parison between bars of different sizes when the disparity in weight is not very considerable. The following is an abstract of the principal observations :—— Nickel. 24 grammes sub- M M V. v. V. w. The temperature co-efficient (u) was determined from observations of the difference in deflection produced by alternately heating and cooling the bar in water through a range of about 30° by the following formula: sin (42 — 1) (t1 - t2) tan 2 representing the smaller angular deviation at to the highest temperature, and 2 that at to the lower temperature. The first observations on the nickel bar gave for t1 — t2 = 30°·5 a mean value of 241 For raising temperature And for falling temperature. The corresponding values of μ per 1° C. being in the first case 0.000623, and in the second 0.000487. A subsequent comparison with the Wolfram steel bar gives The results of the experiments are summed up as follows: 1. Pure nickel, contrary to the behaviour of the analogous metal, iron when pure, is susceptible of being permanently magnetised in a notable degree. But the maximum of such magnetism is only from one-half to one-third of that which is retained by hardened steel under similar conditions, according to the quality of the latter. 2. The magnetism so retained in nickel is less permanent than that of good hardened steel; the slow loss of magnetic power, whether by efflux of time or by alternate heating and cooling, being proportionately greater in nickel than in steel; and this holds good even when the bar, by repeated heating and cooling, has been brought into a certain condition of magnetic permanency. 3. The temperature co-efficient of a nickel magnet in the latter condition is but slightly larger than that of one of good hardened steel. 4. The temporary magnetism of pure nickel is about double that of its permanent magnetic momentum, one-half of that of hardened steel, and one-quarter of that of soft iron. The magnetic qualities of nickel are, therefore, inferior to those of iron and steel. The Author was unable to state whether the nickel magnet in question had been subjected to hardening or any analogous process for the purpose of increasing its coercive power, but he does not think it likely that it had, because the quantities expressing its permanent and temporary magnetic momenta are very similar to those previously obtained by Arndtsen. H. B. New Mode of Duplex Transmission. By O. MOREL. (Annales télégraphiques, 1877, pp. 401-405.) Duplex transmission, based upon the differential system, presents the following inconvenience: if the resistance of one of the differential circuits alters, the current augments in the one and diminishes in the other. Now these two effects combine, and consequently this kind of transmission is more affected than the ordinary transmission by the variations of the resistance of the circuit. The Author states that he has sought to remedy the defect in the following manner :— Two relays, the one with a polarised armature, have their coils in circuit with one pole of a local battery and with the line, the polarised relay being next the line. An operating key is connected to the circuit between the two relays. The armature contacts of the relays are connected through a local battery, the poles of which battery are also connected through the coils of the receiving instrument. The contact levers of the two armatures are connected to earth. From the description it is easy to see that so long as the levers of the two armatures are in connection with their contacts no current will pass through the receiving instrument, and if either of these levers quits this position, the circuit of the local battery will be closed in the receiving instrument. The lever of the operating key, when at rest, communicates with earth, when it is depressed or raised neither of the relays acts; but in both cases the circuit of the line battery is closed from traversing the bobbin of the unpolarised relay, the armature of which remains always attracted. For the other part, the polarised relay is previously arranged in such a manner that the passage of the current from the line battery does not cause the displacement of its armature. A station will then be able to transmit without reproducing its signals on its own receiver, and this receiver will nevertheless receive the signals of the station corresponding. The batteries at the two stations presenting to line poles of the same name, if the operating key at one end is at rest, the current from the opposing station will produce an effect upon the polarised relay inversely to that of the battery at its own end of the line, and its armature is displaced by, and the receiver will reproduce the signals made by, the station corresponding. If the two stations work simultaneously, the currents emitted annul themselves, and the armature of the unpolarised relay ceasing to be attracted, the receiving instrument will still reproduce the signals sent by the opposing station. The experiments that the Author has made with the Morse have been successful, and show that the return current does not produce important perturbations; and, in fact, the polarisation of the relay nearest to the line having been over-excited by the passage of the current of the line battery, the return current has no other effect than re-establishing the magnetism to its normal state. This system does not absolutely necessitate the use of a condenser. Though the different actions of the relays are made in a satisfactory manner with the Morse, they are not produced with sufficient strength to allow of their application to the Hughes receiver. There are, at certain times, delays that can be avoided only by making the relays more sensitive, and in this case the equilibrium is very unstable. The Author has also tried the following arrangement. The receiving instrument has a double coil, the one in circuit from the transmitter (mechanically stamped paper) to line, the other in circuit from the transmitter to one pole of a battery, the same pole of which is also connected to the transmitter through a rheostat, the other pole of the battery is connected to earth. The lever of the transmitter when in repose