wide range of temperatures to enable the exact law to be arrived at, though the change in the specific inductive capacity is probably represented by the formula D= Do + at + Bt2. The equality of the square root of the coefficient of specific inductive capacity and of the index of refraction for waves of infinite length, was also investigated, but even on taking into account the variations due to temperature the numbers do not agree very closely. The author also investigated if a powerful magnetic field would have any effect on the values of the specific inductive capacities, but no trace of any action was apparent. ERIC GÉRARD-SELF-INDUCTION. (La Lumière Electrique, Vol. 20, 1886, pp. 292-298.) Variable currents play a great part nowadays in quick working telegraph instruments, in telephones, in alternate-current machines, etc.; and in all cases where we have variable currents, we have also induced currents either in the same wire or in neighbouring wires. Where induction takes place between two wires, it may be expressed by the equation 7 being the length for which the wires are parallel, and h their distance apart. In the case of self-induction, if E is the E.M.F. in the circuit, R the resistance, L the coefficient of self-induction, the base of the natural logarithms, i the strength of the current, t the time since the closing of the circuit, then and as Ꭱ L is generally a large number, if t becomes of some value, the equation becomes practically that of Ohm. If now the E.M.F., instead of being constant, as supposed in the preceding case, varies according to a given law, then we obtain a more complicated expression. In the case where the circuit has a coefficient of self-induction L, a resistance R, and the E.M.F. has a periodic time T, we obtain for each moment a current The phenomenon of self-induction has the effect of producing a retardation in the undulations of the current, and of diminishing its strength, as if the 42 L2 ; this quan. 12 resistance had increased in the ratio of R to R2 + tity under the root representing the apparent resistance of the circuit. Self-induction in the bobbins of the telephonic translators considerably weakens the current, but the self-induction is itself diminished by the mutual induction of the neighbouring bobbins; or, as it is sometimes stated, the mutual induction diminishes the apparent resistance. Not only may self-induction occur in the case where the current follows a spiral path, as in a bobbin, but it may also arise in straight wires. For the rectilineal current in a straight conductor may be looked upon as made up of several parallel elementary currents which react on each other so as to give rise to an E. M.F. of induction opposed to that which produces the current. The formula for the induction of parallel currents has been already given, and in the case of a single wire of radius r, in which the mean distance of the several elementary currents is h 0-07788 r, the coefficient of self-induction becomes 1 (1-21-0-75) This is in the case of non-magnetic wires; but for wires of magnetic metals the induction is more powerful, for each time that a current is started in the wire the external layers are magnetised. The coefficient of self-induction has therefore to be increased by a quantity depending upon the magnetisa. tion, and becomes The author has carried out some experiments on the general plan of Professor Hughes, but with some differences in the arrangement of the apparatus; his results confirm the calculations given above. Conductors of square section have less self-induction than those of circular section, because the elementary currents have a greater mean distance in the former case. The use of ribbon conductors for lightning-rods does not there. fore depend on their greater surface-conductivity, as used to be supposed, but on their lower self-induction. In the case of compound wire, i.e., a steel core electro-plated with copper, part of the current passes through the steel core, and part through the copper covering these two parallel currents magnetise the exterior layers of the core in opposite ways, and consequently the self-induction is less. If the copper were inside and the steel outside, the opposite effect would be produced. J. WETZLER-NEW SYSTEM OF DUPLEX TELEGRAPHY. Edison has lately brought out a new system of duplex working between any two stations. This is the Phonoplex, or Way-Duplex. Each station is provided, in addition to the ordinary relay and sounder, with a phone. This instrument is, in fact, a telephone with a permanent horse-shoe magnet and a steel ring resting on the diaphragm. This ring, being able to move in a vertical plane only, gives very distinct raps when a current passes in the telephone. To work the phone there is a local battery with a key, the circuit being completed through a relay: this relay puts in circuit with another battery the primary of an induction coil. When the key is depressed, the lever of the relay opens the circuit of the battery, and an extra current is set up in the induction coil, whence it passes to the line: the extra current is reinforced by a condenser being joined up to the circuit. The intense extra current has no effect on the sounder relay, which, however, responds to the ordinary current, but it acts on the phone, causing the steel ring to give very distinct signals. G. COLOMBO-CENTRAL STATION AT MILAN. (La Lumière Electrique, Vol. 20, 1886, pp. 481-483.) The lighting is effected by means of the transformers of Zipernowski, Deri, and Blathy. The generating machine is of the type S W of Ganz & Co., with 20 magnets, and giving therefore, at a speed of 250 revolutions, 5,000 alternations per minute. The current for which the machine was built is 55 ampères at an E.M.F. of 1,300 volts, but for the present only 22 ampères are required. The exciting current is 30 ampères and 100 volts, and is furnished by part of the current of the machine being converted