!42 



NATURE 



[November io, 192 i 



the theory of Bohr, like the magneton theory, 

 points to the existence of discrete magnetic tubes. 

 In 1916 A. L. Bernoulli came to the conclusion 

 that when an electron is in movement in a uniform 

 molecular magnetic field the number of lines of 

 force cut by the radius vector at each revolution 

 is one and the same universal constant. In a 

 paper read before the Royal Society of Edinburgh 

 in November, 1920, the present writer attempted 

 to show that, without any restriction as to the 

 uniformity of the magnetic' field, when any 

 number of point charges are revolving round an 

 axis with a common angular velocity, the number 

 of magnetic tubes passing through the stationary 

 circular orbits is equal to an integral number of 

 times the constant hfe. Recently an attempt has 

 been made to extend the result to the more 

 general case of an electron revolving round the 

 positive nucleus in an elliptic orbit. It has been 

 shown independently by Sommerfeld and by W. 

 Wilson that the size and shape of the ellipse 

 depend upon iu'o integers n and n', the first. intro- 

 duced by the application of the quantum theory 

 to the angular motion, the second by the applica- 

 tion of the theory to the radial motion. The sum 

 of these two integers determines the value of 

 Bohr's W, the total energy of the system with 

 the negative sign prefixed. Making certain 

 plausible assumptions, it appears that the total 

 number of quantum magnetic tubes passing 

 through the elliptic orbit is simply this sum, 

 n^n'. This result is obtained by employing the 

 generalised form of the quantum theory first put 

 forward by W. Wilson and used with such 

 success by Sommerfeld and others. 



On this theory the mean value of the kinetic 

 energy corresponding to a particular degree of 

 freedom is equal to ^n/iv, where the mean value 

 is taken over the period, i/v, corresponding to 

 the co-ordinate under consideration. It is now 

 assumed that this mean energy may be identified 

 with electrokinetic energy. The periodic motion 

 of an electric charge e in an orbit with high fre- 

 quency V is regarded as equivalent to a current 

 ev, and the electrokinetic energy may then be 

 written ^Nev, where N is the number of magnetic 

 tubes passing through the actual orbit, but corre- 

 sponding to the particular co-ordinate in ques- 

 tion. Equating the two expressions for the 

 energy, we find at once 



N = n(?i/e). 



It must, of course, be admitted that we do not 

 get out of the equations more than we put into 

 them, so that the assumptions made above virtu- 

 ally imply the existence of discrete tubes of mag- 

 netic induction. It is to be noted that we are 

 concerned twice over with the process of taking 

 a time average of a certain quantity, first in 

 evaluating the mean kinetic energy, and secondly 

 in evaluating the electrokinetic energy and assum- 

 ing the moving charge as equivalent to a current 

 ev. In the words of Dr. Norman Campbell, 

 NO. 2715, VOL. 108] 



" Classical dynamics, it is clear, is only ' statist- 

 ical ' ; what are the principles of the elements 

 of the statistical group is the main problem of the 

 physics of the future." The suggestion now made 

 is that the quantum tube is the element referred 

 to. 



The physical existence of Faraday's magnetic 

 tubes conforms in many respects to the mode of 

 representation suggested by Sir Joseph Larmor : 

 "One or more electrons constrained to move 

 round a channel would be like an amperean 

 current. It is not unlikely that constraint of this 

 kind will have to be introduced into molecular 

 models to give an account of paramagnetism and 

 ferromagnetism — namely, structure in space or 

 atom involving channels more or less definite for 

 the electrons to circulate in." On the present 

 view such channels or partitions would be pro- 

 vided in consequence of the discrete nature of 

 the tubes of magnetic induction, which would 

 determine the radius of the permissible orbit 

 which an electron describes about the nucleus and 

 account for the property of rigidity. 



Sir Oliver Lodge, in a recent paper {Phil. Mag., 

 vol. 41, p. 942, 192 1), writes as follows : — 

 "Magnetic lines are always closed curves; there 

 is no known way of generating them ; they always 

 pre-exist, though they may be- of atomic or mole- 

 cular magnitude, and in a magnetic field are 

 opened out so as to enclose a perceptible area. 

 This is generally admitted to be the process of 

 magnetisation, and when the magnetism ceases 

 the lines shrink up into infinitesimal, or practic- 

 ally infinitesimal, orbits again. That the quantum 

 is associated with these ultimate magnetic units 

 is exceedingly likely." 



If we accept the existence of quantum magnetic 

 tubes, many questions of great interest suggest 

 themselves. What happens in the emission or 

 absorption of radiation? Does radiation imply 

 the separation or ejection of a quantum tube from 

 an atomic system, and absorption the incorpora- 

 tion of an external tube? Then, 3.gam, how are 

 electrostatic forces to be regarded? Sir Joseph 

 Thomson has pictured a magnetic field as due to 

 the motion of electrostatic tubes. It would, of 

 course, be possible to reverse the process and 

 regard an electrostatic field as set up by moving 

 magnetic tubes. In a suggestive communication 

 to the British Association at Edinburgh Prof. 

 Whittaker discussed the properties of tubes of 

 force in four dimensions, and pointed out that 

 such a tube, which would satisfy all the require- 

 ments of the relativity theory, would involve both 

 the electric and the magnetic vector. Further, in 

 the four-dimensional world it is action, not energy, 

 which is conserved, so that the field appears open 

 for a direct application of the quantum principle. 

 The experimental physicist may feel somewhat 

 appalled at the prospect of such a solution of his 

 difficulties, but it may yet be necessary to invoke 

 a four-dimensional tube of force as the unit brick 

 from which a universe may be constructed. 



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