378 



NATURE 



{March ii, 1875 



the solid, which is bounded entirely by lines of force, no altera- 

 tion is made in the distribution of the current when that limited 

 space is entirely removed from the conducting space around it. 



Several cases are taken in a sheet of tinfoil l8 inches square, 

 with several battery poles about 3 inches apart near the centre of 

 the sheet, and the equipotential curves traced out by means of 

 two poles attached to a delicate galvanometer, these poles being 

 at points of the same potential when the galvanometer needle is 

 at zero ; a sheet limited in size by cutting along lines of force is 

 then taken, and in each case it is shown that tliere is no altera- 

 tion of the equipotential curves. The forms of these curves are 

 traced out for one positive, and four negative poles at equal 

 distances from it at tlie corners of a square in the centre of a 

 large sheet of tinfoil ; also the curves for one positive and two 

 negative poles at equal distances on either side of it on the same 

 straight line. 



When there are four electrodes, two of each kind on an tin- 

 limited sheet, an equipotential curve is given by the equation, 



,y = cr.,r{. 

 If the four points lie on a circle, and the comf)lete quadrilateral 

 be drawn through them, the circles which have their centres at 

 the intersections of opposite sides of the quadrilateral, and which 

 cut the first circle at right angles, will also cut one another at 

 right angles. One of these circles is shown to be an equi- 

 potential curve for the four electrodes, and the other is a line of 

 force. 



Hence, if we cut the unlimited sheet along the edge of this 

 latter circle, we shall not alter the forms of the equqioteiitial 

 curves ; and within it we shall have one electrode of each kind, 

 the others being their electric images, the product of tlie distances 

 of an electrode and its image from the centre being equal to the 

 square of the radius of the disc. If an electrode is at the edge of 

 the disc, then the electrode and its image coincides, and the 

 equation to the equipotential curve is 



When one pole is at the edge and the other is at the centre of 

 a circular disc, since the electric image of the centre is at an 

 infinite distance, the equation to the equipotential curve is 



'■" = ^''i- 

 This is an interesting case, as showing that tbe equipotential 

 curves do not always cut the edge of the disc at right angles. 



On placing one of the galvanometer electrodes at the extremity 

 of the diameter through the battery electrodes, and tracing with 

 the other, it is found that the equipotential curve through that 

 point cuts the edge of the disc at an angle of 45°, and that there 

 are two branches cutting one another at right angles. 



These peculiarities are explained on tracing tlie curve 

 r'- = 4.r;-i 

 corresponding to this case. The extremity of the diameter is a 

 point through which two branches of the curve pass at right 

 angles to one anothei'. 



The forms of the equipotential surfaces and lines of force in 

 space may be determined experimentally by taking a large vessel 

 containing a conducting liquid and placing two points, the ends 

 of two covered wires, for batiery electrodes at a given depth in 

 the liquid and away from the sides and ends of the vessel, taking 

 similar covered wires immersed to the same depth for galvano- 

 meter electrodes. 



For two electrodes the equipotential surfaces will be surfaces 

 of revolution around the straight line joining them, and so will 

 cut any plane drawn through this straight line or axis everywhere 

 at right angles. 



Hence we may suppose sections of the liquid made along such 

 planes without altermg the forms of the equipotential surfaces. 

 This shows that we may place our battery electrodes at the side 

 of a rectangular box containing the liquid, and with the points 

 only just immersed below the surface ol the liquid, and the equi- 

 potential surfaces will be the same as if the liquid were of 

 unlimited extent in every direction about the electrodes. 



We shall obtain the section of the equipotential surface by 

 taking for galvanometer electrodes two pomts in the surface of 

 the liquid, keeping one fixed and tracing out points of equal 

 potential with the other. 



