598 



NATURE 



[February 5, 1920 



would have realised that our greatest investigators 

 rarely "work in splendid isolation," but that only a 

 man who has proved his capacity as an investigator 

 can lead and co-ordinate research. It is certain that 

 British scientific men will not submit to control and 

 direction from the practical man ; thus a definite 

 breach is opened between science and an important 

 branch of industry. 



It has not been sufficiently clearly realised that 

 scientific and industrial research is passing out of the 

 control of the recognised scientific and technical socie- 

 ties and institutions and of the universities into the 

 hands of the Department of Scientific and Industrial 

 Research, and, in accordance with Government policy, 

 the secretary of this Department is an administrator 

 without practical knowledge of science, industry, or 

 research. The associations which are formed under 

 the asgis of the Department are governed bv councils 

 upon which organised science is unrepresented, but 

 to which the Department mav nominate scientific 

 men. To the council of the Glass Research Associa- 

 tion the Department has nominated two scientific 

 representatives, one of whom is in India. On the 

 executive committee science is not represented ; and 

 when this appointment was discussed between that 

 body and the secretary of the Department, fhe 

 scientific aspects of the case can have received no 

 consideration. .As the Department controls funds for 

 research which are vastly greater than those at the 

 disposal of the Royal Society and all the other 

 societies and universities put together, the outlook 

 for science is a poor one unless scientific men are 

 prepared to take united action with the view of 

 securing a proper share in the control of research. 



Morris W. Travers. 



The Predicted Shift of the Fraunhofer Lines. 



May I submit the following two propositions for the 

 consideration of relativists? 



(i) An occurrence takes place at a point S. Light- 

 signals are dispatched from S at the beginning of the 

 occurrence to two observers K and A', and signals are 

 again dispatched at the conclusion of the occurrence. 

 By means of these A and A' measure the time of the 

 occurrence to be dt and At' respectivelv. Then 



where ^„ and ^„ are the values of Einstein's 

 44 potential at \ and A'. 



(2) An occurrence takes place at S, and is measured 

 by an observer there to take the time dt. .Another 

 occurrence takes place at S', and is measured bv an 

 observer there to take time dt' . By means of light- 

 signals dispatched from S and S' at the beginning 

 and conclusion of each occurrence, an observer .A 

 measures the times of each occurrence to be equal 

 Then 



-J g».dt= -J ^ „M\ 



where g^^ and /,. are the values of Einstein's 

 44 potential at S and S'. 



Prop, (i) seems to be a correct inference from 

 Einstein's theory, and prop. (2) is deduced by applying 

 (i) to the occurrence at S as measured by S and A, 

 and then to the occurrence at S' as measured by S' 

 and A. 



If these propositions are sound, how does the 

 Einstein theory predict the displacement of the 

 solar lines? For it seems to me that the criterion 

 for "similarity" of two radiating mechanisms in 

 different parts of a gravitational field is that the 

 invariant space-time elements corre.sponding to one 

 oscillation of each should be equal. For two 

 NO. 2'62 3, VOL. 104] 



mechanisms at rest in the field this condition reduces 

 to si g,,.di= >j g\^.dt' . James Rick. 



I'niversity of Liverpool. 



Ei.nstein's prediction of a shift of the Fraunhofer 

 lines to the red can be analysed into two assertions : — 

 (i) That the period of vibration of an atom at rest 

 on the sun differs from that of a similar terrestrial 

 atom ; and (2) that this difference is preserved un- 

 changed by the light-waves travelling from the solar 

 atom to the earth, so that it is revealed by a com- 

 parison made in a terrestrial laboratory. It is the 

 second assertion that is challenged by Mr. Rice ; and, 

 so far as I can make out, the same objection was at 

 the root of the criticisms formerly made by Sir Joseph 

 Larmor. Since criticism centres entirely round the 

 second assertion, I will deal with it solely. I may 

 state, however, that although I regard the first asser- 

 tion as highly probable, I do not regard it as proved 

 with complete rigour ; and had the criticism been 

 directed against this, I should have been much less 

 willing to take sides in the controversy. 



The interval ds between two events is a quantity 

 having an absolute significance independent of co- 

 ordinate systems ; and when the two events take place 

 at the same place, d.s=V^«4.df. Mr. Rice's first pro- 

 position states that if we have two light-pulses travel- 

 ling from the sun to the earth, the int.^rval ds between 

 their passages through any point is the same all the 

 way along the track. The statement has a certain ap- 

 pearance of plausibility, but I cannot see any definite 

 argument in favour of it. Space-time round the sun 

 is non-Euclidean ; the geodesies have, accordingly, 

 defined but rather complicated tracks, and there need 

 be no constancy of interval between points on neigh- 

 bouring geodesies. The rule deduced from Einstein's 

 theory for comparing the passage of two light-pulses 

 at the points .A and A' respectively is not ds = ds', but 

 dt = dt', provided the co-ordinates used are such that 

 the velocity of light does not change with t. 



If we found that the velocity of light changed 

 secularly, we should at once condemn our time- 

 reckoning as non-uniform ; accordingly, the proviso is 

 satisfied in practice. With the co-ordinates most com- 

 monly adopted the velocity of light is i — 2m/r, which 

 depends on the position r, but not on the time (. Then 

 if ti and t^ are the times of the two pulses at r, t',, t'^ 

 the times at r', since the mean velocity of the first 

 pulse {t\ — tt)l(r'—r) has to be the same as the mean 

 velocity (t\-t:i)l{r'-r) of the second pulse, over the 

 same course but at a later time, it follows at once 

 that t'2 — f'l is equal to <z-<,, which proves the state- 

 ment made. The time between the two light-pulses 

 is preserved unchanged on the journey from the sun 

 to the earth. 



In his letter (Nature, January 22, p. 530) Sir Joseph 

 Larmor describes this condition, that the velocitv of 

 light (or the formula for ds) shall not contain the 

 time explicitly, as "a reasonable assumption." I 

 cannot see that any assumption is involved ; nor can 

 I agree that it is of "an absolute type." The well- 

 known expression 



ds^=-{i-2mlr)-'dr'-r''de'-r- sW edf+ 



il-2m/r)dt' ... (A) 



is, in the first place, simply a particular integral of 

 Einstein's differential law of gravitation. It can be 

 shown that it is an appropriate solution for the case of 

 an isolated particle. But there is a fourfold infinity 

 of other solutions applicable to the same case ; .so 

 there can be nothing absolute about this solution, or 

 about the co-ordinates r, 6, f, t which it defines. It 

 is, in fact, often more convenient to write r = r'+m. 



