April 7, 1921] 



NATURE 



169 



Letters to the Editor. 



\T]ie Editor does not 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 communications.] 



Light and Electrons. 



Referring to a paper of mine in the current April 

 issue of the Philosophical Magazine, in which a pos- 

 sible generation of electrons is suggested, and assuming 

 that the result obtained by the late Lord Rayleigh 

 (Phil. Mag., August, 1916) for the area of wave-front 

 which can be tapped and have its energy extracted by 

 an infinitely small resonator, viz. something compar- 

 able with A*/n-, holds generally to a fair degree of 

 approximation, the length of a ray of terrestrial sun- 

 light sufficient for an electron is given by l\^l7i = 

 o-oi c.c, or 1 = 3 X 10' cm. for A = 3 x 10-", which would 

 pass in the thousandth of a second. 



Perhaps Sir W. H. Bragg may be tempted to try 

 whether corpuscles are still projected by radiation 

 reduced in intensity, not continuously but inter- 

 mittently, by a revolving slit. If there is a critical 

 length of effective beam, it would be instructive to 

 know it. Oliver Lodge. 



April 3. 



Relativity and the Velocity of Light. 



As neither Sir Oliver Lodge (Nature, March 17) 

 nor Mr. Bartrum (March 31) appears to find my ex- 

 planation very satisfying, may I further explain as 

 briefly as may be how and why I consider that the 

 Majorana experiments add valuable new knowledge to 

 that previously yielded by the classical Michelson- 

 Morley experiment? 



In discussing this and similar questions there are 

 two distinct avenues of approach. We may think and 

 write in terms of the old-fashioned fixed aether, the 

 FitzGerald-Lorentz contraction, and absolute time, or 

 alternatively in terms of the four-dimensional con- 

 tinuum. But if Mr. Bartrum and myself, or either 

 of us, embark on an argument in which we mix 

 indiscriminately the conceptions of the two schemes, 

 there is bound to be confusion and either apparent or 

 real contradiction. I prefaced my mathematical 

 argument (March 10) by the stipulation that we should 

 "consider the problem in terms of an aether and a 

 FitzGerald-Lorentz contraction." Mr. Bartrum, ap- 

 proaching the problem apparently in terms of the four- 

 dimensional continuum, objects that I have not dis- 

 tinguished between a source and mirror " moving 

 relatively to the observer " and the same appliances 

 ; "at rest with the observer." My answer is that so 

 long as I argue, as I was doing, in terms of an 

 aether, etc., the distinction does not arise. The ob- 

 server becomes immaterial, and may move or not as 

 he pleases ; the aether provides a fixed standard of 

 measurement. My symbols u, v, a, ^ referred to 

 velocities measured, in terms of unit-lengths 

 mapped out in a supposed fixed aether, by 

 synchronised clocks ticking absolute seconds. If we 

 ■ argue in terms of the old aether conceptions, such 

 measurements are theoretically possible, although, of 

 course, the relativist maintains that they are in prac- 

 tice impossible. If my argument is read throughout 

 in terms of these conceptions, I believe it "will be 

 found consistent, and I hope it will be found con- 

 vincing. 



The problem can, of course, alternatively be stated 

 and discussed in the language of relativity. The Hghf- 



NO. 2684, VOL. 107] 



source of the Michelson-Morley experiment has a 

 world-line AB and the mirror has a parallel world- 

 line PQ. A light signal is sent from source to mirror 

 and back to the source. Its emission from the source 

 is represented by a point A on the world-line AB, its 

 reflection by a point C on the world-line PQ, and its 

 return to the source by a second point B on the 

 original world-line AB from which it started. The 

 Michelson-Morley experiment gives us knowledge of 

 the absolute interval AB, but none at all of the posi- 

 tion of C on the world-line PQ of the mirror. So 

 far as the Michelson-Morley experiment alone is con- 

 cerned, the directions of AC, CB in the continuum 

 are unknown. My contention is that the experiments 

 of Majorana fix these directions for us, and so fix the 

 position of C. 



In the problem under discussion the light signal 

 moves entirely in a two-dimensional section of the 

 continuum, namely, the plane containing the parallel 

 world-lines AB and PCQ. Let us take x and ct for 

 co-ordinates (not necessarily orthogonal) in this plane. 

 These refer to a particular observer, and a second 

 observer will use different axes and co-ordinates, the 

 latter being related to x and ct by the ordinary Lorentz 

 transformation. Because the equation x' — c't^=o is 

 invariant for the Lorentz transformation, the pair of 

 lines x=±ct have the very special property that for 

 every observer, no matter what his velocity of motion, 

 they form the internal and external bisectors of the 

 angle formed by his axes of length and time. A 

 world-line parallel to either of these directions repre- 

 sents for each and every observer motion with the 

 same Velocity c, which each observer independently 

 will call the velocity of light. Now Majorana 's experi- 

 ment showed in effect that the direction in the con- 

 tinuum of the world-line of light from a source or 

 mirror moving relative to him was the same as that 

 of the world-line of light from a source or mirror at 

 rest relative to him. The directions were obtained by 

 measuring their inclinations to the experimenter's 

 special axes of time and space, but when the direc- 

 tions have been shown to be the same the observer's 

 axes fade from view and the identity of direction 

 becomes absolute. It now follows that the rays of 

 light in a Michelson-Morley apparatus, moving with 

 any velocity whatever, have world-lines parallel to 

 these two special directions. Or, to come back to 

 common language, both the outgoing and returning 

 signals move with the velocity of light. The con- 

 clusion is, of course, subject to the limitations of 

 Majorana's experiments — limitations which, it ought 

 to be added, the author himself states with scrupulous 

 care. J. H. Jeans. 



April 2. 



A Difficulty in Einstein's Gravitational Theory. 



In order to obtain from Schwarzschild's equation 



(fs^=-y-i8r*-r^8e*-r'sin^e8(f)^+y8f^ . (i) 



an expression for the gravitational deflection of light 

 which is independent of direction, it is necessary, as 

 pointed out by Prof. Anderson, to make the substitu- 

 tion r = (2r,+rn)V4''i, which giviss 



^s*= -^?!l±^^y|«r,« + ri28^ + ri2sin2 db<p-^] 





(2) 



■ml 

 and for the velocity of light 



ir-^—m t 2r, y 



2ri4-w\2ri4-w/ 

 Here r^ is now regarded as the radius vector. The 

 transformation, although, it gives two values of r,, can 



