578 



A 7 A TURE 



[Oct. 11, 1888 



strains of dielectrics — all the main phenomena of static electricity 

 admit of explanation on the basis of hollow vortices in the ether. 

 Moreover, the theory is applicable to chemical valency and to 

 Faraday's law of electrolysis. It places Faraday's ideal lines 

 of force on a basis of reality, and it adds one more nail to the 

 coffin of the material theory of electricity which it is to be hoped 

 has now been safely buried. 



During a thunderstorm which lately burst over Barcelona, 

 the captive balloon in the Exhibition was struck by a lightning - 

 flash and destroyed. The connecting-rope was probably of 

 wire. 



The lightning-conductor discussion at the Bath meeting of 

 the British Association has raised the question of the oscillatory 

 character of the Leyden jar discharge. This was suggested by 

 Helmholtz, in 1852, as an explanation of the fact observed by 

 Faraday, that when electrolysis of water took place through a 

 Leyden jar discharge passing through it, the gases at each elec- 

 trode were mixed H and O. It was proved by Thomson, in 

 1853, that if self-induction existed in the discharging circuit 

 it must occur, and the oscillations were actually observed by 

 Feddersen. The fact that needles and iron bars are magnetized 

 militates rather against the theory, but Prof. Ewing {Electri- 

 cian, October 5, p. 712) suggests that oscillations in which the 

 period lengthens while their amplitude decays would account 

 for magnetization in layers. 



MOLECULAR PHYSICS: AN ATTEMPT AT A 

 COMPREHENSIVE DYNAMICAL TREAT- 

 MENT OF PHYSICAL AND CHEMICAL 

 FORCES} 



III. 



Part II.— Electricity and Magnetism. 



§ 12. Electrostatic Attraction. 



'"PHOMSON'S investigations, considered in § 1 (August 23, 

 p. 404), rest on the assumption that the diameter of a 

 molecule or atom is indefinitely small in comparison with the 

 wave-length of the light, and therefore the conclusions do not 

 hold good for light-vibrations of such small wave-length as to 

 be comparable with the molecular diameters. The consideration 

 of vibrations of this kind shows that they give rise to what are 

 called electrical phenomena. 



These vibrations, like the former, will affect the internal 

 energy of the molecules, and the molecules will also have 

 critical periods with respect to them. But instead of assuming, 

 as before, that within a finite but very short interval, only one 

 wave impinges upon a molecule, it must now be assumed that 

 an indefinitely large number of waves impinge upon the mole- 

 cule at the same time, and that the effect of these waves is of a 

 constant character. Suppose a sphere of a diameter differing 

 only by an indefinitely small amount from that of a molecule, to 

 be separated from the ether, and let vibrations of short wave- 

 length impinge upon it from a fixed point, P. The first step 

 will be to determine the energy, due to these vibrations, of the 

 ether within the sphere. 



Let r be the least and r x the greatest distance of P from the 

 spherical surface. The energy will be inversely proportional to 

 the square of the distance, so that, where k is a constant, the 

 energy of the vibrating ether within the sphere will be — 





k5 



surface of the sphere of radius R*, the total energy of the ether 

 within the space considered will be proportional to — 



hfa+hl 4 '^ 



where 5 = i\ - ;- , and r lies between r and r r 



Now consider a finite space bounded by spherical surfaces of 

 radii Fx and R, having their common centre at P, and by a cone 

 with its vertex at P, and suppose it to be filled with spheres of 

 diameters indefinitely near to those of molecules.; then a finite 

 number of concentric spherical surfaces may be inserted between 

 the two bounding spheres, at distances equal to ths diameter of 

 a molecule. The number of small spheres between any pair of 

 these spherical surfaces will be proportional to the spherical I 

 surface included within the cone, so that, if da* is the element of I 



v,' ^ T? a P? r read b5fore the Physico-Economic Society of Konigsberg, by i 

 1 rot. *. Lindemann, on April 5, i838. Continued from p. 461. 



