60 ELECTRICITY [DISRUPTIVE DISCHARGE. experiments; Wiedemann, on the other hand, gives ela borate accounts of the more modern results of De la Rive, Pliicker, Hittorf, and others. Theoreti- When induction is exerted across a dielectric, we may 2al con- consider the action at any point of it in one or other of sidera- j. wo wa y g ~y e ma y regard the resultant electromotive force arising from the action at a distance of all the free electricity in the field as tending to separate the two elec tricities in the molecules of the dielectric. In this view, we might measure the dielectric strength of the medium by the value of the electromotive force, when the electricity is on the point of passing from one molecule to the next. We might, on the other hand, consider, with Faraday and Maxwell, that the dielectric is the seat of a peculiar kind of stress, consisting of a tension p along the lines of force, and an equal pressure perpendicular to them, p being equal to R 2 (Maxwell, vol. i. 104). We shall adopt the latter alternative, and when we speak of tension hencefor- TT 1 ward it means R . In this view the dielectric strength may be defined as that tension under which the dielectric just begins to give way. The reader who prefers the other way of looking at the matter will find no difficulty in translating any statement from the one language into the other. We have started by considering any point of the di electric, and it is obvious that the dielectric (supposed homogeneous) will first give way at that point which first reaches the limiting tension -a- } just as an elastic solid begins to give way where the stress first reaches the breaking limit. It may be proved, however, that R 2 can not have a maximum value at any point where there is no free electricity, which shows us at once that the point at which the limiting tension is first reached must always be on some electrified surface, in general therefore on the sur face of one of the conductors of the system. 1 Disruptive discharge, thus begun at the surface of a conductor, spreads out into the dielectric. Its farther course is influenced by a variety of circumstances very hard to define in the great majority of cases. An attempt will be made by-and-by to give an idea of the varieties of luminous discharge that arise in this way; meantime we concentrate our attention on a feature common to all disruptive discharges, viz., the definite limiting tension at which under given circumstances they begin. Dielec- Dielectric Strength of Gases. The earlier measurements tr f c bearing on this subject were conducted under circumstances Bn ^ which render a compa r ison of the results with the theory, Striking as at present developed, very difficult. Harris found that striking distance between two balls connected with the armatures of a condenser was directly proportional to the charge of the condenser as measured by a Lane s jar. Riess used a Leyden battery, and varied the number of jars and the charge of the battery. The balls of his spark micrometer were of diameters 5 7 and 4 4 lines respectively, while the distance between them varied from 5 to 2 5 lines. Under these circumstances, he found the striking distance to be proportional to the charge of the battery directly, and to the number of jars inversely. The results of Harris and Riess might be summed up in the statement that the striking distance between two balls connected with the armatures of a condenser varies as the electro motive force or difference of potential between the arma tures. This result is purely empirical, and must not be extended beyond the experimental limits within which it 1 The dielectric is supposed to be homogeneous. Prof. Maxwell has pointed out that exceptions might occur in the case of a weak dielectric interposed between two strong ones, e.ff., a current of hot air passing through cold. distance. was found. Even Riess s experiments themselves show that the striking distance increases more rapidly than the difference of the potentials. The experiments of Knochenhauer 3 led to a similar result. Gaugaiti 3 made experiments of the same kind through a wider range of striking distances, and found, in conformity with the result of Riess, that, with balls of 10 or 15 mm. diameter, the striking distance is proportional to the potential difference between the balls, when the distance between them lies between 2 and 5 millimetres. Beyond these limits the ratio of potential difference to striking dis tance falls off ; whereas, for smaller jdistances, it increases very rapidly. He also found that the deviation from the law of Harris and Riess is more marked when unequal spheres (3 mm. and 10 mm.^) are used, and still more when a ball (3 mm. diam. used as + electrode) and a disc (35 mm. diam.) were used as electrodes. Experiments leading to similar conclusions are cited by Mascart, 4 who finds that, for spheres of diameter 3 to 5 centimetres, the striking distance for given potential difference is sensibly the same; whereas for plates, both the striking distance and the law of the whole phenomenon is different. The same experimenter examined the striking distances between two equal balls (3 cm. diam.) from 1 mm. up to 150 mm. Taking the potential difference for one millimetre as unity, he found for 10, 20, 40, 80, 150 mm. the potential differences 8 3, 11 8, 15 9, 20 5, 23 3. The deviation from proportionality is obvious ; the potential differences in fact tend to become constant. Wiedemann and Riihlmann, in their experiments on the passage of electricity through gases (see below, p. 61), made some experiments on the influence of the form and distance of the electrodes. They used two brass balls of 13 8 and 2 65 mm. diameter respectively, and sent between them the dis charges of a Holtz machine. The distance (8) between the nearest points varied from 3 to 22 3 mm. They found that the quantity of electricity (y) required to produce discharge, could be represented by the formulae y K- - and j/ = C + D5 2 , according as the larger o sphere formed the positive or negative electrode. The constants A, B, C, D depend on the pressure, which varied in these experi ments between 25 and 60 rum. of mercury. In most of the experiments that have just been de scribed the effect of the form of fc the electrodes and the surrounding conductors could not be estimated theoreti cally. Experiments in which the theoretical conditions are simple have been made by Sir Wm. Thomson. 5 The spark was taken between two parallel plates of consider able area; one of these was plane, and the other very slightly curved, to cause the spark to pass always at a definite place. The electrical distribution on the opposing surfaces can be found (see above, Math. Theory of Elec trical Equilibrium), as if the plates were plane and of in finite extent. This distance between the plates was measured by a micrometer, the contact reading being determined by observing when the electricity ceased to pass between the plates in the form of a spark. The potentials were measured in absolute electrostatic (C.G.S.) units, by means of Thomson s absolute electrometer (see art. ELECTROMETER). The limiting tension or dielectric strength is given in each case in grammes per centimetre, the formula for calculating it being V Sir Thorn son s exper 7iient( in which V represents the potential difference or electro motive force between the plates, and d the distance in centimetres. If we take the older view of Poisson s time that the action of the electricity on the surface of a con ductor is simply a fluid pressure, then p represents that pressure. If we could consider the air between the plates as a homogeneous dielectric, then, for air at a given pressure (and temperature 1 ?) and given state of dryness, p, which measures its dielectric strength, would have a constant value independent of the distance between .the plates, and Y would be proportional to d. A glance at Sir Wm. Thomson s 6 tables shows that this is not the case. For a 2 Mascart, t. i. 463, or Fogg. Ann., Iviii. 3 Mascart (I.e.). 4 t. i. 478. 8 Proc. R.S., 1860, or Reprint, p. 247.
6 Reprint, pp. 252, 258.