NA TURE 



[May 23, 1907 



LETTERS TO THE EDITOR. 



[The Editor does nnl hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous conimtmications.] 



The Structure of the Ether. 



The recent interesting communication of Sir Oliver 

 Lodge to Nature (March 28) and the Philosophical 

 Magazine on the density of the ether recalls an objection 

 to theories of the ether which identify magnetic intensity 

 with resultant ethereal velocity that does not seem to have 

 received the attention it deserves. The objection arises 

 when the distribution of momentum in the system is taken 

 into consideration. 



It will be remembered that Sir Oliver Lodge commences 

 by pointing out that the volume occupied by the electrons 

 which constitute a mass of platinum is small compared 

 with the volume of the platinum itself, whence it follows, 

 if the mass of the electrons is that of the ether they carry 

 with them, that the density of the ether must be enormous 

 compared with that of platinum. This conclusion appears 

 to be inevitable if we are to have a hydrodynamical theory 

 of the ether. I do not wish to contest the contention that 

 the density of the ether is enormous. 



The second method used by Lodge to evaluate the density 

 of the ether assumes that the magnetic intensity at any 

 point is always proportional to the speed of the ethereal 

 flow. By equating the mechanical and magnetic ex- 

 pressions for the energy of the field, and assuming that 

 the ethereal circulation at the equator of an electron is 

 equal to the velocity of its forward motion, Lodge arrives 

 at the relation 



v; 



1 o ue'-«-sii 



or 



pw 



_e*(U« smfl 



e=4va' 



4Tr^' 



where e is the charge and a the radius of an electron, and 

 p is the density and fi the magnetic permeability of the 

 ether. This may be combined with the known values 

 cV=io-''" gm. cms. and = 1-2x10-'^ cms. to give 

 P = 383Xio'° gms. per c.c. This gives for the velocity 

 of ether drift in a inagnetic field of intensity equal 

 to I electromagnetic unit the value iti = 1-44x10-'' cms. 

 per sec. These figures enable us to calculate the 

 momentum due to any given magnetic distribution. 



A moment's consideration of the simplest possible case, 

 that of a moving charged sphere or an electron, will serve 

 to show that this distribution of ethereal velocitv leads to 

 impossible results. We have seen that p = c-/if^-n-a'^, and 

 by making use of the expression for the magnetic field due 

 to a moving charged sphere of radius a we find that the 

 velocity of ethereal flow w, at a point the coordinates of 

 which are r, 6 with respect to the electron and its line of 

 motion, is given by 



Hence the momentum per unit volume at a point r, B from 

 the centre of a sphere of radius a and charge e moving 

 with velocity n is given by 



Since the momentum is distributed in circles round the 

 line of motion there is no resultant momentum, but if 

 the above expression be integrated it will be seen that 

 there is an infinite quantity of momentum in the field for 

 any finite value of u, and, moreover, there is an infinite 

 moment of momentum about the line of motion. The 

 existence of this momentum would make it impossible to 

 set a charged sphere in motion ; the same result would be 

 arrived at by any theory which makes the velocity of the 

 ether proportional to the magnetic force. 



Electrodynamic theory has led to an expression for the 



momentum per unit volume of the ether by ways which 



are less speculative. This expression is i/47r times the 



product of the electric and magnetic displacements, and it 



NO. i960, VOL. 76J 



has the merit of making the momentum in the ether equal 

 to the product of the (electric) mass and velocity of the 

 moving charge. If we are to have a hydrodynamical 

 theory of the ether it seems reasonable to make this agree 

 with the fluid momentum. We thus get for the case of 

 the charged sphere 



fie-n sin 9 



p7U=— , 



4ir/-* 

 and from the energy expressions 



.> u£"ii" .sin-9 



whence iti = usin9 and p=ii.e^l4irr'. This result makes the 

 velocity of flow of the ether independent of the radial 

 distance from the electron, but the amount moved varies 

 inversely as the fourth power of the distance. It has been 

 pointed out by J. J. Thomson that this result can be 

 interpreted hydrodynamically by supposing that the ether 

 is carried along by the tubes of electric force, and that the 

 extent to which the ether is " gripped " by the tubes of 

 force is proportional to the square of their concentration. 

 If we suppose the whole of the ether to be carried along 

 at the equator of the electron, this method would give the 

 same estimate for the density of the ether as that found 

 by Lodge. If only part of the ether were carried along 

 by the tubes of force even at the equator of an electron, 

 the density of the ether would h.ave to be correspondingly 

 increased, so that this method can be regarded as giving 

 the value p = ;ie"/4?rn' = 3-85X 10'° gms. per c.c. as an 

 inferior limit to the density of the ether. The actual value 

 may be much greater than this. 



The hypothesis of no ether slip at the equator of the 

 electron leads to what seems to be a difficulty, at present 

 at least. From what has been said it will be seen that it 

 definitely establishes the relation e = ^Tra' ^pJAirfi, so that 

 the charge on an electron is equal to its superficial area 

 multiplied by a quantity which depends only on the proper- 

 ties of the ether. Thus the size and mass of any electron 

 are determined as soon as its charge is known, and any 

 one of these quantities is determined by any non-identical 

 combination of the others. The experiments of Bragg on 

 the stopping power of different substances for a rays lend 

 support to the suggestion, first put forward by H. .\. 

 Wilson, that these are positive electrons. Now the ex- 

 periments of Rutherford have shown that the value of 

 e/iij for the a rays emitted by a large number of radio- 

 active elements is very nearly 5X10" e.m.u. per gm. This 

 value of elm leads, on the hypothesis of no equatorial 

 slip, to the value c„=io-" e.m.u., or 10' times the charge 

 on the negative electron. It would be difficult to make 

 an electron with a charge of this magnitude the foundation 

 of atomic structure. This difficulty occurs with at least 

 equal force on the assumption of magnetic ether flow. 



The argument of the last paragraph, so far as it is 

 deserving of weight, tends to show that the ethereal density 

 is greater than the limiting value. The considerations 

 brought forward earlier would appear to show that the 

 ethereal flow, if it exists, is at right angles to, and not 

 along, the lines of magnetic force, and that the effect 

 sought for experimentally by Sir Oliver Lodge is not to be 

 expected. O. W. Richardson. 



Princeton, N.J., May 12. 



Radium and Geology. 



With apologies to Prof. Joly (p. 55), I think my estimate 

 of a gradient of 1° F. for 98 feet in the Simplon Tunnel 

 will bear examination. From a contemporary notice in the 

 Daily Mail of October 3, 1004, it is clear that the heat in 

 the tunnel was endurable until the hot spring was tapped. 

 The water is stated to have been at 131° F., which agrees 

 exactly with 55° C, " the highest temperature " of Prof. 

 Joly. Surely, then, this was the temperature of the spring, 

 and not of the rocks. 



I would also remark that Mr. Strutt considered that the 

 amount of radium in the igneous rocks examined by him 

 would, on his theory, account for a gradient as high as 

 1° in 42-2 feet, a very different thing from the 1° in 70 

 mentioned by Mr. Fox. O. Fisher. 



Graveley, Huntingdon, May 17. 



