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features:-Three heavy brass plates, A, B, and C (fig. 1), each 12 × 14 inches, are fastened parallel to one another, and are capable of being separated each from the other through a range of several inches. Each plate is held in position by four insulating strips of ebonite which extend out from its edge; four iron rods, with a screw-thread cut upon their entire length, pass through the ends of the ebonite strips, which may be secured in any position upon the rods by bolts one above and one below each strip (figs. 1, 2, and 3). At the centre of each of the two outside plates, and perpendicular to them, is fastened a heavy brass tube. A rod, half of which is brass and half ebonite, slides in this tube, the ebonite portion extending between the plates; and the whole is capable of being moved in the tube by means of a rack and pinion. A scale, divided into twentieths of a centim., is marked upon the brass portion of the rod, and a vernier is attached to the side of a section cut in the tube. Each of the ebonite rods carries at its end between the large plates a thin plane plate of glass; its surface facing the centre plate being covered with a thin metal foil. These two small plates are as nearly as possible parallel to the parallel large plates, and their position between them is given by the vernier scale. The two outside plates, B and C, are connected by a brass rod, as shown in fig. 1. At the centre of this rod is a brass ball kept well polished, which is capable of adjustment towards or away from the centre plate, by having the ends of the brass rod made to slide in tubes fitted to the two outside plates. The ball may also be rotated about the rod as an axis, or moved up and down. Another ball, nearly opposite the first, is fastened to the centre plate by a short metal pin, which permits it also to be rotated. This arrangement of the two balls allows them to have a wide range of adjustment in relation to each other, and permits different portions of their untarnished surfaces to be brought opposite.
This apparatus is arranged as follows:-The two outside plates are connected to the earth. One terminal of a large induction-coil is also connected to the earth, while the other is attached to the ball, n, which is fastened to the centre plate. When the balls are separated about 6 or 8 millim., sparks pass between them when the coil is put in operation.
We have here an oscillating electric system. The lines of force divide themselves between the two halves of the apparatus, reaching from the centre plate to the two outside plates. In the region of the small plates, the field may be considered as practically uniform. Hence, if these two small plates are at equal distances from the centre plate, which we consider for
the present as midway between the outside plates, they are always at the same potential with respect to each other.
If a slab of dielectric be now placed upon the centre plate and beneath the movable plate, it will have two effects: 1st, to make the capacity upon its side of the centre plate greater than it is upon the other side; and, 2nd, to raise the potential at any point above it to a higher value than is the potential at a corresponding point upon the opposite side of the middle plate. Therefore, in order to keep the two small plates at an equal potential in reference to each other, they must be placed at unequal distances from the centre plate. The value of the specific inductive capacity of a substance is deduced in a manner presently to be shown, from the relative positions of these plates. Either one or two slabs of dielectric may be used, and several different dispositions may be given to the apparatus in a manner serving to prove the correctness of the determinations.
As the object of the experiment is to make a comparison of the values of the specific inductive capacity when obtained under slowly and rapidly oscillating fields, it becomes necessary, in obtaining the value under the latter condition, to completely separate out any slow changes in potential, which the centre plate may be subject to, from the rapid changes which take place when oscillation occurs, and which alone are to be made use of. It follows as a consequence of the large self-induction of the secondary of the induction-coil, that the potential of the plate to which the coil is attached rises slowly at first, until, finally, it becomes sufficiently high to break down the dielectric of the spark-gap; the rapid oscillations occurring only during the passage of the sparks. The following method was successfully employed to tell when the movable plates had the same potential in reference to each other, and to "weed" out the effects of the rapid oscillation to be used from any effects of slow changes in potential which might take place.
