Journal of Electrostatics, 6 (1979) 1--13 1 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands TWO HUNDRED YEARS OF LICHTENBERG FIGURES YUZO TAKAHASHI Department of Electrical Engineering, Chuo University, Kasuga 1--13--27, Bunkyo-ku, Tokyo (Japan) (Received April 4, 1978) Summary Lichtenberg discovered dust figure phenomena of electrical discharges in 1777. His discovery came to the notice of many scientists because it was considered that the figures should show the motion of the electric fluid. Photographic Lichtenberg figures were obtained in the middle of the nineteenth century. Both of these figures, usually called "Lichtenberg figures", have been utilized in the study of electrical discharges. There are many figures, other than Lichtenberg figures, that give a pattern indication of the influence ~r result of a discharge.The era of modern studies of Lichtenberg figures and creepage discharges was opened by Toepler late in the nineteenth century. Some useful figures, such as liquid-crystal Lichtenberg figures and figures by the liquid-development method, have been introduced recently. 1. Introduction When powder is dusted over a dielectric plate after an electrical discharge has been on it, the power adheres to the surface and appears as a characteristic pattern. Such a pattern can also be obtained on a photographic plate or film by developing in the usual way. Both patterns are called "Lichtenberg figures/ Lichtenberg'sche Figuren"; the former are called "dust figures/Staubfiguren", the latter "photographic Lichtenberg figures". In this paper, photographic Lichtenberg figures are referred to as "photographic figures" for short. Two hundred years have passed since G.Chr. Lichtenberg discovered dust figure phenomena in 1777. His discovery came to the notice of many scientists in those days because of the expected possibility of being able to study the electric fluid. They have been utilized as a method of investigating electrical discharges up to the present. The history of the study of Lichtenberg figures and related figures is surveyed in the present paper. Some examples of Lichtenberg figures are shown in Figs. 1 and 2. Lichten- berg figures are more or less perm_anent records of discharges. It is not easy to measure characteristics of discharges, because they develop and diappear very quickly. When Lichtenberg figures are utilized, the residual charge or the dis- charge channels can be seen after the discharge has disappeared, and so Lichtenberg figures can be very useful. Since they give information as patterns, rod erectrode /dielectric ,\ (a) plane electrode Fig. 1. Dust figures in a mixture of 1% SF~ and 99% N2 at atmospheric pressure, applied voltage: 1)< 40 us lightning impulse. (a) Electrode arrangement; (b) negative figure (-25 kV); (c) positive figure, enlarged (+20 kV). By courtesy of Mr. M. Chiba. they are particularly useful in the study of creepage discharges where the length and form of the channel are to be investigated. In the case of dust figures, one can discriminate the polarity of the residual charge using a mixture of certain powders. The form or dimension of Lichtenberg figures depends upon the polarity, magnitude and wave shape of the applied voltage, and also upon the kind and pressure of the gas: positive figures in the air are star-like, and negative moon-like; positive figures develop as trees with increasing applied voltage, while negative ones become fan-shaped figures; positive figures are larger than negative ones at a given applied voltage; the length of figures decrease as the gas pressure is raised; at low pressure, figures are larger than those at atmos- pheric pressure. 2. Discovery of Lichtenberg figures Lichtenberg, who was a Professor of GSttingen University, found his dust figures unexpectedly, and his discovery was reported at the Royal Society of Science of GSttingen on May 3, 1777. Because of his illness, the report was read not by himself but by his teacher, Professor A.G. K~istner. At the public Fig. 2. Photographic Lichtenberg figures in air, applied voltage: 15 ms × 15 min impulse. (a) Negative figure (-15 kV), pressure 0.2 MPa; (b) positive figure (+15 kV), 0.1 MPa; (c) positive figure (+20 kV), 0.6 MPa. meeting on February 21, 1778, Lichtenberg read a report entitled "De nova methodo naturam ac motum fluidi electrici investigandi" (On a new method to investigate the motion of electric fluid.). Part of its text [1] is as follows: "(At that time Lichtenberg made a huge electrophorus of about 2 m in diameter. It was so powerful that a spark of about 40 cm in length could be produced.) ... The occasion of observing this phenomenon (dust figure) was as follows: About the beginning of spring 1777 my electrophorus was just finished. In my room all was still covered with very fine rosin powder that had risen during planing and polishing