end of the wire a; the upper was so near the end B that, in discharging the battery, a small bluish spark passed. After discharging through the main spiral the upper plate was removed and tested by the electrometer. For a positive charge of the battery the condenser plate, which touched the end ß, was found electro-negative. The rayed figure (fig. 65) is, therefore, always produced by the end charged with negative electricity; and, consequently, the secondary current has always the same direction as the main current. The experiment made by Riess for ascertaing the direction of the lateral current by the decomposition of iodide of potassium failed, as he did not succeed in producing the decomposition by the secondary current.-(Pog. Ann., XLVII, 74.) § 67. Deflection of the magnetic needle by frictional electricity.—The coils of a multiplier, used for producing a deflection of the magnetic needle by a current of frictional electricity, must be very well insulated. Riess has constructed such a multiplier (Pog. Ann., XL, 348) of a copper wire 105 feet long and one-sixth line in diameter, which, covered with three coats of silk and in 260 coils, formed 5 layers on being wound upon a suitable frame. Before winding a length of the wire it was twice covered with shellac varnish, and the wrapping put on before the varnish was perfectly dry. Each layer was again varnished after wrapping. The cylindrical astatic needles belonging to this coil were 22.5 lines long, 0.4 line in diameter, and 5 lines apart. The combined needles made one oscillation in 6.6 seconds. One of the wire ends of such a multiplier being placed in conducting connexion with the conductor, the other with the cushion of the electrical machine, a deflection of 10 to 20 degrees could be maintained by turning. When it is desired to deflect the needle by the discharge current of the electrical battery the discharge of course must be retarded by the insertion of bad conductors, such as moist strings, glass tubes filled with water, &c. The latest experiments made by Riess on this point (Pog. Ann., XLVII, 535) gave results showing that the deflection of a magnetic needie by the wire which slowly discharges an electrical battery is independent of the surface of the battery, provided a perfect discharge of the bat-tery takes place. It is therefore immaterial to the deflection of the needle whether the same quantity of electricity is distributed over one or over several jars. Faraday had attempted (Experimental Researches, 363, Pog. Ann., 29) to compare the discharge current of the electrical battery with that of a voltaic current. After obtaining a given deflection of the magnetic needle by discharging a battery he constructed a voltaic pair, which, acting 31 seconds, produced the same deflection as the discharge of the battery; and he concluded that the quantity of electricity yielded by the pair was equal to that accumulated in the battery. Riess justly remarks, that this conclusion is not well founded, because the instantaneous action of the discharge current of the battery on the needle is essentially different from that of a galvanic current. I have reported Riess' researches without interrupting the course of the narration by speaking of what has been done by others on the same subject. Let us now turn to these labors. $ 68. Knochenhauer's researches on the current.-In a second article, with the title “Experiments on Latent Electricity,” (Versuche über die gebundene, Elektricitât, Pog. Ann., LVIII, 391,) Knochenbauer presents the law according to which the force of the secondary current decreases when the distance from the main wire increases. Riess has shown, as already mentioned, $ 61, that the force of the secondary current decreases in the same proportion in which the axial distance of the secondary wire from that of the main wire increases. Knochenhauer thinks this law is “evidently insufficient." Starting, apparently, from the idea that the lateral current is a phenomenon of induction, Knochenhauer attempts to apply here his law.* That a law stating the relation between action and distance, adapted to the case of spherical bodies only, in which all action can be considered as starting from a single point, cannot hold good for wires running parallel to each other does not stop Herr Knochen hauer. His law has such an astonishing elasticity that, by barely changing the coefficient, it serves for the secondary current. In his opinion there subsists between the force of the secondary current (measured by the air thermometer) and the distance of the wire the relation 0 = Aava in which a denotes the temperature of the thermometer in the secondary wire, and n the distance of the secondary from the main wire. This n, however, is not the axial distance, but the distance of the wire in the clear, in which he assumes three lines as unity ; hence the magnitude of n has first to be computed from the axial distance a given by Riess. He first compares his formula with the results found by Riess. A series of these observations he arranged in the following table, with the values computed by his formula : In fact the values observed and those computed by the above formula correspond sufficiently well by making A = 0.401, a= 0.489. Indeed, the formula answers for very short distances, for which the law of Riess, on evident grounds, is no longer applicable. But does this accordance of Knochenhauer's formula with the observa * See Report of 1856. tions prove its correctness ? Certainly not. When there are two constants at our disposal it is easy to invent a whole mass of formulas which would serve just as well ; that is, they will accord with the few numbers observed within narrow limits, quite as closely as the limits are narrow. As a proof I propose 0= A + b log. D; the first best arbitrary formula that occurs to me. In this formula let o denote the temperature of the secondary wire, D the axial distance of the wires. Making A = 0.276, and b = 0.16, this formula will agree with Riess' observations as well as that of Knochenhauer; as the following table shows, in which the third vertical column contains the values computed by the above formula: In spite of this harmony between observation and computation, this formula expresses just as little as Knochenhauer's, the law according to which the force of the secondary current decreases with the distance from the main wire. Knochenhauer has himself made a series of experiments to confirm his formula, and by which he would show that the magnitude of a depends upon the conducting capacity of the main circuit, of the secondary circuit, &c. The description of the modus operandi of the experiments, how the wires were extended, &c., is exceedingly obscure, and since, I think, I have proved the inaccuracy of his formula, a further account of these experiments is unnecessary. This memoir forms the introduction to further researches, which relate to the secondary current and currents in branched circuits. The following are the titles of the memoir on these subjects: On the lateral current in divided conducting wires of the battery.