into a continuous current by means of a commutator. Both the main current and the exciting current pass through a "compensator," by the action of which the E.M.F. at the terminals of the transformers is kept constant. The main current is conveyed from the central station to the Theatre Dal Verme by means of a concentric cable, the distance being 1,260 yards. In the theatre there are at present three transformers of 10 horse-power each, by which the E.M.F. is reduced to 96 volts. P. H. LEDEBOER-DETERMINATION OF THE COEFFICIENT OF SELF-INDUCTION. (La Lumière Electrique, Vol. 20, 1886, pp. 529-538.) The method employed is that of the Wheatstone bridge, the coil or electro-magnet being in one branch. The resistance of the coil is first balanced in the ordinary way. The opening and closing of the battery circuit then give rise to induced currents depending on the electro-magnetic capacity of the coil; and from the deflection of the galvanometer the coefficient of self-induction can be determined. From the application of Kirchoff's laws to the currents and resistances in the bridge, four equations are obtained, which, when simplified, reduce to the general formula LUI fio dt = T (K' + l') + 9 (l +U) where L is the coefficient of self-induction of the coil, I the current in it, 7, l', R' the resistances of the three arms of the bridge, g that of the galvanometer, and i, the current in the galvanometer circuit. To determine L from the above equation, we must know not only the resistances above mentioned, but also the quantity of electricity, fi, dt, which passes through the galvanometer. This may be arrived at by comparing the throw of the galvanometer needle due to the induced current with the deflection occasioned by the permanent current which passes when the balance of the bridge is upset by the addition of a small resistance, r, to one arm, for we have finally, supposing I has not been altered by introducing r, To compare the throw, d, produced by the quantity of electricity under the integral with the deflection, a, produced by the current, i'o, we have where a is the logarithmic decrement, the right-hand side of which equation for a ballistic undamped galvanometer becomes simply where T is the time of one oscillation, which can be readily determined. P. H. LEDEBOER MEASUREMENT OF THE COEFFICIENT OF GALVANOMETER (La Lumière Electrique, Vol. 21, 1886, pp. 6-18.) OF To make a measurement of the coefficient of self-induction by means of this galvanometer (see Journal, Vol. 14, p. 448), we begin by determining the constants of the galvanometer, viz., the time of one oscillation without a current, the deflection corresponding to one micro-ampère, and the resistance for which the galvanometer is just dead beat. These constants having been determined once for all, a Wheatstone bridge arrangement is set up, the experimental coil being in one arm, and the resistance of the galvanometer circuit being so arranged as to be always the same, and equal to that for which the square roots of the equation of motion of the coil of the galvanometer are equal. The actual measurement then consists of nothing more than the observa tion of the deflection produced on making or breaking the battery circuit, the strength of the current being determined both before and after this observation. When the deflection is too great the galvanometer can be shunted. The formulæ used are T i The term e П α is a constant factor dependent on the galvanometer, T being expressed in seconds and i in ampères. As to a, if D is the distance from the mirror to the scale, and d the deflection, both reckoned in centimètres, α then a = but since = 2 D d' 2D ୪ d' -= and it is unnecessary to know D. The term within the bracket depends on g, the resistance of the whole galvanometer circuit which is determined once for all; the several resistances, R, R', 1, and s, are all known in ohms. The deflection & has, of course, to be observed each time; it is to be expressed in the same units as a and I, the strength of the current, which is reckoned in ampères. The value of L is then finally expressed in terms of T, reckoned in seconds, and of a resistance in ohms. Hence L is determined in the practical system of units, i.e., in 109 centimètres, since its dimensions are those of a length. The accuracy of the formula has been determined by experiments described in the original article, which also contains details of some particular cases. P. H. LEDEBOER-RELATION BETWEEN THE COEFFICIENT OF AND THE MAGNETIC ACTION OF AN SELF-INDUCTION ELECTRO-MAGNET. (La Lumière Electrique, Vol 21, 1816, pp. 51-70 and 112-113.) In a system made up of bobbins containing soft iron cores, there is a simple relation between the coefficient of self-induction and the magnetic state. In fact, in such a system the increase of induction corresponds with an increase of the magnetic force. Now the increase of the magnetic force is the product of the intensity of the magnetic field by the surface, and the increase of the induction is equal to the product of the coefficient of self-induction by the strength of the current. It follows that this latter product is proportional to the magnetic field, so long as the lines of force do not change their position. Generally, the distribution of the lines of force varies slightly in a system of bobbins containing iron, and the author has therefore sought to determine experimentally how far the proportionality between the magnetic field and the product of the coefficient of self-induction by the intensity of the current in the bobbins holds good. With this object in view determinations were made simultaneously of the magnetic moment and the coefficient of self-induction of a bobbin containing a soft iron core. The magnetic moment was determined by the method of Gauss, by means of a dead-beat magnetometer of Weber, and the coefficient of self-induction by the method described in the preceding abstract. On examin |