The potential at any point in space, due to two equal and 

 opposite electrodes, is 



A 



iT-k) 



where ;■ and r^ are the distances of the point from the electrodes, 

 so that for an equipotential surface 



— - — = constant. 

 r ?-i 



These surfaces are cut at right angles by the curves 



cos B — cos <p ~ c, 

 which are also the magnetic lines of force, 6 and (p being the 

 angles which the distances from the electrodes make with the 

 axis. That the lines of force in a vessel of finite size should 

 agree with the lines of force in space, the form of the boundary 

 ot the vessel in a plane through the axis should everywhere be 

 a line of force ; but the ends of a rectangular vessel coincide 

 very closely with certain lines of force, either when the electrodes 

 are at the ends, or when there are two electrodes within the 

 vessel, and two supposed electrodes at their electrical images at 

 an equal distance outside the ends of the vessel. 



The equipotential surfaces are given in this case by the 

 equation, 



1-1- i— i -L = constant, 

 r r" ri r-^ 

 and the lines of force by the equation, 



cos 6 + cos Sj — cos <p — cos (/>i = c. 

 The curve, for which c — 2 coincides very closely with the ends 

 of the box. 



The equipotential surfaces were traced out in sulphate of copper 

 and in sulphate of zinc by the following method : — 



A rectangular box was taken, and the battery electrodes 

 attached to pieces of wood which could be clamped at the centre 

 of the end of the box, and could be brought to any required 

 point in the line joining the middle points of the end of the box. 

 The galvanometer-electrodes were attached to 1" pieces which 

 rest on the ends and side of the box, and the position of the 

 electrodes read off by millimetre-scale placed on the ends and 

 sides of the box. 



When the electrodes are parallel lines extending throughout 

 the depth of the liquid the equipotential surfaces are cylindrical, 

 and their sections are given by the equation, 



\og(rr . . .) — (logri?-i' . . .) = logi", 

 where there are several positive and several negative electrodes, 

 r . r' . , . &c. being measured from the points where the elec- 

 trodes cut the plane of the section. 



Hence the forms of these equipotential curves are the same as 

 in a plane sheet, so that the forms traced out in tinfoil will be 

 the same as the corresponding forms in space for line electrodes. 

 These forms may be traced out in sulphate of copper with 

 copper electrodes, or in sulphate of zinc, with amalgamated zinc 

 electrodes. 



The results of these investigations show how closely the expe- 

 rimental determination of equipotential surfaces and lines o' 

 force agrees with the theory of electrical distribution in space. 



Linnean Society, March 4. — Dr. G. J. AUman, president, 

 in the chair. — Messrs. W. W. Scofield and T. Atthey were 

 elected fellows. — Mr. Hanbury exhibited a fungus from South 

 America, a species of Phallus allied to P. impiiJicus. — Mr. 

 J. G. Baker exhibited specimens of tbe two species of plane-tree, 

 Platanus occiJciitalis and oyientalis, and of the variety of the 

 latter known as acerifolia, and pointed out the distinctions 

 between them ; also a curious modification of bulb-form in a 

 species of Driniia. — Mr. J. R. Jackson read a paper on plants 

 in which ants make their homes ; exhibiting specimens of two of 

 the most remarkable of these, Myrmccodia and Ilvdiwphylliim. — 

 Prof. Thiselton Dy£r read a brief note on the slructnre of the 

 so-called iminbrana uiuici in the seeds of Cycads. Heinzel had 

 described this as a cellular structure, the cells ol which had thick 

 walls penetrated by ramifying tubes. There was reason, how- 

 ever, lor believing that the membrane only represented the wall 

 of a single cell, and was in fact probably the greatly enlarged 

 primary embryo-sac. What Heinzel had taken for tubes seemed 

 really to be solid. They were arranged all over the membrane 

 after the fashion of what carpet-manufacturers call a " moss- 

 pattern." They were possibly the debris of the thickened walls 

 of the cells of the nucleus which had been destroyed by the en- 

 largement of the primary embryo-sac. — Prof Dickson exhibited 

 and described a series of microscopic slides illustrating the mode 

 of growth of TropiColum sfieciosiim. — A paper was taken as read 

 by Mr. Bentham, on the classification of the natural orders Cam- 

 panulacea? and Oleacece. 



Geological Society, Feb. 24. — Mr. John Evans, V. P.R.S., 

 president, in tlie chair. — Before proceeding to the business of 

 he meeting the President spoke of the death of Sir C. Lyell, 