If, however, we assume that the small spheres are not suf- 

 ficiently numerous to completely fill the space, but that they 

 may all be arranged along a circular arc of radius R, then R," 

 in these denominators must be replaced by R„ so that, writing 

 dR for 5, we find for the total energy — 



K o 

 where dx dy dz represents an element of volume in the most 

 general form. We therefore obtain the following important 

 result : — 



If a portion of space infinitely large in proportion to the dia- 

 meter of a molecule contains a number of spheres of the size of 

 a molecule, so sparsely scattered that they can all be arranged 

 on a surface within the space, then the total energy of the ether 

 within all these spheres will be the same as if the space were 

 completely occupied by the spheres, and the energy of each 

 element of space were inversely proportional to the first power 

 of the distance of the element from the point P. 



Now suppose these spheres to be replaced by molecules with 

 a similar scattered distribution, then the vibrations correspond- 

 ing to their critical periods will increase their energy, while 

 vibrations of different period will traverse the space unaltered, 

 and therefore the molecules may still be regarded as specially 

 susceptible to certain vibrations of very short period, just as in 

 the case of luminous vibrations. Let KR" 1 be the energy of the 

 ether within the space occupied by the molecules, then the 

 ponderable portions of the molecules will have their energy in- 

 creased by an amount 0KR" 1 , where is a proper fraction — 

 that is to say, a force varying inversely as the square of the 

 distance will act on the ponderable molecules. 



Now, it was shown in § 1 that for comparatively slow mole- 

 cular motions the ether behaves like a perfect fluid, and there- 

 fore it follows from the principles of hydrodynamics that the 

 molecules must move in the direction in which the energy of the 

 surrounding ether diminishes most rapidly — that is, towards P ; 

 for the increase in the energy of a molecule a; it approaches P 

 must be accompanied by a decrease in the energy of the ether 

 surrounding it. 



It therefore follows that the vibrations of very short wave- 

 length proceeding from P will have the same effect as if P had 

 a charge of electricity, which suggests that electrostatic pheno- 

 mena may be due simply to these vibrations in the ether, and it 

 will be found that further investigation confirms this conclusion. 

 For the sake of brevity, the internal energy of a molecule due 

 to vibrations of the short wave-length here considered will 

 henceforth be called electrical energy, and a molecule will 

 be said to be electrically excited when its electrical energy 

 differs from zero. The demonstration given in § 5 (p. 407), that 

 there is a maximum value for the possible internal energy of a 

 molecule, will apply also to the present case, so that there will 

 be a maximum possible value of the electrical energy of a mole- 

 cule, depending upon the values of the constants which deter- 

 mine its internal constitution. This result leads to the following 

 proposition : — 



Two electrically excited particles will attract each other when 

 the electrical energy of either one of them is, under the existing 

 circumstances, susceptible of further increase. In the opposite 

 ca^e there will be repuls'on. l 



The truth of the latter pirtion of the preceding proposition 

 is easily seen, for if two equally excited particles, or two excited 

 to the maximum amount, were to approach each other, the 

 energy of the intervening ether would increase in the direction 

 of motion, for the ether at a point in the neighbourhood of one 

 of the particles would receive an increase of energy from the 

 approach of the other, while there could be no absorption of 

 energy by the molecule. This would, however, be in contra- 

 diction with the law of hydrodynamics according to which the 

 motion takes place in the direction of decreasing energy. - 



1 The^ction of electrified glass and sealing-wax on each other and on 

 pith-balls is easily explained from this. The difference between pjsitive 

 and negative electricity being merely relative, appears, toj, to re:nove a 

 good many difficulties in the explanation of electrostatic phenomena. 



2 We therefore assume the truth of Maxwell's the >rv that light-vibrations 

 exert a pressure in the direction of propagation (" Electricity and Mag- 

 netism," § 792) : this will only be modified when the vib-ations are abjjrbed 

 by the ponderable molecules. 



