12 ELECTRICITY [HISTORY. by Kirchhoff to the case of conductors in three dimensions. The most important of all the recent contributions to this part of electrical science is the theory of Clerk Maxwell, which aims at deducing the phenomena of the electromag netic field from purely dynamical principles with the aid of the fewest possible hypotheses (Phil. Trans., 1864; Elec tricity and Magnetism, 1873). He has established the gene ral equations which determine the state of the electric field, and he has by means of these equations constructed an electromagnetic theory of light, which is full of suggestions for the philosopher, whether speculative or experimental. The theory of Helmholtz, and his valuable criticisms on the works of those that have laboured in this department, are to be found in three memoirs already alluded to. Magneto-electricity has been largely applied in the arts. One of the first machines for producing electricity by induction was made by Pixii. It consisted of a fixed chines, horseshoe armature wound with copper wire, in front of which revolved about a vertical axis a horseshoe mag net. The machine was furnished with a commutator for delivering the alternating currents in a common direction. By means of this machine Faraday and Hachette decomposed water and collected the disengaged gases separately. Many variations of this type of ma chine were constructed by Ritchie, Saxton, Clark, Von Ettingshausen, Stohrer, Dove, "Wheatstone, and others. In 1857 Siemens effected a great improvement by in venting the form of armature which bears his name. The next improvement was to replace the fixed magnets by electromagnets, the current for which was furnished by a small auxiliary machine. Wilde s machine (1867) is of this kind. Siemens, Wheatstone, and others sug gested that the fixed electromagnet should be fed by a coil placed on the armature itself, so that starting from the residual magnetism of the armature the ma chine goes on increasing its action up to a certain point. Ladd s machine (1867) is constructed on this principle. The most recent of these machines is that of Gramme, the peculiarity of which is that the coil of the armature is divided up into a series of coils arranged round an axis, the object being to produce a continuous instead of a fluctuating current. It has been proposed of late to employ electromagnetic machines in lighting streets and workshops, and the experiment has been tried with some success. They have been employed for some time back in lighthouse work. The most important inductive appa ratus for the physicist is the induction coil or inducto- rium, which has been brought to great perfection in the workshop of Ruhmkorff. Poggendorff (Annalen, 1855) suggested several improvements in this kind of appa ratus. Fizeau, who added the condenser (1853), Fou- cault, who designed the interrupter which bears his name (1855), and Ritchie, who devised the plan of dividing the coil into sections by insulating partitions, have all aided in bringing the instrument to perfection. Very powerful machines of this kind have been constructed. A large one in the Polytechnic Institution, London, gives a 29-inch spark, and one recently constructed by Apps for Mr Spottiswoode gives a spark of 4-2 inches. The mathe matical theory of magneto-electric machines has been treated by Maxwell (Proc. Roy. Soc., 1867). He has also given a theory of the action of the condenser in the induc- iorium (Phil. Mag., 1868). Two papers by Strutt (now Lord Rayleigh) in Phil. Mag., 1869-70, are very interest ing in connection with the same subject. Ohm s In the year 1827 Dr G. S. Ohm rendered a great service law. to the science of electricity by publishing his mathematical theory of the galvanic circuit (Die Galvanische Kette mathematisch bearbeitet). Before his time the quantita tive circumstances of the electric current bad been indicated in a very vague way by the use of the terms " intensity " Elec "and " quantity," to which no accurately defined meaning mot i was attached. Ohm s service consisted in introducing and ? J " defining the accurate notions electromotive force, current ai)( i strength, and resistance. He indicated the connection of eurn these with experiment, and stated his famous law that the stiei electromotive force divided by the resistance is equal to the strength of the current. The theory on which Ohm based his law may be and has been disputed, but the law itself and the applications which Ohm and others have made of it are in the fullest agreement with all known facts. The merit of Ohm really con sists in having satisfactorily analysed a great group of phenomena which had up to his time baffled all those who attempted the task. How great his service was is easily seen when we remark the progress of those who adopted his ideas as compared with those who for a time hesitated to do so. Ohm was guided in his mathematical work by analogy with the problem of the flux of heat, and intro duced for the first time into the theory of the pile, the equivalent of the modern word potential. Ohm s word was electroscopic force or tension (Spannung), and he showed that the fall of the potential is uniform along a homogeneous linear conductor. He considered that the potential was analogous to the temperature, and the flow of electricity to the flow of heat, so that the former just as much as the latter obeys the law of continuity, Ohm verified his theo retical conclusions with thermo-electric piles, and he ob served, as Erman (Gi/b. Ann., 1801) had done before him, the differences of potential at different points of the cir cuit. Davy, Pouillet, and Becquerel laboured at the experimental verification of Ohm s law, and a great body of evidence was given by Fechner in his Maashestim-_ mungen iiber die Galvanische Kette (1831). The law of the fall of potential was verified by the elder Kohlrausch, who employed in his researches Volta s condenser and Dell- mann s electrometer (Pogg. Ann., Ixxv., 1848). Later researches of a similar nature were made by Gaugain and Branly. Among recent investigations bearing on Ohm s law, the most remarkable is the verification for electrolytes by Kohlrausch (the younger) and Nippoldt. They principally used alternating currents in their researches, which were furnished by a " sine inductor," the measuring instrument employed being the electro-dynamometer of Weber. In the report of the British Association for 1876 an account is given of some experiments, 1 in which the testing of this law seems to have been carried to the limit of experimental resources. It must now be allowed to rank with the law of gravitation and the elementary laws of statical electricity as a law of nature in the strictest sense. Many remarkable applications of Ohm s law have been made of late, in par ticular to linear conductors by Ohm, Poggendorff, and especially Kirchhoff (Pogg. Ann., 1845-7-8). The works of Helmholtz, Smaasen, and Kirchhoff on conduction in three dimensions must also be mentioned. Very import ant, on account of the experimental results with which they deal, are the calculations of Du Bois Reymond (Pogg., Ixxi., 1845) and Riemann (Werke, Leipsic, 1876) on Nobili s rings, and of Kirchhoff (Por/y., Ixvii., 1848), W. R. Smith (Proc. Roy. Soc. Edin., 1869-70), Quincke, Stefan, Adams, and others on conduction in plates. Theo retical applications to the varying currents in submarine cables of great interest have been made by Thomson (Phil. Mag., 1856) and Kirchhoff (Pogg. Ann., 1857), while practical researches of the greatest importance to tele graphy have been made on this and kindred subjects by Faraday, Wheatstone, Guillemin,Varley, Jenkin, and others. Great improvements in galvanometers and galvanometry 1 Suggested mainly by Prof. Clerk Maxwell, and carried out by the
present writer.