Two fine wires were led from the movable plates to the primary of a highly insulated transformer which was distant about 2 feet from the apparatus (figs. 1 and 2). The secondary of the transformer had its terminals end in a sparkgap. This was made by approximating the points of two needles, fastened to the end of a small slab of paraffin held in a wooden clamp. One needle was made to slide in a fine glass tube, to allow the length of the spark-gap to be readily adjusted. It may be mentioned here that any device which has an appreciable capacity as compared with that of the movable plates cannot be employed to show when these plates have
the same potential, if the spark-gap is used directly connected. to the plates; and such is the case when the apparatus is used with slowly varying fields. When the plates are connected with the primary of the transformer, it is not a disadvantage to add capacity to the secondary. However, after trying a large number of devices such as a telephone, electrometer, electroscope, &c., a spark-gap was found to be the simplest, most accurate, and in all respects the most convenient arrangement both with slowly changing and oscillating fields. One reason why the spark-gap best serves the purpose is because it requires at least 300 volts to make a spark pass, and consequently small and irregular alterations in potential are not shown. An electrometer-needle, on the other hand, keeps up a continual oscillation which is very confusing. A lens was adjusted in front of the spark-gap, and the room darkened when readings were taken. The transformer which was finally adopted, after many trials of different forms, consisted of fine wire wound upon two glass tubes which slid over each other; the wire upon the inner one forming the primary, that upon the outer one the secondary. The inside tube was 14 inches in diameter and 7 inches long. This tube was given a thin coating of paraffin to insure high insulation; and in this was traced, with the aid of a lathe, a uniform spiral groove, there being in all 55 turns, 16 to the inch. No. 42 copper wire was wound in this groove, and the ends, soldered to terminal loops of somewhat larger wire, were secured at the ends of the tubes with drops of sealing-wax. The secondary, made in the same manner, consisted of 116 turns of wire of the same size, wound in a groove 35 turns to the inch. When all is in proper adjustment for oscillating fields, and the two small plates are at unequal potentials, bright sparks pass at the detector spark-gap, whenever rapid oscillations in the potential of the centre plate occur. If, however, the two balls (p and n, fig. 1, Pl. III.) are so far separated that no sparks can pass between them, the potential of the centre plate is then only varying at a slow rate and no sparks pass at the detector spark-gap, for the change of induction in the secondary is not sufficiently rapid to raise the potential to the 300 volts or more required to break down the dielectric. This point was carefully tested by working the coil-which had a sparking distance of 4 inches-to its full capacity and so placing the movable plates as to be always at the greatest difference of potential in reference to each other. Unless sparks passed between the balls, no sparks whatever passed at the detector spark-gap. But whenever sparks did pass between the balls, so that rapid oscillations were taking place, Phil. Mag. S. 5. Vol. 39. No. 236. Jan. 1895. G
bright sparks at the spark-gap always occurred. This was considered proof that whenever the transformer was employed, only the effects of the rapid oscillations were being observed.
If, now, the transformer is dispensed with, and the wires from the movable plates are connected directly to the sparkgap, and the two balls (p and n, fig. 1) are separated so that no sparks can pass between them, then evidently we have a slowly changing field, and the movable plates are, as before shown, at the same potential in reference to each other when the sparks go out at the detector spark-gap. The manner of taking the observations and the results obtained will be given after describing the mathematical theory of the method.
THEORY OF THE METHOD.
The apparatus may be disposed in two distinct ways:-1st. Where one block of dielectric is used which is placed in the apparatus, as shown in fig. 1. 2nd. Where two equal slabs of dielectric are used and disposed, as shown in fig. 4.
CASE I. Where one Slab of Dielectric is used. Let V be the potential at any instant of the plate A, while the potentials of B and C are always kept at zero. Let the adjustable plates, M and N, be so placed as to have partitions upon opposite sides of A where the potential at any instant is Then for the side AB of the double condenser,
where K is the specific inductive capacity of the dielectric to be measured (K, fig. 1), and d1, d4 are the distances shown in fig. 1, and o' is the surface-density upon the upper side of plate A. This gives
where σ is the surface-density upon the lower side of plate A. Equating the second members of (1) and (2) we obtain
Considering a unit area in the middle of plate A, o'=e'
for the upper side of the plate, and σe for the under side, where e' and e are the quantities of electricity upon unit area of the respective sides. Whence we have for the capacities d and c of unit areas of the two sides, c'e'V=V and
Now, if the dielectric is as large as the plates, and these are not too far apart, the field may be taken as uniform over an area, A, equal to that of one of the small plates, M or N.
Substitute these values of d and c in (4) and
We shall now determine the best thickness to give to the dielectric so that errors made in adjusting the plate N will produce the smallest error in deducing the value of K. The errors made in measuring d and d may be neglected in comparison with the error made in setting the plate N. Now, taking the case where d4=0, and where each pair of large plates are the same distance apart,