ATMOSPHERIC for certain hours of the day, along with some corresponding data obtained by Michie Smith in January 1885 on Dodabetta (8642 feet), the highest summit of the Neilgherries in India {Trans. R.S.E. vol. xxxii. p. 583), are given in Table YI. (afternoon hours dashed). Table YI. 10 Noon. Sonnblick 200 218 240 214 224 220 Dodabetta 55 67 93 108 93 69 The unit in which the potential is measured is not the same in the two cases, and the hours are not exact local mean time. Elster and Geitel’s results, except that for 6 p.m., depend on three days’ observations ; Michie Smith’s are means from five days nearly free from mist. In support of their view Elster and Geitel refer to a few observations by Exner on a hill near St. Gilgen, and to a considerable number of observations made more recently, but with apparently somewhat primitive apparatus, on the Sonnblick. In view of the large variation observed on Dodabetta, more experiments on the subject are clearly wanted. § 12. Many of the data referred to below are taken from Le Cadet’s interesting book Etude du champ electrique de VAtmosphere, Paris, 1898. For small heights use may be made of captive balloons, provided with a burning fuse, and carrying a wire attached to an electroscope on the ground. With such apparatus Exner ( Wien. Sitz. xciii., 1886, p. 222) found the potential gradient nearly uniform up to heights of 30 or 50 metres above the ground. At great heights the potential differs so much from that of the earth that captive balloons are unsuitable. Accordingly, in 1885 a free balloon ascent was made at Vienna by Lecher, at Exner’s suggestion. The potential gradient was found by using two water-droppers, with their jets at a difference of 2 metres in level. The mean of the few measurements taken made the potential gradient at a height of 550 metres nearly double that at the ground. More recent experiments, however, tend to show that Lecher’s observations, if correct, were exceptional. Perhaps the most important of these experiments are those due to Le Cadet himself. Like Lecher he employed two collectors—either water-droppers or flame-collectors—but usually with an arrangement for altering their difference of level. Table VII. gives some of Le Cadet’s results. Each value is usually the mean of a series of readings. H is the height of the balloon in metres, P the potential gradient in volts per metre. Table VII. Balloon Observations by Le Cadet.
On 11th September the value found for P at the ground was 150. The marked tendency shown in the table for P to diminish as the height increases is equally prominent in other observations by Le Cadet. Thus on 24th March 1897, at heights between 1680 and 2300 metres, P varied from 32 to 28, while its mean value at the ground as deduced from the simultaneous records of the Lyons water-dropper was 99. Similar results were observed in Germany by Baschin, during an ascent on 17th February 1894. Using two “ water-droppers ”—with 65 per cent, alcohol in the water—he found for P values of 49, 28, and 13, answering to the heights of 760, 2400, and 2800 metres respectively. During the ascent the value of P at the ground varied from 98 to 181 at Potsdam, and from 85 to 200 at Wolfenbiittel. In opposition to these results Tuma, during an ascent at Vienna in
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1892, found P to increase as the height increased from 410 to 1900 metres; but several recent ascents {Met. Zeit. for 1899, p. 280, or Wien. Sitz., March 1899) lead him to the same conclusion as Le Cadet, viz., that under normal conditions the potential gradient diminishes as the height increases. The possibility that a free balloon may carry off a charge as it leaves the earth has been discussed by Bornstein {Met. Zeit., 1898, p. 65), who shows how such a charge could be measured if the balloon carried three water-droppers at different levels. Supposing however a charge to exist initially, it would tend, as Baschin points out, to disappear when ballast was discharged. Tuma, from experiments made on several of his recent ascents, concluded that no charge existed on the balloon. § 13. If Y be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth’s centre, we2 have, sneglecting variations of Y in horizontal directions, r~ {d/dr){7 dV/dr) -t- inp — O. Throughout the limited portion of the earth’s atmosphere open to experiment, we may for practical purposes treat r2 as constant in this equation, and so take p= - {l/4:Tr)(d/dr)(dY/dr). Thus p is positive if, as recent experiments seem to show, the potential gradient, dY/dr, diminishes as We recede from the earth. If <r be the surface density of the charge on the earth, we have <r= - (l/iTr)(dV/dr) where dY/dr is the potential gradient close to the ground. As dY/dr is normally positive, the inference is that normally the earth’s surface has a negative charge. If we take a tube of force 1 cm. cross-section, and suppose it cut by the equipotential surfaces at the heights hi and above the ground, then under the conditions assumed above the total charge, M, included within the specified portion of the tube is given by 4’rM = ^Tidr=li+hi ~ where R is the earth’s radius. Le Cadet applies equivalent formulae to his balloon ascent of 11th September 18^7, assuming the potential gradient to be 150 (volt/metre) at the ground, and 13'4 (volt/metre) at 4000 metres. Supposing a volt equal to '0033 C.G.S. electrostatic units, the charge on the ground per sq. cm. is - (150/100) x -0033-^4^, or-14 approximately - '000395 electrostatic unit (in coulombs - 13 x 10 ). The charge in the unit tube of force between the ground and the height of 4000 metres works out at +'00036 C.G.S. electrostatic unit, leaving only about + '000035 electrostatic units above this level. These figures give for the average density of the charge between the height of 4 kilometres and the ground the value 9 x 10-10 electrostatic units (3 x 10~19 coulombs). This is insignificant compared with the density of the charges recently given to air by Kelvin, Maclean, and Galt (see § 17). Trabert {Met. Zeit., 1898, p. 40l) makes a similar calculation in discussing the probability-12of the existence of vertical earth-air currents of the order 17 x 10 amperes per sq. cm. The existence of such currents seems indicated by the researches of A. Schmidt and others, who have concluded that a portion of the earth’s magnetic field cannot be accounted for by a Gaussian potential (see Magnetism, Terrestrial, § 24). Trabert takes 130 (volt/metre) as the most probable mean value of the potential gradient at the ground. Answering to this, a calculation similar to Le Cadet’s makes the surface density - 11 x 10-14 coulombs per sq. cm. Thus Schmidt’s hypothetical mean current would transmit in one second fully 150 times as much electricity as exists at the instant on the earth’s surface. This would imply a rate of dissipation about one million times larger than that found by Linss and by Elster and Geitel in the absence of photo-electric action (see § 18). § 14. Elster and Geitel have attempted to measure the charge brought down by rain falling into an insulated vessel, as well as the simultaneous potential gradient in the atmosphere {Met. Zeit., 1888, p. 95; Wien. Sitz. xcix. Abth. ii., 1890, p. 421 ; Terrestrial Magnetism, March 1899, p. 15). There are various serious difficulties— splashing of rain-drops, influence of apparatus, surgings in the electrometer, Ac.—and though Elster and Geitel have done their best to surmount these, they seem somewhat doubtful of their complete success. The conclusions indicated by the experiments are : (1) raindrops almost invariably carry a charge; the sign may be positive or negative, and may change repeatedly in the course of a single rainstorm; (2) the charge is more often than not opposite in sign to the simultaneous value of the potential gradient near the ground. On 11th May 1892, S. L—98
