May 2, 1878] 



NATURE 



13 



surrounded by an atmosphere containing sufficient hydrogen 

 sulphide, the opposite effect occurs. Now the needle, when 

 vitreously electrified, turns from copper to iron ; when resmously, 

 from iron to copper. The conclusion to be drawn from these 

 results seems to be that the electrical behaviour of metals in 

 contact is almost, if not entirely, due to the difference of their 

 affinities for one of the elements of such compound gases as 

 maybe in the atmosphere surrounding them. This would be 

 entirely analogous to their behaviour in electrolytes containing 

 these same elements, e.^. iron is positive to copper in an oxidis- 

 ing electrolyte such as water, because of the affinity of oxygen 

 for iron being greater than for copper, while iron is negative to 

 copper in potassium sulphide solution, because of the affinity of 

 sulphur being greater for copper than for iron. J. Brown 



Edenderry House, Belfast 



Solar^Halo 



The following was noticed at Bordeaux on April 4, at 

 II A.M:— I. A well-defined and very complete circumzenithal 

 circle (80° in diameter), of a brilliant white light, passing 

 through the sun. 2. An iridescent circle, larger than the first, 

 and cutting it at two points 60° distant from the sun. The 

 second circle showed more especially the red rays on its con- 

 cavity {i.e. towards the sun), except at the parhelia, where it 

 was bright iridescent. Near the western parhelion the bril- 

 liancy of the mock sun was quite insufferable to naked eyes. 



The morning was very warm, but the night had been very 

 cold. E- RODIER 



29, Rue Saubat, Bordeaux, April 20 



FLOATING MAGNETS 



THE extract from the American Journal of Science 

 describing experiments with floating magnets by 

 Mr. Alfred M. Mayer to illustrate the equilibrium of 

 mutually-repellent molecules each independently attracted 

 towards a fixed centre, which appeared in NATURE, vol. 

 xvii. p. 487, must have interested many readers. 



It has interested me particularly because the mode of 

 experimenting there described, with a slight modification, 

 gives a perfect mechanical illustration (easily realised 

 with satisfactory enough approximateness) of the kinetic 

 equilibrium of groups of columnar vortices revolving in 

 circles round their common centre of gravity, which 

 formed the subject of a communication I had made to 

 the Royal Society of Edinburgh on the previous Monday. 

 In Mr. Mayer's problem the horizontal resultant repul- 

 sion between any two of the needles varies according to a 

 complicated function of their mutual distaiice readily 

 calculable if the distribution of magnetism in each needle 

 were accurately known. Suppose the distributions to be 

 precisely similar in all the bars and in each to be accord- 

 ing to the following law :— Let the intensity of magneti- 

 sation be rigorously uniform throughout a very large 

 portion, c D, of the whole length of the bar (Fig. i), and let 

 it vary uniforpily from C and D to the two ends A and B. 

 The bar will act as if for its magnetism were substituted 

 ideal magnetic matter,' or polarity, as it may be called, 

 uniformly distributed through the end portions C A and 

 D B ; the whole quantity in D B to be equal in amount and 

 opposite in kind to that of c A, For example, suppose 

 true northern polarity in A B and true southern in B D. 

 The lengths of CA and db need not be equal. Let 

 now A' c' D' B' be another bar with an exactly similar 

 distribution of magnetism to that of A C D B, and let the 

 two be held parallel to one another. The mutual repul- 

 sion will vary inversely as the distance, if the distance be 

 infinitely small in comparison with D B or C A, and if each 

 of these be infinitely small in comparison with C D. If the 

 true south pole s of a powerful bar-magnet be held in a 

 line midway between B A and b' a', at a distance from the 



* Repr'nt of papers en Electrostatics and Magnetism, § 469 (W. 

 Thomson). 



ends B and b' infinitely great in comparison with B b', and 

 comparable with the length of each needle, the horizontal 

 component of its effect on each magnet will be a force 

 varying directly as its distance from the central axis. 

 Under these conditions Mr. Mayer's experiments will 

 show configurations of equilibrium of two, or three, or 

 four, or any multitude of ideal points in a plane, repelling 

 one another with forces inversely as the mutual distances, 

 and each independently attracted towards a fixed centre 

 with a force varying directly as the distance. This, as I 

 showed in my communication to the Royal Society of 

 Edinburgh, is the configuration of the group of points in 

 which a multitude of straight columnar vortices with 

 infinitely small cores is cut by a plane perpendicular to 

 the columns ; the centre of inertia of a group of ideal 

 particles of equal mass placed at these points being the 

 fixed centre in the static analogue. 



The consideration of stability referred to by Mr. 

 Mayer has occupied me much in the numerical problem, 

 and it is remarkable that the criterion of stability or 

 instability is identical in the static and kinetic problems. 

 In the static problem it is of course that the potential 

 energy of the mutual forces 

 between the particles, to- 

 gether with that of the 

 attraction towards a fixed 

 centre is less for the configu- 

 ration of stable equilibrium 

 than for any configuration 

 difTering infinitely little from 

 it.- The potential energy of 

 the attractive force is a func- 

 tion of distance from the 

 central axis, diminishing as 

 the distance increases, and 

 the statement of the criterion 

 may be conveniently modified _g 

 to the following : — 



For a given value of this 

 function the mutual potential "" 

 energy of the atoms must be 2> 

 a minimum for stable equi- 

 librium. When, as supposed 

 above, the attractive force 

 varies directly as the distance 

 its potential energy is :— 

 C - i r 2r2 



where C, c, denote constants, 

 and 2r^ the sum of the 

 squares of the distances of 

 all the particles from the 

 attractive centre. And when 

 the law of force between the 

 particles is the inverse dis- 

 tance, their mutual potential 

 energy is equal to — 



K-/&log. (DD'D'....) 

 where K, k, denote constants, 

 and D, D', D", &c., denote C 

 the mutual distances between 

 the particles. Thus the con- <* 

 dition of stable equilibrium 

 becomes that the product of j^ 

 the mutual distances between 

 the particles must be a trua 

 maximum for a given value of the sum of the squares of 

 their distances from the attractive centre. A first con- 

 clusion from this condition must be that the centre of 

 gravity of the particles must be the attractive centre. 

 Now the condition of kinetic equilibrium of a group of 

 vortex columns, that is to say the condition that they may 

 revolve in circles round their common centre of inertia is, 

 asproved in mycommunicationtothe Royal Society of Edin- 



P=ii? 



B' 



C' 



Fig. I. 