of the cake and the metal disk, and later it lay on walls and books. When air motion occurred, it deposited on the metal disk of the electrophorus, to my great annoyance. However, it was not until I had hung the disk on the ceiling of the room many times, that the powder deposited on the cake; then I could not cover it uniformly as had occurred on the metal disk, but to my great joy it was arranged like small stars at certain points. These were dull in the beginning and difficult to see; when I sprinkled more dust intentionally, however, they became very clear and often resembled embossed work. Sometimes innumerable stars, the Milky Way and bigger suns appeared. The bows were dull on their concave side, and decorated manifoldly with rays on their convex side. Marvellous small twigs emerged; the twigs produced by frost on window glass resemble them. Small clouds of many various forms and grades of shading and finally different figures of particular shape were seen .... However, a very pleasant play occurred to me, when I saw that these figures could scarcely be destroyed. Even if I wiped off the dust carefully with a feather or a hare's paw, I could nevertheless not prevent that the figures, which were destroyed just before, quickly developed again to some extent anew and still wonderfully. Therefore, I painted a piece of black paper with adhesive paste, laid it down on the figures and pressed it on them lightly. So I succeeded in making several copies of the figures. I have presented these six copies to the Royal Society. This new variety of printing was very favourable for me in order to progress further very quickly, because I had neither pleasure nor time to sketch or destroy all the figures." These figures must have been extraordinarily impressive. Lichtenberg noticed that they appeared where light sparks had gone from the metal disk to the cake of electrophorus. So it was, in this way, that Lichtenberg figures were found. Lichtenberg thought that the figures should show the true nature of electricity or motion of the electric fluid. He confirmed that "+E" figures were star-like, and "-E" figures moon-like. He tried various dusts and cakes; fine sulphur or rosin in a linen pouch was best for powdering; he used also amber, cinnaber, lycopodium, sugar, wheat flour, metal filings, etc. He carried out experiments in vacuum and concluded that both "+E" and "-E" figures were bigger than those in the air. Lichtenberg's discovery aroused great interest in scientists and natural philosophers of the day because of the fine impressive shape of the figures and also because of the expectation that the true nature of the electric fluid could be clarified by the figures. There were "the two-fluids theory" and "the one- fluid theory" of electricity. Scientists expected that the controversy between the theories would come to an end through the study of Lichtenberg figures. Lichtenberg himself, however, remained wary of the theoretical interpretations of his figures and did not take sides. He introduced sumbols of "+" and ..... into the description of electricity instead of "positive" and "negative", as he thought that these symbols could suggest "too much or too little fluid" or "two fluids". Lichtenberg stated that the figures could be utilized to discriminate the polarity of electricity. He proposed an instrument that would be of use to indicate atmospheric electricity. It was composed of a rotating cylinder, driven by clockwork, with a rod on it. If an iron string from a kite would be connected to the rod, the change in atmospheric electricity could be recorded on the cylinder, which was coated with resin. This idea is similar to the klydonograph of our day. However, it is not likely that Lichtenberg constructed this instrument. 3. Georg Christoph Lichtenberg G.Chr. Lichtenberg was born on July 1, 1742 in Oberramstadt, near Darm- stadt in Germany, as the seventeenth child of a pastor. His body was weak throughout his life, but he was a versatile and prominent thinker. His father passed away when he was nine years old. Georg Christoph, however, was able to study at GSttingen University with the aid of the Lord of Hessen; he specialized in mathematics. In 1770 he was appointed as Professor (Extra- ordinarius) in pure and applied mathematics of G5ttingen University. He later became Ordinarius, and stayed at G5ttingen University until the end of his life. He brought about remarkable changes in geophysics, geodesy and astronomy, and took great interest in experimental physics in his later years. In the field of electricity, the discovery of the phenomenon of Lichtenberg figures is one of the most famous and important, and led to his development of the double electrophorus. In addition, the study of atmospheric electricity and a lightning rod, and the idea of a shielding cage were included in his work.