specific heat is proportional to the increase of the rise of temperature. Whether this be true or not we shall not attempt to decide; but if it were the case, the converse would be proved, of what Müller desires; for, according to the determinations of Lenz, the increase of resistance to conduction is not proportional to the increase of temperature; the hypothesis of Müller would, perhaps, accord better with the measurements of Becquerel. Müller now compared the increase of the specific heat of mercury, platinum, copper, zinc, silver, and iron, with the corresponding increase of resistance; the accordance is not remarkable. This, however, in Müller's opinion, does not militate against his assumption of the dependence of the increase of resistance on the specific heat, because the determinations of specific heat at different temperatures have not been carried to the requisite degree of accuracy. If this want of accuracy be admitted, as in fact it must be, we must also admit that to try to prove such a relation with our present knowedge of facts is, to say the least, a fruitless endeavor. § 31. Resistance of the human body to conduction.-Lenz and Ptschelnikoff have investigated this subject, and made use of a magneto-electrical spiral as an electro-motor. According to their determinations, the resistance of the human body, the whole hand being immersed in water with the addition of part of sulphuric acid, is equal to that of 91762 metres of copper wire 1 millimetre in diameter. This can be considered as only a rude approximation, consequently the description of the details of the experiment is not necessary. Pouillet previously (P. A. XLII, 305) estimated the resistance of the body at metres of standard wire. 49082 Although these numbers may be very inaccurate, they nevertheless show us that the resistance of the body is very great, and that, therefore, the strength of the currents which produce physiological effects is always very feeble. Suppose a human body introduced into the closing circuit of a Bunsen's battery of 50 cups, the strength of the current will be by assuming the electro-motive force of a Bunsen element to be in round numbers = 800, and the resistance of the battery (about 500) being disregarded when compared with that of the body, provided we take for the resistance of the body the smaller number of Pouillet. This force of current corresponds to a deflection of about of a degree of our tangent compass. A single Bunsen element closed by the body would thus give a force of current of only |