(Pog. Ann,. LX-LXX, 235.) On the electrical current in divided conducting wires of the battery. (Pog. Ann., LXI, 55.) On the diminution of the main current with divided conducting wires of the battery.-(Pog. Ann., LXII, 353.) On the relation of the formulas which determine the development of heat by the electrical and the galvanic current.—(Pog. Ann., LXII, 207.) Experiments on the electrical secondary current.-(Pog. Ann., LXIV, 64, and Pog. Ann., LXVI, 235.) Determination of the compensating length of wire without the air thermometer.—(Pog. Ann., LXVII, 327.) Fig. 68. Solution of the problems recently proposed on branched galvanic currents, for the discharge current of the electrical battery.-(Pog. Ann., LXVIII, 136.) On the ratio of tension in the discharge current of the electrical battery.-(Pog. Ann., LXIX, 77.) On the comparison of the electrical formula with the galvanic.(Pog. Ann., LXIX, 421.) The experiments mentioned in these memoirs are very badly described; the discussions inflated, confused, and full of difficult formulas, which do not lead to simple, clear, and well founded results. Since the design of this report is to present to the reader the progress of physics, and not to weary him with criticisms on fruitless labors, I need say no more of Knochenhauer's memoir on the lateral current and kindred subjects. The criticism on the abovementioned paper suffices to justify me in this respect. § 69. Charging current of the electrical battery.-In Fig. 68 let a and b denote two electrical batteries, both of which are insulated The exterior coatings of both batteries being in metallic connexion, suppose a to be charged and b to remain uncharged. Now, if any suitable discharger, fitted to the knob of the jar b, approaches the knob of the charged jar, a spark passes, the jar a becomes partially discharged, a part of the (e. g.) positive electricity, 6 which was accumulated on the inner coating of a, passes with a spark to the inner coating of b, while a corresponding quantity of negative electricity passes without a spark, by the conducting connexion of the outer coatings, from a to b. In this manner a is partly discharged and b charged; the charge of b is not gradual, as in ordinary charging of jars, but very rapid. Dove terms the current which, passing from the outer coating of a to that of b, charges the latter battery, the charging current, (Ladungsstrom,) and he has compared the action of this current with the action of the discharge current already amply investigated. He found the following results, (Pog. Ann., LXIV, 81:) 1. Induction. In the outer connecting wire a cylindrical induction spiral was introduced, surrounded by an exterior secondary spiral. The effects were the same as in the discharge stroke. 2. Sparks. The outer connecting wire having been interrupted, a brilliant white spark, with a loud report, appeared at the place of external interruption the instant the spark at the inner conducting wire passed. A moist thread being introduced into the inner conducting wire, the spark assumes a redish yellow color and has a feeble report; the same change is also indicated in the place of interruption of the outer connecting wire, in which there is no moist thread. Dove found further that the “charging current produced in the same manner as the discharge current. at 3. Galvanic effects. The needle of a galvanometer inserted in the connecting wire of the outer coatings is not affected when the inner coatings are brought into metallic contact with a white and loudly sounding spark, without the interposition of a moist thread; but it is sensibly affected when & moist thread is introduced there. The magnetizing of a steel needle placed in a spiral was produced with great effect in the first case, (without interposition,) but feebly in the second case, (with interposition.) The contents of one of Dove's papers in Poggendorf's Annalen, (LIV, 305,) bearing the title, “On the current induced in magnetizing iron by means of frictional electricity,” will have to be presented later, because this subject is closely related to the corresponding effects of the galvanic current. $ 70. Hankel's researches on magnetizing steel needles by the discharge spark of the electrical battery.-Hankel has published two large me moirs on this subject, (Pog. Ann., LXV, 537, LXIX, 321.) In the first he speaks of Savary's observations, and then proceeds to the description of his own experiments, the results of which are as follows: 1. When the discharge stroke passes through a spiral in which a steel needle is placed, a certain minimum of charge is generally necessary to magnetize the needle. Calling the polarity which it receives by the discharge stroke of this minimum, normal, the needle will become abnormally magnetic by gradually increasing discharges, and again normal by still stronger charges, &c. The abnormal magnetism appears with strong charges of the battery, as the pieces of wire introduced into the circuit of the battery are longer in proportion as the charge is stronger. When in addition to the spiral and the pieces of the conducting circuit remaining constant in all the experiments, an iron wire 34 feet long and 0.1 line in diameter was introduced, abnormal magnetism was obtained with a charge 70 (measured by sparks of the measuring jar); on inserting 82 feet of the same wire a charge of 120 was required, and a wire of 154 feet required a charge of 160. 2. When a battery of more, and then one of fewer jars was used with the same conducting circuit, the battery of the less number of jars produced the abnormal period with a less charge. An iron wire of 202 feet having been introduced, a charge of 20 with two jars produced abnormal magnetization, while by using 5 jars it was only obtained with a charge of 70, and with 9 jars, even the quantity of electricity 230, did not produce abnormal magnetization. If with gradually increasing charges, the change- from normal to abnormal magnetization is not always obtained, these periods are nevertheless not wholly wanting; for an increase and decrease of the strength of the normal magnetism is observed, and the minima of the |