is in connection with an earth contact, and the circuit of the battery is closed locally. One part of the current passes by the helix between the battery and the transmitter, the other part by the rheostat, or shunt, also placed between the, battery and transmitter. This shunt permits the augmentation or diminution, at will, of the force which keeps the armature attracted. When the lever of the transmitter is raised, the current goes to line by traversing the helix in circuit between the transmitter and line in such a manner that the armature remains attracted. It results, that one is able to transmit without receiving his own transmission. When the two stations transmit simultaneously, currents are annulled and the armature raises itself. When the opposing station alone transmits, its current traverses the helix in circuit between the transmitter and line in an inverse manner to that of the battery at its own end, and the armature is still raised. They will receive, in the two cases, the transmission from the station corresponding; but the return current also releases the armature. The Author states that he has remedied in a certain measure this inconvenience by regulating the shunt in a manner to make the magnetisation produced by the local circuit inferior to that of the line circuit. The return current is then employed to destroy the excess of residual magnetism. P. H. Proportions of Electro-magnets. By T. DU MONCEL. (Comptes-rendus de l'Académie des Sciences, vol. lxxxv., pp. 466-71 and 652-658.) The deductions formulated by the Author in his last note upon maxima conditions for galvanometers1 can be applied to electromagnets. If in equations expressing the values F and A of the magnetic moment of the electro-magnet, and of the attraction produced, the quantity representing the diameter c of the core of the electro-magnet is varied, and an algebraic relation established between this quantity and the thickness a of the helix, which is easy, because the helix can be supposed to be wound on the iron core itself then, by placing the electro-magnet in its conditions of maximum with relation to the resistance of the exterior circuit, there can be obtained an expression susceptible of a maximum such that the relation of R to H may be that previously established or that generally admitted, or even that deduced by Weber, when there is taken into consideration the depth of the insulating covering of the wire, the relation of which is fixed by the law that the resistance of the helix should be to that of the exterior circuit as the diameter of the bare wire is to the diameter of the same wire covered. Representing by a either of these three relations, and supposing the thickness a of the helix invariable, and consequently the number of convolutions t, the attractive force A and the magnetic moment F have for expression, according to Müller's law, F = 92 Ec = g* E2 c which are susceptible of maxima with relation to c; but the quantities R and H are then supposed to vary at the same time, and in measure as the helix is elongated proportionally as the diameter of the magnetic core is increased. If the derivatives of the preceding expressions are taken with relation to c considered as variable, and equated to zero, the conditions of maximum are α = c, that is to say, the equality in width of the bobbin and diameter of the iron of the electro-magnet. Defining the limitation of Müller's law, the Author shows that direct experiment proves these deductions, and that there is advantage in winding electromagnets in such a manner that the width of the layers should be equal to the diameter of the iron core, this diameter being so 1 Vide Minutes of Proceedings Inst. C.E., vol. 1., p. 307, where the designation of the letters is given. proportioned to the electric intensity acting on the core that sufficient magnetism to approximate to the point of saturation is developed. This point of saturation has been defined by Müller in his researches on this question. Among the advantages of the law is the considerable simplification of the calculation of the elements of construction for electro-magnets. The expression for 2 π b c2 the length of the wire on the helix becomes and if the length b of the electro-magnet is made a function of the diameter c by multiplying this by a co-efficient m, which calculation shows to 2 π c3 m 75.4 c3 be 11, the expression becomes g2 or g2 g2 in which there are only the two quantities c and g to be considered. These may be determined according to the different cases that occur by means of the formulæ For a considerable time it has been the practice to make electro-magnets of small dimensions, such as those used in telegraphy, of a length equal to six times the diameter of the core; and Hughes' experiment confirmed this rule. But, in fact, this conclusion, which gives to the double branches of a horse-shoe electro-magnet a length equal to twelve times that of the cores surrounded by the coils, cannot be deduced as to maximum of effect produced from known laws of electro-magnetic forces. From an exhaustive investigation and experimental research the Author concludes, that the dimensions to be given to an electro-magnet should essentially depend upon the electric force which acts on it, and upon the resistance of the circuit in which it is interposed. When the circuit is long and the electric source of small energy, it should be long and of small diameter; when, on the contrary, the circuit is short and the electric force intense, the core should be of large diameter. For circuits of equal resistances the diameters of the electro-magnets should be proportional to the electromotive forces. For equal electro-motive forces the diameters should be in inverse ratio to the square roots of the resistances of the circuits, comprising the resistance of the batteries. For equal diameters the electro-motive forces should be proportional to the square roots of the resistances of the circuits. For a given electromotive force, and with electro-magnets placed under maximum conditions, the electro-motive forces of the batteries should be proportional to the square roots of the resistances of the circuit. P. H. |