354 



NATURE 



{Feb. 29, 1872 



quadrant, and being entirely on the upper right-lmnd side. He 

 described the colour as being like the upper ground part of a 

 kerosene lamp shade in the cabin to which he pointed. The sun 

 looked watery. When lie first saw it it was coming from behind 

 scud. There was no sky which could be called blue. It was a 

 whitey sky. Cooper's drawing was marked with radial lines 

 extending across the outer annulus from the inner. 



" The return voyage was begun at daylight on the morning of 

 the I3ih of December. The only lasting traces of the astronomers 

 left on the island were the photographers' dark rooms and the 

 brick foundations used for the instruments, in which were en- 

 tombed two bottles containing coins and newspapers and some 

 particulars of the expedition. A member of the party, animated 

 by something of the spirit of Old Mortahty in his desire to pre- 

 serve from oblivion the mortuary memorials of the expedition, 

 inscribed this touching record on the slab which formed the top 

 of one of the^e pedestals : — ' Sacred to the memory of the 

 Australian Eclipse Expedition. 



SOCIETIES AND ACADEMIES 

 London 



Royal Society, Februaryl5. — " On the Induction of Electric 

 Currents in an infinite plane sheet of uniformly conducting 

 matter," by Prof. Clerk Maxwell, F.R.S. 



The currents are supposed to be induced in the sheet by the 

 variation in position or intensity of any system of magnets or 

 electromagnets. 



When any system of currents is excited in the sheet, and then 

 left to itself, it gradually decays, on account of the resistance of 

 the -hee'. At any point on the positive side of the sheet, the 

 electromagnetic action is precisely the same as if the sheet, with 

 its currents, retaining their original intensity, had been carried 

 away in the negative direction with a constant velocity R, where 

 R is the value, in electromagnetic measure, of the resistance of a 

 rectangular portion of the sheet, of length i and breadth 2 ir. 

 This velocity, for a sheet of copper of best quality of one milli- 

 metre thickness, is about twenty-five metres per second, and is, 

 therefore, in general comparable with the velocities attainable in 

 experiments with rotaiing apparatus. 



When an electromagnet is suddenly excited on the positive 

 side of the sheet, a system of currents is induced in the sheet, t!ie 

 effect of which on any point on the negative side is, at the first 

 instant, such as exactly to neutralise the effect of the magnet 

 itself. The effect of the decay of this system of currents is 

 therefore equivalent to that of an image of the magnet, equal and 

 opposite to the real magner, from the position of the real magnet, 

 in the direction of the normal drawn away from the sheet, with 

 the constant ve'ocity R. 



When any change occurs in an electromagnetic system, 

 whether by its motion or by the variation of its intensity, we may 

 conceive the change to take place by the superposition of an 

 imaginary system upon the original system ; the imaginary system 

 being equivalent to the difference between the original and the 

 final state of the system. 



The currents excited in the sheet by this change will gradually 

 decay, and their effect will be equivalent to that of the imaginary 

 system carried away from the sheet with the constant velocity R. 



When a magnet or electro-magnet moves or varies in any con- 

 tinuous manner, a succession of imaginary magnetic systems like 

 those already described is formed, and each, as it is formed, be- 

 gins to move away from the sheet with the constant velocity R. 

 In this way a train or trail of images, is formed, moves off, par- 

 allel to itself, away from the sheet, as the smoke of a steamer 

 ascends in still air from the moving funnel. 



When the sheet itself is in motion, the currents, relatively to 

 the sheet, are the same as if the sheet had been at rest, and the 

 magnets had moved with the same relative velocity. The only 

 difference is, that whereas when the sheet is at rest no difference 

 of electric potential is produced in different parts of the sheet, 

 differences of potential, which may be detected by fixed elec- 

 trodes are produced in the moving sheet. 



The problem of Arago's whirhng disc has been investigated by 

 MM. Felici and Jochmann. Neither of these writers, however, 

 has solved the problem so as to take into account the mutual 

 induction of the currents in the disc. This is the principal step 

 made in this paper, and it is expressed in terms of the theory of 

 images, by which Sir W. Thomson solved so many problems in 

 Statical Electricity. In the case of the whirling disc, the trail 



of images has the form of a helix, moving away from the disc 

 with velocity R, while it revolves about the axis along with the 

 disc. Besides the dragging action which the disc exerts on the 

 magnetic pole in the tangential direction, parallel to the motion 

 of the disc, the theory also indicates a repulsive action directed 

 away from the disc, and an attraction towards the axis of the 

 disc, provided the Dole is not placed very near the edge of the 

 disc, a case not included in the investigation. These pheno- 

 mena were observed experimentally by Arago, Ann. de Chiinic, 

 1S26. 



