692 



NATURE 



[February 26, 1920 



enhanced by such a scheme of centralisation as was 

 indicated in the leading article in the same issue of 

 Nature. There may have been some waste of effort 

 in the past, both at home and overseas, owing to in- 

 sufficient co-operation between men of science work- 

 ing indeijendently, but this is a matter for workers to 

 set right among themselves, and will not be mended 

 by an organisation conceived on the lines of a German 

 military system. Further, it is unlikely that the best 

 men will be attracted to work under such deadening 

 conditions. 



Care must be taken that public money is not wasted 

 in scientific development, but the kind of ofhcial 

 control suggested by a scheme of centralisation does 

 not commend itself as an efficient waste-preventer. 

 Grants of money to scientific societies or institutions 

 might be administered by carefully selected boards of 

 trustees, the scientific work being left to the un- 

 hampered initiative of the scientific staff under a 

 head specially suited to the character of the work. 

 The management of our Natural History Museum, 

 a Government institution, is invested in trustees, who 

 leave to the scientific staff the carrying out of the 

 scientific work as effectivelv as funds and opportunity 

 allow. Research work of the highest value to agri- 

 culture is being carried out at the Rothamsted Ex- 

 perimental Station, the original endowment of which 

 has been generously supplemented by private muni- 

 ficence and bv Government grants. Here also the 

 management is vested in a small committee the 

 members of which represent the various scientific sides 

 of the work carried on. A. B. Rendle. 



British Museum (Natural History). 



Gravitational Deflection of High-speed Particles. 



The investigation of the consequences of Einstein's 

 law as regards the motion of a material paiticle 

 moving through a gravitational field with a velocity 

 comparable to that of light brings out some interest- 

 ing and rather surprising effects, hs Einstein s law 

 is entirely kinematical, involving accelerations instead 

 of forces no account need be taken of variation of 

 mass with velocitv other than that contained in the 

 law itself. Let m denote the mass of the attracting 

 bodv (i.e the sun) in astronomical units divided by 

 the 'square of the velocitv of light. Then the motion 

 of a particle in the field produced by this body is 

 determined by . 



8j y (7^2^)(rfr2^V5^) -(i -2'^yW = o, 



the rS plane being that of the orbit. From the 

 Lagrangian equations corresponding to this Hamil- 

 tonian statement of the law, the energy relation 



idr ' f^\ r) V 



is obtained. If the velocitv of the moving particle is 

 comparable to the velocity c of light, the second term 

 in the parenthesis on the right-hand side may be 

 omitted as negligible compared to the last term. The 

 resulting approximate equation is easily integ-rated, 

 leading to the expression 



.«=.^{.«(t-6-)4-.';}, 



where o is the ratio of the velocity of the particle at 

 infinitv to that of light. _ . 



Consider a particle the velocity of which at infinity 

 is negligibly small compared to that of light. Then 

 the factor a is small, and the second term in the 



NO. 2626, VOL. 104] 



jiarenthesis which it multiplies may be omitted. This 

 gives the energy equation of the Newtonian theory. 



If, however, the particle has a high velocity, the 

 omitted term becomes of importance. In fact, when 

 the velocity is ij-Zy, this term has the same value as 

 the third term, but the opposite sign. Therefore, 

 these two terms annul each other, and the velocity 

 of the moving particle is unaffected in magnitude by 

 the gravitational field. In other words, the tangential 

 acceleration of the particle is zero throughout the 

 course of its motion through the field. If it were 

 headed directly for the attracting centre, it would 

 move along in a straight line with constant speed just 

 as if no field were present. 



Next, consider a particje having a velocity at 

 infinity greater than i/Vsc. The velocity of this 

 particle is actually decreased by the gravitational field. 

 If it were aimed straight at the attracting mass, it 

 would be .slowed down just as if it were repelled with 

 a force varving inversely with the square of the dis- 

 tance. If the velocitv of the particle at infinity is 

 equal to that of light, its velocity decreases as it 

 approaches the centre of attraction in the same amount 

 as that of a light-wave, for Einstein's theory makes 

 no distinction between material particles and electro- 

 magnetic disturbances. 



Consider a particle moving along the X axis with 

 a high velocity v. Let the attracting mass tn be on 

 the Y axis, a distance R below the origin. Then the 

 components of the particle's acceleration are 





mx 

 inR. 





If the particle's velocitv is greater than iji/y, the 

 tangential component /j. is positive, and the particle 

 is slowed down as it approaches the centre of the 

 field. The normal component /„, however, causes the 

 particle to be deflected towards the gravitating mass 

 for all velocities less than c. This deflecting accelera- 

 tion becomes less, however, as the velocity increases, 

 and a particle moving with the velocity of light would 

 travel through a gravitational field in a straight line. 

 Its velocitv, however, decreases as it approaches the 

 gravitating centre, and then increases as it recedes 

 from this point. For velocities close to that of light 

 the deflection is given by 



^m(c2- 



kK 



-7)' \ 



The deflection suffered by a light-wave is of a natur* 

 quite different from that experienced by a material 

 particle. X rav of light is not bent towards the sun 

 by the latter's gravitational attraction, but the velo- 

 city of that portion of the wave-front closest to the 

 sun is decreased more than that of the more remote 

 portion. Therefore, the wave-front is swung round 

 in exactly the same way as when light passes obliquely 

 from a rarer to a denser refracting medium. 



In conclusion, it may be noted that the two con- 

 sequences of Einstein's law which are of great enough 

 magnitude to be tested experimentally have been 

 most conspicuously verified. The predicted shift of 

 the Fraunhofer lines towards the red does not seem 

 to be a necessary consequence either of Einstein's law 

 or of the part of' the theory on which this law is based, 

 but rests on the very doubtful assumption that the 

 system of a freely moving atom near the sun's surface is 

 identical with that of a freely moving atom 93,000,000 

 miles away. If space-time had the same properties in 



