Oct. 



1 1 



iSSSJ 



NATURE 



579 



To determine exactly the conditions for attraction and repul- 

 sion respectively, let M be the electrical energy, at unit distance, 

 of a vibration proceeding from 1', then the energy at the distance 

 R is MR 1 , as far as its effect on a molecule is concerned. Sup- 

 pose a portion, •MR" 1 , of this to be absorbed where € is a 

 proper fraction, then the repulsive force will be proportional to 

 the negative differential coefficients of (i - i)MR"', and there will 

 be at the same time an attractive force proportional to the dif- 

 ferential coefficient of cMR' 1 . The total repulsive force will 

 therefore be proportional to (i-2e)MR~-; its maximum value 

 will be attained for e == o ; it will be zero for t = ^ j it will be 

 attractive for « > }4, and the attractive force will reach its 

 maximum value f c r e = I — that is to say, when the whole of the 

 energy is absorbed. This may take place when the two 

 attracting or repelling particles are of the same substance. The 

 expressions for these forces contain, in addition to R, a factor M 

 depending only on the attracting particle, and a factor I - 2e 

 depending only on the attracted particle. In the same way the 

 second particle will exert upon the first P a force proportional 

 to (i - 27j)NR"' J , where 17 depends only on the first particle, and 

 N only on the second. The electrostatic potential of the mutual 

 acti< n will therefore be — 



(1 - 26)(I - 27?)MN 



R 



(28) 



M and N measure the electricity radiated from the two 

 particles respectively— that is to say, the excess of the internal 

 electrical excitation of the two particles over that of the sur- 

 rounding ether. This excess may be negative, and therefore 

 two unelectrified particles may repel each other (when e = o, 

 77 = o) provided the surrounding medium is excited. The next 

 step would be to determine the further motion of an attracted or 

 repelled electrified particle, but since electricity in motion behaves 

 quite differently from electricity at rest, as will be shown to follow 

 from the author's theory, the consideration of this problem must 

 be postponed, but it may be noted here that an attracted particle 

 can only continue to approach the attracting particle so long as 

 its maximum energy has not been attained. They may therefore 

 either continue to approach until they come into contact, or may 

 cease to approach at a certain critical distance. The latter 

 possibilitydoesnot seem allowable accordingto experience, and in 

 fact is found to be excluded when the motion is more fully con- 

 sidered, and the author merely mentions it in this place to call 

 attention to its relation to the objections brought by von 

 Helmholtz against Weber's theory. 



Attempts have already been made to explain Newtonian 

 gravitation from electrostatic actions. 1 The attempt to explain 

 gravitation in this manner derives additional interest from the 

 author's theory of electrostatic action, according to which the 

 earth receives from the sun's rays, not only heat and light, but 

 also electrical energy. 



The theory of planetary motion should be capable of being 

 derived from the laws of electro-dynamics, and the author's 

 theory may therefore possibly prove of great value for the 

 explanation of the phenomena of terrestrial magnetism, of 

 meteorology, and may perhaps also throw some light upon the 

 natt r_- of comets. 



§ 13. Electro-dynamie Potential of Two Currents. 

 Electrostatic action may be compared, according to the 

 author's theory, with heat radiation, since both series of pheno- 

 mena are due to the transference of energy from the ether 

 to ponderable molecules. Similarly, heat conduction may 

 be compared with electrical conduction. A body will be 

 defined as a conductor when its molecules, in virtue of 

 specially favourable values of its critical periods and other 

 constants, are so sensitive to electrical energy as to easily absorb 

 the maximum amount of internal energy, after which the centres 

 of gravity of the molecule will begin to execute exceedingly small 

 vibrations, which will be transmitted from molecule to molecule, 

 accompanied by an absorption of electrical energy by each mole- 

 cule, in exactly the same way that the molecules become 

 luminous by the absorption of energy in the form of heat vibra- 

 tions. Conduction, then, will take place? by electrostatic radia- 



1 By Mossotti. for example, in 1836; see Zollner's " Wissenschaftliche 

 Abhandlungen," vol. ii. p. 417 ([-'■ " z «• ' '-V> ■ <>" P- lf ' '* **?•» WWUS 

 hypotheses regarding action at a distance are collected together, but the 

 author state* that he does not agree with Zollner's criticisms on them. See 

 also Maxwell's " Electricity and Magnetism," Aiticles 37, 59, et «</., ar.d 



846 Ct SCij. 



tion from molecule to molecule. 1 Those substances, on the other 

 hand, in which the molecules absorb with difficulty the maximum 

 amount of electrical energy, or in which internal electrical vibra- 

 tions are only excited with difficulty, will be non-conductors. 