February 22. — " On a New Hygrometer." By Mr. Wildman 

 O. Whitehouse. 



" On the Contact of Surfaces." By William Spottiswoode, 

 M A., Treas. R.S. 



In .a paper published in the "Philosophical Transactions" 

 (1870, p. 2S9), t have considered the contact, at a point P, of 

 two curves which are c i-planar sections of two surfaces (U, V) ; 

 and have examined somewhat in detail the case where one of the 

 curves, viz., the section of V, is a conic. In the method there 

 employed, the conditions that the point P should be sextatic, 

 involved the azimuth of the plane of section measured about an 

 axi; passing through P ; and consequently, regarded as an equa- 

 tion in the azimuth, it showed that the point would be sextatic 

 for certain definite sections. It does not, however, follow, if 

 conies having six-pointic contact with the surface U be drawn in 

 the planes so determined, that a single quadric surface can be 

 made to pass through them all. The investigation therefore of 

 the memoir above quoted was not directly concerned with the 

 contact of surfaces, although it may be considered as dealing with 

 a problem intermediate to the contact of plane curves and that 

 of surfaces. 



In the present investigation I have considered a point P com- 

 mon to the two surfaces, U and V ; an axis drawn arbitrarily 

 through P ; and a plane of section passing through the axis and 

 capable of revolution about it. Proceeding as in the former 

 memoir, and forming the equations for contact of various de- 

 grees, and finally by rendering them independent of the azimuth, 

 we obtain the conditions for contact for all positions of the cutting 

 plane about the axis. Such contact is called circumaxal ; and 

 in particular it is called uniaxal, biaxal, &c , according as it 

 subsists for one, two, &c. axes. If it holds for all axes through 

 the point it is called superficial contact ; and in the memoir some 

 theorems are established relating to the muuber of sections along 

 which contact of a given degree must subsist in order to ensure 

 uniaxal contact, as well as to the connection between uniaxal 

 and multiaxal contact. At the conclusion of sec. 3 it is shown 

 that the method of plane sections may, in the cases possessing 

 most interest and importance, be replaced by the more general 

 method of curved sections. 



In the concluding section a few general considerations are 

 given relating to the determination of surfaces having superficial 

 contact of various degrees with given surfaces ; and at the same 

 time have indicated how veiy much the general theory is affected 

 by the particular circumstances of each case. The question of a 

 quadric having four-pointic superficial contact with a given sur- 

 face is considered more in detail ; and it is shown how in general 

 such a quadric degenerates into the tangent plane taken twice. 

 To this there is an apparently exceptional case, the condition for 

 which is given and reduced to a comparatively simple form ; but 

 I must admit to having so left it, in the hope of giving a fuller 

 discussion of it on a future occasion. 



The subject of three-pointic superficial contact was considered 

 by Dupin, •' Developpements de Geometric," p. 12, and, as I 

 have learnt since the memoir was written, a general theorem 

 connecting superficial contact and contact along vuin is branches 

 of the curve of intersection of two surfaces (substantially the same 

 as that given in the text) was enunciated by M. Moutard. * 



In a corollary to this theorem, M. Moutard states that through 

 every point of a surface there can be drawn twenty-seven conies, 

 having six-pointic contact with the surface. This number is 

 perhaps open to question ; and I have even reason to think, from 

 considerations stated to me by Mr. Clifford, that the number ten, 

 given in my memoir above quoted, may be capable of reduction 

 by unity to nine. But this question refers to the subject of that 

 earlier memoir rather than to this. 



Geological Society, February 7. — Mr. Prestwich, F.R.S. , 

 president, in the chair. I. " Further Notes on the fJeology of 

 the neighbourhood of Malaga," by M. D. M. d'Orueta. In 

 this paper, which is a continuation of a former note laid 



* Poiicelet, " Applications d'Analyse a la G6om6trie," 1864, torn. ii. p, 363 



