Hence, since the time occupied in obtaining a reading of the electrometer is large in comparison with the time during which the discharge through the galvanometer takes place, it is probable that the estimate of the discharge in electrostatic measure is too high, and the value of v, derived from it, is probably also too high. II. v expressed as a Resistance. 772.] Two other methods for the determination of v lead to an expression of its value in terms of the resistance of a given conductor, which, in the electromagnetic system, is also expressed as a velocity. The In Sir William Thomson's form of the experiment, a constant current is made to flow through a wire of great resistance. The electromotive force which urges the current through the wire is measured electrostatically by connecting the extremities of the wire with the electrodes of an absolute electrometer, Arts. 217, 218. strength of the current in the wire is measured in electromagnetic measure by the deflexion of the suspended coil of an electrodynamometer through which it passes, Art. 725. The resistance of the circuit is known in electromagnetic measure by comparison with a standard coil or Ohm. By multiplying the strength of the current by this resistance we obtain the electromotive force in electromagnetic measure, and from a comparison of this with the electrostatic measure the value of v is obtained. This method requires the simultaneous determination of two forces, by means of the electrometer and electrodynamometer respectively, and it is only the ratio of these forces which appears in the result. 773.] Another method, in which these forces, instead of being separately measured, are directly opposed to each other, was employed by the present writer. The ends of the great resistance coil are connected with two parallel disks, one of which is moveable. The same difference of potentials which sends the current through the great resistance, also causes an attraction between these disks. At the same time, an electric current which, in the actual experiment, was distinct from the primary current, is sent through two coils, fastened, one to the back of the fixed disk, and the other to the back of the moveable disk. The current flows in opposite directions through these coils, so that they repel one another. By adjusting the distance of the two disks the attraction is exactly balanced by the repulsion, while at the same time another observer, 774.] METHODS OF THOMSON AND MAXWELL. 373 by means of a differential galvanometer with shunts, determines the ratio of the primary to the secondary current. In this experiment the only measurement which must be referred to a material standard is that of the great resistance, which must be determined in absolute measure by comparison with the Ohm. The other measurements are required only for the determination of ratios, and may therefore be determined in terms of any arbitrary unit. Thus the ratio of the two forces is a ratio of equality. The ratio of the two currents is found by a comparison of resistances when there is no deflexion of the differential galvanometer. The attractive force depends on the square of the ratio of the diameter of the disks to their distance. The repulsive force depends on the ratio of the diameter of the coils to their distance. The value of v is therefore expressed directly in terms of the resistance of the great coil, which is itself compared with the Ohm. The value of v, as found by Thomson's method, was 28.2 Ohms * by Maxwell's, 28.8 Ohms †. III. Electrostatic Capacity in Electromagnetic Measure. ; 774.] The capacity of a condenser may be ascertained in electromagnetic measure by a comparison of the electromotive force which produces the charge, and the quantity of electricity in the current of discharge. By means of a voltaic battery a current is maintained through a circuit containing a coil of great resistance. The condenser is charged by putting its electrodes in contact with those of the resistance coil. The current through the coil is measured by the deflexion which it produces in a galvanometer. Let be this deflexion, then the current is, by Art. 742, H π= tan 4, where H is the horizontal component of terrestrial magnetism, and G is the principal constant of the galvanometer. If R is the resistance of the coil through which this current is made to flow, the difference of the potentials at the ends of the coil is E = Ry, * Report of British Association, 1869, p. 434. + Phil. Trans., 1868, p. 643; and Report of British Association, 1869, p. 436. and the charge of electricity produced in the condenser, whose capacity in electromagnetic measure is C, will be Q Now let the electrodes of the condenser, and then those of the galvanometer, be disconnected from the circuit, and let the magnet of the galvanometer be brought to rest at its position of equilibrium. Then let the electrodes of the condenser be connected with those of the galvanometer. A transient current will flow through the galvanometer, and will cause the magnet to swing to an extreme deflexion . Then, by Art. 748, if the discharge is equal to the charge, Q = HT 2 sin 0. We thus obtain as the value of the capacity of the condenser in electromagnetic measure The capacity of the condenser is thus determined in terms of the following quantities :— T, the time of vibration of the magnet of the galvanometer from rest to rest. R, the resistance of the coil. 0, the extreme limit of the swing produced by the discharge. 