The energy of an electrical vibration is inversely proportional 

 to the square of the period of vibration, and therefore to the 

 square of the wave-length, A. A very good conductor (and these 

 alone are con-idered in electro-dynamics) must have a very large 

 number of critical wave-lengths lying so close together that their 

 sum may be represented by a definite integral. Let \ l be the 

 smallest, and A., the greatest, of the electrical wave-lengths to be 

 considered in any given case, then the internal electrical energy 

 of the molecule will be proportional to 



/ ' aX = r - -L = -" ~ A| 



J Ai \ 2 A, A a A r 



where A 1 is a value of A lying between A x and A 2 . Owing to the 

 number of critical wave-lengths being necessarily very large, 

 A„ - A x will be a finite quanity in comparison with A 1 . We 

 therefore arrive at the conclusion that the total internal electrical 

 energy of a molecule of a good conductor is inversely proportional 

 to a certain mean critical wave-length A 1 . 



If we now make the assumption that the electrified particles 

 are moving relatively to each other with a given velocity, their 

 mutual electrostatic action will be modified in the same manner 

 as if the wave-length of the elec:rical vibration proceeding from 

 each of them were increased or diminished by an amount AA. 

 Let c be the velocity of light, and p the relative velocity of the 

 two electrified particles, in the direction of the line joining 

 them, then we know that AA = \p/c. Let r be the initial distance 

 between the particles, and E/>A = M/r the initial electrostatic 

 potential of one due to the presence of the other, then during the 

 motion it will be — 



E 

 r{\ + AA) 



M 



r\ 1 + £ 



+ 



Let ds be the element of length of the first conductor, and ds' 

 that of the second, and let 9 and 9' be the angles which they 

 make with the joining line, then — 



ds „ ds' a , 



- cos 6 - cos 9 

 dt dt 



.(29) 



To determine the mutual action of the two current elements, 

 each element must be assumed to consist of a pair of molecules, 

 one of which has transmitted electrical energy to the other with- 

 out having itself received a fresh supply, an assumption in com- 

 plete accordance with the representation of a molecule as consist- 

 ing of a series of distinct shells, and which takes the place of the 

 assumption usually made that at each moment the quantities of 

 positive and negative electricity on every current-element are 

 equal. The two original elements will repel each other if the 

 internal energy is electrically excited to an equal extent, or to 

 the maximum amount possible in each. In order to fix the ideas 

 this may be assumed to be the case in what follows. 



Let 1, 2, represent the two molecules of the ^element ds, and 

 1', 2', those old/, then the mutual potential of "the two elements 

 will be represented by the sum — 



P 2a - + P 12 < + P r , + P u < ; 



where Pa represents the mutual potential of two molecules i 

 and k. The author takes the potential such that its positive 

 differential coefficient in any direction is equal to the component 

 of force in that direction, and therefore we have — 



Pltf 



M 



I - r + r -. 



M 



/ ds cos 9 

 r[ 1 + - 

 \ dt c 



Pi-.=-: 



) (30) 



_M/ ds cos0 ,/ds cos 9V- _ \ , x 



<\~7\ * <-■ *2 C ) '") "' u 



_ M/ J/ cos (,' Us' cosfl'V +\ ...( 32) 

 ?/cos*\ r\ dt c ^\dt c ) J Ki 



M 



dt e 



I'..- 



M 



(33) 



1 ECundt has recently shown that heat conduction is probably effected in 

 a similar manner (Sitzungsberichte der Berliner Akmdtmie, 1888, p. 271). 



