I40 



NATURE 



[August 4, 19 10 



be no radiometer action. He measured the energy of 

 the beam by its heating effect, and the mean of his 

 resuhs showed a pressure of very nearly the amount 

 required by Maxwell's theory. 



At the same time, Profs. Nichols and Hull were 

 working at the subject. They used air pressures of 

 one or two centimetres of mercury, that peculiar reg-ion 

 of pressure where convection nearly ceases and where 

 radiometer action has scarcely begun. They allowed 

 the beam to fall on a silvered disc, thus obtaining a 

 double pressure — that of the incident plus that of the 

 reflected beam. To eliminate the action of the sur- 

 rounding gas they made use of the fact that the 

 light pressure has its full force the instant the beam 

 falls on the surface, while the convection and radio- 

 meter actions only slowly develop as the disc gets 

 heated. Nichols and Hull, therefore, only allowed the 

 beam to fall on the disc for a short tiine — six seconds, a 

 quarter period of the suspended system — and thus they 

 eliminated the gas disturbances. Thev measured the 

 energy of their beam by determining its heating effect, 

 and the observed pressure was found to agree with 

 Maxwell's theory to within i per cent. 



When a beam of light, then, falls normally on an 

 absorbing surface, it presses against it with a force 

 per sq. cm. equal to the energy density. It is giving 

 momentum to the surface at this rate. The beam 

 is therefore a carrier of momentum. The waves of 

 light carry momentum, momentum forward in the 

 direction of propagation, just as surely as if they 

 were material corpuscles ; and on either theory the 

 momentum given per second is equal to twice the 

 '.kinetic energy per unit volume, since in the waves 

 we may assume that the total energy is half kinetic 

 and half potential. 



H we trace back this momentum it must have been 

 put into the train of waves at its source, at the 

 luminous surface from which they issued. The waves 

 are there acquiring forward momentum. The source 

 is losing forward momentum, or is gaining back- 

 ward momentum. That is, the source is being 

 pressed back with a force per sq. cm. equal to the 

 energy density in the issuing waves. Thus, if the 

 total energy emitted by one sq. cm. in one second is 

 R, and U is the velocity of propagation, we have the 

 pressure given by 



^ U 



Tt is here assumed that all the energy is emitted 

 normally to the surface. If, however, the surface is 

 emitting in all directions according to the cosine 

 law, it is easily shown that the effect of the spreading 

 round the hemisphere is to make 



The pressure against the receiver is a proved experi- 

 mental fact independent now of anv particular hypo- 

 thesis which we may adopt as to the nature of light; 

 and it does not appear possible to avoid the conclusion 

 that the momentum revealed in that pressure against 

 the receiver was derived from the source. 



The experiment which we now describe has been 

 made to detect the starting of the momentum from 

 the source. It should be manifested as a back pres- 

 sure, a recoil of the emitting body from the light, or 

 radiation, which it sends forth. 



The most direct method would, no doubt, consist in 

 suspending a disc black on one side, silvered on the 

 other. Inside the disc should be a coil of wire, and 

 this coil should be heated by a current introduced 

 through the suspension. The heat would be given out 

 as radiation by the black surface, and hardly at nil 

 by the bright surface, with the result that the black 



NO. 2127, VOL. 84] 



surface should be pushed back. But the experimental 

 difficulties in the way of such a direct method appear 

 insuperable. The disc was, therefore, heated by allow- 

 ing radiation to fall upon it and to be absorbed. This 

 heat issued again as radiation, and it is the back 

 pressure of this issuing radiation that had to be de- 

 tected. 



The nature of the action to be looked for may be 

 seen by considering an ideal case in which we allow 

 a beam with energy P per cubic centimetre to fall 

 normally in a perfect vacuum in turn on each of four 

 discs, the front and back surfaces of these discs being 

 respectively as in Fig. i, where B represents a fully 

 absorbing or "black " surface, and S a fully reflecting 

 or non-radiating surface. 



When the radiation falls on an absorbing face, as 

 in the case of either of the discs (i) and (2), the tem- 

 perature of the disc rises until a steady state is reached 

 in which emission equals absorption. We may sup- 

 pose that the discs are so thin that the two faces are 

 sensibly at the same temperature. It we did not take 

 into account the pressure due to issuing radiation, or 

 if we only considered the initial effects before heating 

 took place, the pressures on the first two discs would 

 be P in each case, due to the incident beain alone, 

 and on the last two would be 2P, due to the sum 

 of the incident and reflected beams. Wo should have, 

 therefore, 



(■) W (0 (4> 



P P 2P 2P 



But when a steady state is reached, the discs (i) 

 and (2) must be giving out as much radiant energy as 

 they receive. The first disc gives out equal amounts 



F 



B B 



S S 



SB 



on the two sides, producing equal and opposite pres- 

 sures. All the radiation from the second disc is given 

 out at the front side, and is equal in energy to that of 

 the incident beam. Assuming this emitted radiation 

 is distributed according to the cosine law, the pressure 

 resulting from it is easily shown to be jP, so that 

 the total pressure on this disc is fjP. 



.Since there is no absorption by discs (3) and (4), we 

 still have the pressures 2P ; hence we have now 



(!) (2) (<i (4) 



P |P 2P 2P 



In a real case these results are modified in two 

 ways : — 



(i) By the possession of some small reflecting power 

 by surface 13, and of some small absorbing and 

 radiating power by surface S. 



(2) By an inequality of temperature between front 

 and back surfaces conditioned by the energy which is 

 carried through from front to back to be radiated 

 thence. The" vacuum is not perfect, and there is 

 radiometer action due to the residual gas. which, owing 

 to the inequality of temperature, is not the same on the 

 two sides. This is probably the only way in which 

 gas action is sensible, for the effects due to ordinary 

 convection and conduction in the residual gas are 

 negligible. 



in the final form of the experiment each disc 

 consisted of a pair of circular cover glasses, i'2 cm. 

 in diameter and about o"i mm. thick, between which 

 was squeezed a layer of asphaltum also about o'l mm. 

 thick, the temperature being first raised sufficiently to 

 render the asphaltum molten. Such a compound disc 

 appears to be perfectly opaque, and its surface is 

 extremely black and little diffusing. 



