December i8, 1919] 



NATURE 



395 



for the one outstanding failure of Newton's 

 scheme, and, we may note, does not introduce any 

 discrepancy where hitherto there was agreement. 



The Deflection of Light by Gravitation. 



The new theory having justified itself so far, 

 it was thought worth while for British astro- 

 nomers to devote their main energies at the recent 

 solar eclipse to testing its prediction of an entirely 

 new phenomenon. 



As was remarked above, the propagation of 

 light in the ordinary case of freedom from gravita- 

 tional effect is represented by the equation ds = o. 



This Einstein boldly transfers to his generalised 

 theory. After all, it is quite a natural assumption. 

 The propagation of light is a purely objective 

 phenomenon. The emission of a disturbance from 

 one point at one moment, and its arrival at 

 another point at another moment, are events dis- 

 tinct and independent of the existence of an 

 observer. Any law that connects them must be 

 one which is independent of the map the observer 

 uses; ds being an invariant quantity, ds = o ex- 

 presses such an invariant law. 



This leads at once to a law of variation of the 

 velocity of light in the gravitational field of the 

 sun. 



v = c(i — 2m/r). 



Here m, as before, is the mass of the sun in 

 gravitational units, and is equal to 147 kilometres, 

 while c is the velocity of light at a great distance 

 from the sun. Thus the path of a ray is the 

 same as that if, on the ordinary view, it were 

 travelling in a medium the refractive index of 

 which was (i— 2m/r)-^ In this medium the re- 

 fractive index would increase in approaching the 

 sun, so that the rays would be bent round towards 

 the sun in passing through it. The total amount 

 of the deflection for a ray which just grazes the 

 sun's surface works out to be 175", falling off 

 as the inverse of the distance of nearest approach. 

 The apparent position of a star near to the sun 

 is thus further from the sun's centre than the 

 true position. On the photographic plate in the 

 actual observations made by the Eclipse Expedi- 

 tion the displacement of the star image is of the 

 order of a thousandth of an inch. The measure- 

 ments show without doubt such a displacement. 

 The stars observed were, of course, not exactly 

 at the edge of the sun's disc; but on re- 

 duction, allowing for the variation inversely as 

 the distance, they give for the bend of a ray just 

 grazing the sun the value 1-98", with a probable 

 error of 6 per cent., in the case of the Sobral 

 expedition, and of 1-64" in the Principe expedition. 

 The agreement with the theory is close enough, 

 but, of course, alternative possible causes of the 

 shift have to be considered. Naturally, the sug- 

 gestion of an actual refracting atmosphere sur- 

 rounding the sun has been made. The existence 

 of this, however, seems to be negatived by the 

 fact that an atmosphere sufficiently dense to pro- 

 duce the refraction in question would extinguish 

 the light altogether, as the rays would have to 

 NO. 2616. VOL. 104I 



travel a miUion miles or so through it. The 

 second suggestion, made by Prof. Anderson in 

 Nature of December 4, that the observed displace- 

 ment might be due to a refraction of the ray in 

 travelling through the earth's atmosphere in 

 consequence of a temperature gradient within the 

 shadow cone of the moon, seems also to be nega- 

 tived. Prof. Eddington estimates that it would 

 require a change of temperature of about 20° C. 

 per minute at the observing station to produce 

 the observed effect. Certainly no such tempera- 

 ture change as this has ever been noted; and, in 

 fact, in Principe, at which the Cambridge expedi- 

 tion made its observations, there was practically 

 no fall of temperature. 



Gravitation and the Solar Spectrum. 

 It was suggested by Einstein that a further 

 consequence of his theory would be an apparent 

 discrepancy of period between the vibrations of 

 an atom in the intense gravitational field of the 

 sun and the vibrations of a similar atom in the 

 much weaker field of the earth. This is arrived 

 at thus. An observer would not be able to infer 

 the intensity of the gravitational field in which he 

 was placed "from any observations of atomic vibra- 

 tions in the same field : that is, an observer on 

 the sun would estimate the period of vibration of 

 an atom there to be the same that he would find 

 for a similar atom in the earth's field if he trans- 

 ported himself thither. But on transferring him- 

 self he automatically changes his scale of time ; 

 in the new scale of time the solar atom vibrates 

 differently, and, therefore, is not synchronous with 

 the terrestrial atom. 



Observations of the solar spectrum so far are 

 adverse to the existence of such an effect. What, 

 then, is to be said? Is the theory wrong at 

 this point? If so, it must be given up, in spite 

 of its extraordinary success in respect of the other 

 two phenomena. 



Sir Joseph Larmor, however, is of opinion that 

 Einstein's theory itself does not in reality predict 

 the displacement at all. The present writer shares 

 his opinion. Imagine, in fact, two identical atoms 

 originally at a great distance from both sun and 

 earth. They have the same period. Let an ob- 

 server A accompany one of these into the gravita- 

 tional field of the sun, and an observer B accom- 

 pany the other into the field of the earth. In 

 consequence of A and B having moved into dif- 

 ferent gravitational fields, they make different 

 changes in their scales of time, so that actually 

 the solar observer A will find a different period 

 for the solar atom from that which B, on the 

 earth, attributes to his atom. It is only when 

 the two observers choose so to measure space 

 and time that they consider themselves to be in 

 identical gravitational fields that they will esti- 

 mate the periods of the atoms alike. This is 

 exactly what would happen if B transferred him- 

 self to the same position as A. Thus, though an 

 important point remains to be cleared up, it 

 cannot be said that it is one which at present 

 weighs against Einstein's theory. 



E. Cunningham. 



