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Rh exactly similar to that which would exist if the sphere were removed and a negative point charge −qr/d were placed at B. Hence this charge is the electrical image of the charge +q at A in the spherical surface.

We may generalize these statements in the following theorem, which is an important deduction from a wider theorem due to G. Green. Suppose that we have any distribution of electricity at rest over conductors, and that we know the potential at all points and consequently the level or equipotential surfaces. Take any equipotential surface enclosing the whole of the electricity, and suppose this to become an actual sheet of metal connected to the earth. It is then a zero potential surface, and every point outside is at zero potential as far as concerns the electric charge on the conductors inside. Then if U is the potential outside the surface due to this electric charge inside alone, and V that due to the opposite charge it induces on the inside of the metal surface, we must have U + V = 0 or U = −V at all points outside the earthed metal surface. Therefore, whatever may be the distribution of electric force produced by the charges inside taken alone, it can be exactly imitated for all space outside the metal surface if we suppose the inside charge removed and a distribution of electricity of the same sign made over the metal surface such that its density follows the law

= − dU /dn (27),

where dU/dn is the electric force at that point on the closed equipotential surface considered, due to the original charge alone.

—For further developments of the subject we must refer the reader to the numerous excellent treatises on electrostatics now available. The student will find it to be a great advantage to read through Faraday’s three volumes entitled Experimental Researches on Electricity, as soon as he has mastered some modern elementary book giving in compact form a general account of electrical phenomena. For this purpose he may select from the following books: J. Clerk Maxwell, Elementary Treatise on Electricity (Oxford, 1881); J. J. Thomson, Elements of the Mathematical Theory of Electricity and Magnetism (Cambridge, 1895); J. D. Everett, Electricity, founded on part iii. of Deschanel’s Natural Philosophy (London, 1901); G. C. Foster and A. W. Porter, Elementary Treatise on Electricity and Magnetism (London, 1903); S. P. Thompson, Elementary Lessons on Electricity and Magnetism (London, 1903)·

When these elementary books have been digested, the advanced student may proceed to study the following: J. Clerk Maxwell, A Treatise on Electricity and Magnetism (1st ed., Oxford, 1873; 2nd ed. by W. D. Niven, 1881; 3rd ed. by J. J. Thomson, 1892); Joubert and Mascart, Electricity and Magnetism, English translation by E. Atkinson (London, 1883); Watson and Burbury, The Mathematical Theory of Electricity and Magnetism (Oxford, 1885); A. Gray, A Treatise on Magnetism and Electricity (London, 1898). In the collected Scientific Papers of Lord Kelvin (3 vols., Cambridge, 1882), of James Clerk Maxwell (2 vols., Cambridge, 1890), and of Lord Rayleigh (4 vols., Cambridge, 1903), the advanced student will find the means for studying the historical development of electrical knowledge as it has been evolved from the minds of some of the master workers of the 19th century.

ELECTROTHERAPEUTICS, a general term for the use of electricity in therapeutics, i.e. in the alleviation and cure of disease. Before the different forms of medical treatment are dealt with, a few points in connexion with the machines and currents, of special interest to the medical reader, must first be given.

Faradism.—For the battery required either for faradism or galvanism, cells of the Leclanché type are the most satisfactory. Being dry they can be carried in any position, are lighter, and there is no trouble from the erosion of wires and binding screws, such as so often results from wet cells. The best method of producing a smooth current in the secondary coil is for the interruptor hammer to vibrate directly against the iron core of the primary coil. For this it is best that the interruptor be made of a piece of steel spring, as a high rate of interruption can then be maintained, with a fairly smooth current in the secondary coil. This form of interruptor necessitates that the iron core be fixed, and variation in the primary induced current is arranged for by slipping a brass tube more or less over the iron core, thus cutting off the magnetic field from the primary coil. The secondary current (that obtained from the secondary coil) can be varied by keeping the secondary coil permanently fixed over the primary and varying the strength of the primary current. Where, as suggested above, the iron core is fixed, the primary and secondary induced currents will be at their strongest when the brass tube is completely withdrawn. As there is no simple means of measuring the strength of the faradic current, it is best to start with a very weak current, testing it on the muscles of one’s own hand until these begin to contract and a definite sensory effect is produced; the current can then be applied to the part, being strengthened only very gradually.

Galvanism.—For treatment by galvanism a large battery is needed, the simplest form being known as a “patient’s battery,” consisting of a variable number of dry cells arranged in series. The cells used are those of Leclanché, with E.M.F. (or voltage) of 1.5 and an internal resistance of .3 ohm. Thus the exact strength of the current is known; the number of cells usually employed is 24, and when new give an E.M.F. of about 36 volts. By using the formula C = E/R, where E is the voltage of the battery, R the total resistance of battery, electrodes and the patient’s skin and tissues, and C the current in amperes, the number of cells required for any particular current can be worked out. The resistance of the patient’s skin must be made as low as possible by thoroughly wetting both skin and electrodes with sodium bicarbonate solution, and keeping the electrodes in very close apposition to the skin. A galvanometer is always fitted to the battery, usually of the d’Arsonval type, with a shunt by means of which, on turning a screw, nine-tenths of the inducing current can be short-circuited away, and the solenoid only influenced by one-tenth of the current which is being used on the patient. In districts where electric power is available the continuous current can be used by means of a switchboard. A current of much value for electrotherapeutic purposes is the sinusoidal current, by which is meant an alternating current whose curve of electromotive force, in both positive and negative phase, varies constantly and smoothly in what is known as the sine curve. In those districts supplied by an alternating current, the sinusoidal current can be obtained from the mains by passing it through various transformers, but where the main supply is the direct or constant current, a motor transformer is needed.

Static Electricity.—For treatment by static electricity the Wimshurst type of machine is the one most generally used. A number of electrodes are required; thus for the application of sparks a brass ball and brass roller electrode, for the “breeze” a single point and a multiple point electrode, and another multiple point electrode in the form of a metal cap that can be placed over the patient’s head. The polarity of the machine must always be tested, as either knob may become positive or negative, though the polarity rarely changes when once the machine is in action. The oldest method of subjecting a patient to electric influence is that in which static electricity is employed. The patient is insulated on a suitable platform and treated by means of charges and discharges from an electrical machine. The effect is to increase the regularity and frequency of the pulse, raise the blood pressure and increase the action of the skin. The nervous system is quieted, sleep being promoted, the patient often becoming drowsy during the application. If while the patient is being treated a point electrode is brought towards him he feels the sensation of a wind blowing from that point; this is an electric breeze or brush discharge. The breeze is negative if the patient is positively charged and vice versa. The “breeze discharge” treatment is especially valuable in subduing pain of the superficial cutaneous nerves, and also in the treatment of chronic indolent ulcers. Quite recently this form of treatment has been applied with much success to various skin lesions—psoriasis, eczema and pruritus. Static electricity is also utilized for medical purposes by means of “sparks,” which are administered with a ball electrode, the result being a sudden muscular contraction at the point of application. The electrode must be rapidly withdrawn before a second spark has time to leap across, as this is a severe form of treatment and must be administered slowly. It is mainly employed for muscular stimulation, and the contractions resulting from spark stimulation can be produced in cases of nerve injury and degeneration, even when the muscles have lost their reaction to faradism. The sensory stimulation of this form of treatment is also strong, and is useful in hysterical anaesthesia and functional paralysis. Where a milder sensory stimulation is required friction can be used, the electrode being in the form of a metal roller which is moved rapidly outside the 