Frictional machines were, in time, gradually superseded by the second class of instrument mentioned above, namely, influence machines. These operate by electrostatic induction and convert mechanical work into electrostatic energy by the aid of a small initial charge which is continually being replenished and reinforced. The first suggestion of an influence machine appears to have grown out of the invention of Volta's electrophorus. The electrophorus is a single-plate capacitor used to produce imbalances of electric charge via the process of electrostatic induction. The next step was when Abraham Bennet, the inventor of the gold leaf electroscope, described a "doubler of electricity" (Phil. Trans., 1787), as a device similar to the electrophorus, but that could amplify a small charge by means of repeated manual operations with three insulated plates, in order to make it observable in an electroscope. Erasmus Darwin, W. Wilson, G. C. Bohnenberger, and (later, 1841) J. C. E. Péclet developed various modifications of Bennet's device. In 1788, William Nicholson proposed his rotating doubler, which can be considered as the first rotating influence machine. His instrument was described as "an instrument which by turning a winch produces the two states of electricity without friction or communication with the earth". (Phil. Trans., 1788, p. 403) Nicholson later described a "spinning condenser" apparatus, as a better instrument for measurements.
Others, including T. Cavallo (who developed the "Cavallo multiplier", a charge multiplier using simple addition, in 1795), John Read, Charles Bernard Desormes, and Jean Nicolas Pierre Hachette, developed further various forms of rotating doublers. In 1798, The German scientist and preacher Gottlieb Christoph Bohnenberger, described the Bohnenberger machine, along with several other doublers of Bennet and Nicholson types in a book. The most interesting of these were described in the "Annalen der Physik" (1801). Giuseppe Belli, in 1831, developed a simple symmetrical doubler which consisted of two curved metal plates between which revolved a pair of plates carried on an insulating stem. It was the first symmetrical influence machine, with identical structures for both terminals. This apparatus was reinvented several times, by C. F. Varley, that patented a high power version in 1860, by Lord Kelvin (the "replenisher") 1868, and by A. D. Moore (the "dirod"), more recently. Lord Kelvin also devised a combined influence machine and electromagnetic machine, commonly called a mouse mill, for electrifying the ink in connection with his siphon recorder, and a water-drop electrostatic generator (1867), which he called the "water-dropping condenser".
Between 1864 and 1880, W. T. B. Holtz constructed and described a large number of influence machines which were considered the most advanced developments of the time. In one form, the Holtz machine consisted of a glass disk mounted on a horizontal axis which could be made to rotate at a considerable speed by a multiplying gear, interacting with induction plates mounted in a fixed disk close to it. In 1865, August J. I. Toepler developed an influence machine that consisted of two disks fixed on the same shaft and rotating in the same direction. In 1868, the Schwedoff machine had a curious structure to increase the output current. Also in 1868, several mixed friction-influence machine were developed, including the Kundt machine and the Carré machine. In 1866, the Piche machine (or Bertsch machine) was developed. In 1869, H. Julius Smith received the American patent for a portable and airtight device that was designed to ignite powder. Also in 1869, sectorless machines in Germany were investigated by Poggendorff.
The action and efficiency of influence machines were further investigated by F. Rossetti, A. Righi, and F. W. G. Kohlrausch. E. E. N. Mascart, A. Roiti, and E. Bouchotte also examined the efficiency and current producing power of influence machines. In 1871, sectorless machines were investigated by Musaeus. In 1872, Righi's electrometer was developed and was one of the first antecedents of the Van de Graaff generator. In 1873, Leyser developed the Leyser machine, a variation of the Holtz machine. In 1880, Robert Voss (a Berlin instrument maker) devised a form of machine in which he claimed that the principles of Toepler and Holtz were combined. The same structure become also known as the Toepler-Holtz machine. In 1878, the British inventor James Wimshurst started his studies about electrostatic generators, improving the Holtz machine, in a powerful version with multiple disks. The classical Wimshurst machine, that become the most popular form of influence machine, was reported to the scientific community by 1883, although previous machines with very similar structures were previously described by Holtz and Musaeus. In 1885, one of the largest-ever Wimshurst machines was built in England (it is now at the Chicago Museum of Science and Industry). In 1887, Weinhold modified the Leyser machine with a system of vertical metal bar inductors with wooden cylinders close to the disk for avoiding polarity reversals. M. L. Lebiez described the Lebiez machine, that was essentially a simplified Voss machine (L'Électricien, April 1895, pp. 225–227). In 1894, Bonetti designed a machine with the structure of the Wimshurst machine, but without metal sectors in the disks. This machine is significantly more powerful than the sectored version, but it must usually be started with an externally-applied charge.
In 1898, the Pidgeon machine was developed with a unique setup by W. R. Pidgeon. On October 28 that year, Pidgeon presented this machine to the Physical Society after several years of investigation into influence machines (beginning at the start of the decade). The device was later reported in the Philosophical Magazine (December 1898, pg. 564) and the Electrical Review (Vol. XLV, pg. 748). A Pidgeon machine possesses fixed inductors arranged in a manner that increases the electrical induction effect (and its electrical output is at least double that of typical machines of this type ). The essential features of the Pidgeon machine are, one, the combination of the rotating support and the fixed support for inducing charge, and, two, the improved insulation of all parts of the machine (but more especially of the generator's carriers). Pidgeon machines are a combination of a Wimshurst Machine and Voss Machine, with special features adapted to reduce the amount of charge leakage. Pidgeon machines excite themselves more readily than the best of these types of machines. In addition, Pidgeon investigated higher current "triplex" section machines (or "double machines with a single central disk") with enclosed sectors (and went on to receive British Patent 22517 (1899) for this type of machine).
Multiple disk machines and "triplex" electrostatic machines (generators with three disks) were also developed extensively around the turn of the 19th to 20th century. In 1900, F. Tudsbury discovered that enclosing a generator in a metallic chamber containing compressed air, or better, carbon dioxide, the insulating properties of compressed gases enabled a greatly improved effect to be obtained owing to the increase in the breakdown voltage of the compressed gas, and reduction of the leakage across the plates and insulating supports. In 1903, Alfred Wehrsen patented an ebonite rotating disk possessing embedded sectors with button contacts at the disk surface. In 1907, Heinrich Wommelsdorf reported a variation of the Holtz machine using this disk and inductors embedded in celluloid plates (DE154175; "Wehrsen machine"). Wommelsdorf also developed several high-performance electrostatic generators, of which the best known were his "Condenser machines" (1920). These were single disk machines, using disks with embedded sectors that were accessed at the edges.
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