NATURE 



[December 4, igiy 



Gravitation and Light. 



As 1 said last wtc-k (p. jj4), and also in the 

 December PhxX. Mag. (p. 737), the refractivity m- 1, 

 necessary at every point of a gravitational held to 

 produce 'the Einstein deflection, is the ratio of the 

 energy of a constant-mass particle fallen there from 

 infinity to the energy of the same particle moving with 

 the speed of light; but it is not permissible to say that 

 the solar gravitational field acts like a lens, for it has 

 no focal length. If the sun were backed by a nebula 

 or any luminous area, the light grazing the rim all 

 round' would be brought to a focus at a place seventeen 

 times the distance of Neptune, while light from any 

 larger circle would focus still further off in proportion 

 to the area of the circle. So from a uniformly 

 luminous area there would result a focal line of con- 

 stant brightness. The moon is, unfortunately, im- 

 potent to make an annular eclipse interesting. 



For an extended solar atmosphere to produce the 

 deflection, its density would have to vary with the 

 inverse distance, which seems unlikely- but this is 

 just the way in which an aether tension ought to vary 

 in order to cause gravitation — as Newton knew. The 

 extra ather-tension factor, m'-'. would be twice the 

 refractivity. 



Possibly the concluding sentence in the Phil. Mag. 

 article above referred to is not expressed with sufficient 

 clearness. Permit me to explain my points thus : — 



(i) The quasi-elasticity of aether— th; property 

 which enables it to transmit light and to effect elec- 

 trical discharge— is probably due to exceedingly fine- 

 grained constitutional vorticity with high-speed cir- 

 culation, as argued in my book "The Ether of Space." 

 Consequently it would' have facility for gyrostatic 

 action, yielding a perpendicular result to an acting 

 force. 



(2) That a gravitational force acting obliquely on light 

 would probably be unable to alter speed, but, through 

 the co-operation of its transverse and longitudinal com- 

 ponents, it might be expected to produce an extra dose 

 of (deflection— assuming light to be subject to gravita- 

 tion, as Newton surmised. So that by the time _ a 

 beam of light coming from infinity had arrived at its 

 nearest point to the sun, it would already have been 

 deflected as much as an ordinary heavy particle would 

 be deflected alonf its whole course. 



I am aware that these are only suggestions for 

 working out. • 



Einstein's equations, based on the impossibility of 

 observing motion through aether, seem powerful 

 instruments for extracting results ; just as more 

 familiar equations, based on the impossibility of 

 "perpetual motion," have proved themselves effective; 

 but neither set of equations explains, nor attempts to 

 explain, the mechanism, of the consequences they 

 deduce. Dynamics have served us so well in the past 

 that it must be still legitimate to try, whenever 

 possible, to apply well-established principles to new 

 phenomena. ' Oliver J. Lodge. 



Edgbaston, Birmingham, November 30. 



The Displacement of Light Rays Passing near the Sun. 



The part of the earth's atmosphere within the 

 conical shadow of the moon during a total solar 

 eclipse may be regarded as approximately a right cir- 

 cular cylinder, the area of the base of which depends 

 on the length of the shadow. Observations have shown 

 that there are temperature and pressure gradients in 

 this cylinder. The latter gradient at the surface of 

 the earth is usually slight, but the temperature 

 gradient may be considerable, so that, assuming that 

 there is eqiiilibrium, we have, roughly speaking, a 

 cylinder of air the density of which decreases outwards 



NO. 2614, VOL. 104] 



in all directions perpendicular to its axis. When we 

 remember that the light from stars at small angular 

 distances from the sun's centre makes small angles 

 with the axis of this cylinder, it is easy to see that a 

 verv small density gradient would be sufficient to 

 account for the displacements that were observed in 

 the total .solar eclipse of the present year. 



Suppose the cylinder to be made up of two parts, 

 an inner and an'outer, the common boundary being a 

 coaxial cylinder, and let a rav of light in the outer 

 portion inclined at a small angle a to the axis fall on 

 the boundary, the deviation 8 is given by 



cos = /" cos (a + 8), 

 where n is the index of refraction for rays passing 

 from the outer portion to the inner. 



Since S is verv small in comparison with o, we 

 have, approximately. 



M-i 



u- I 



very nearly. 



fL tan a tan a 

 since n does not differ much from unity. 



If = 30' and 8=1-7", we get 



;i=i-f8tana, 

 8 being expressed in circular measure. 



Thus ;i=F 100000007, and for small values of a it 

 is clear that 8 is inversely proportional to the angular 

 distance of the star from' the centre of the sun's disc. 



If we take /i,, the absolute index of refraction of, 

 the outer portion, to be 10003, fi„ the absolute index 

 of refraction of the inner portion, will be iooo;..ooo7, 

 and consequently 



til 

 Mr 



= I 0002, 



which will be the ratio of the density of the air in 

 the inside portion to the density of the air in the out- 

 side portion. On the assumption that there is no 

 gradient of pressure, this would imply a difference of 

 temperature of about. 1/18° C, a very small amount 

 when it is remembered that the lowering of tempera- 

 ture at the surface of the earth during an eclipse may 

 be as much as 5° C. 



In the actual case the path of a ray will be a .-urve, 

 but the above remarks will serve to show th.it the 

 density gradient yvould probably be sufficient to pro- 

 duce the observed effect. It is clear, too, that the 

 displacement in the actual case will be inversely pro- 

 portional to the angular distance of the star from the 

 sun's centre, and that it will depend on local condi- 

 tions, so that the amount of displacement will be 

 different for different places. . 



I think it is quite likely that if the refraction of 

 the atmosphere of the earth due to density changes 

 during an eclipse could be accurately obtained and 

 allowed for, it would be found that there is no 

 Einstein effect at all. Ai-EXR. Anderson. 



University College, Galway. 



EINSTEIN'S RELATIVITY THEORY OF 



GRAVITATION. 



I. 



THE results of the Solar Eclipse Expeditions 

 announced at the joint meetine: of the Royal 

 Society and Royal Astronomical Society on 

 NoveiTiber 6 broug-ht for the first time to the 

 notice of the general public the consummation of 

 Einstein's new theory of gravitation. The iheorv 

 was already in being before the war; it is one of 

 the few pieces of pure scientific knowledge which 

 have not been set aside in. the emergency; pre- 