4, the constant deflexion due to the current through the coil R. This method was employed by Professor Fleeming Jenkin in determining the capacity of condensers in electromagnetic measure *. If c be the capacity of the same condenser in electrostatic measure, as determined by comparison with a condenser whose capacity can be calculated from its geometrical data, The quantity v may therefore be found in this way. It depends on the determination of R in electromagnetic measure, but as it involves only the square root of R, an error in this determination will not affect the value of v so much as in the method of Arts. 772, 773. Intermittent Current. 775.] If the wire of a battery-circuit be broken at any point, and *Report of British Association, 1867. 776.] WIPPE. 375 the broken ends connected with the electrodes of a condenser, the current will flow into the condenser with a strength which diminishes as the difference of the potentials of the condenser increases, so that when the condenser has received the full charge corresponding to the electromotive force acting on the wire the current ceases entirely. If the electrodes of the condenser are now disconnected from the ends of the wire, and then again connected with them in the reverse order, the condenser will discharge itself through the wire, and will then become recharged in the opposite way, so that a transient current will flow through the wire, the total quantity of which is equal to two charges of the condenser. By means of a piece of mechanism (commonly called a Commutator, or wippe) the operation of reversing the connexions of the condenser can be repeated at regular intervals of time, each interval being equal to T. If this interval is sufficiently long to allow of the complete discharge of the condenser, the quantity of electricity transmitted by the wire in each interval will be 2 EC, where E is the electromotive force, and C is the capacity of the condenser. If the magnet of a galvanometer included in the circuit is loaded, so as to swing so slowly that a great many discharges of the condenser occur in the time of one free vibration of the magnet, the succession of discharges will act on the magnet like a steady current whose strength is 2 EC T If the condenser is now removed, and a resistance coil substituted for it, and adjusted till the steady current through the galvanometer produces the same deflexion as the succession of discharges, and if R is the resistance of the whole circuit when this is the case, We may thus compare the condenser with its commutator in motion to a wire of a certain electrical resistance, and we may make use of the different methods of measuring resistance described in Arts. 345 to 357 in order to determine this resistance. 776.] For this purpose we may substitute for any one of the wires in the method of the Differential Galvanometer, Art. 346, or in that of Wheatstone's Bridge, Art. 347, a condenser with its commutator. Let us suppose that in either case a zero deflexion of the galvanometer has been obtained, first with the condenser and commutator, and then with a coil of resistance R, in its place, then T the quantity will be measured by the resistance of the circuit of 2 C which the coil R1 forms part, and which is completed by the remainder of the conducting system including the battery. Hence the resistance, R, which we have to calculate, is equal to R1, that of the resistance coil, together with R2, the resistance of the remainder of the system (including the battery), the extremities of the resistance coil being taken as the electrodes of the system. In the cases of the differential galvanometer and Wheatstone's Bridge it is not necessary to make a second experiment by substituting a resistance coil for the condenser. The value of the resistance required for this purpose may be found by calculation from the other known resistances in the system. Using the notation of Art. 347, and supposing the condenser and commutator substituted for the conductor AC in Wheatstone's Bridge, and the galvanometer inserted in OA, and that the deflexion of the galvanometer is zero, then we know that the resistance of a coil, which placed in AC would give a zero deflexion, is су The other part of the resistance, R2, is that of the system of conductors 40, OC, AB, BC and OB, the points A and C being considered as the electrodes. Hence R2 = B(c+a) (y+a)+ca (y + a) + ya (c + a) (4) In this expression a denotes the internal resistance of the battery and its connexions, the value of which cannot be determined with certainty; but by making it small compared with the other resistances, this uncertainty will only slightly affect the value of R. The value of the capacity of the condenser in electromagnetic measure is t C= 2 (R1+R2) (5) 777.] If the condenser has a large capacity, and the commutator is very rapid in its action, the condenser may not be fully discharged at each reversal. The equation of the electric current during the discharge is dQ Q+R2C + EC = 0, (6) where is the charge, C the capacity of the condenser, R, the |