Complete Radiation at a given Temperature, 463 



In his excellent memoir, Sur le mouvement luminenx* , M. 

 Gouy suggests that the nature of white light may be best 

 understood by assimilating it to a sequence of entirely irre- 

 gular impulses. It was by means of this idea that Young f 

 explained the action of gratings ; and although J. Herschel % 

 took exception, there is no doubt that the method is perfectly 

 sound. The question that I wish to raise is whether it is 

 possible to define the kind of impulse of which an irregular 

 sequence would represent the complete radiation of any 

 temperature. 



The first thing to be observed is that it will not do to 

 suppose the impulses themselves to be arbitrary. In proof 

 of this it may be sufficient to point out that in that case there 

 would be no room for distinguishing the radiations of various 

 temperatures. If the velocity at every point were arbitrary, 

 that is independent of the velocity at neighbouring points 

 however close, the radiation could have no special relation to 

 any finite wave-length or frequency. In order to avoid this 

 discontinuity we must suppose that the velocities at neigh- 

 bouring points are determined by the same causes, so that it 

 is only when the interval exceeds a certain amount that the 

 velocities become independent of one another. This inde- 

 pendence enters gradually. When the interval is very small, 

 the velocities are the same. As the interval increases, the 

 arbitrary element begins to assert itself. At a moderate dis- 

 tance the velocity at the second point is determined in part 

 by agreement wdth the first, and in part independently. With 

 augmenting distance the arbitrary part gains in importance 

 until at last the common element is sensibly excluded §. 



* Journ. de Physique, 1886, p. 854. I observe tliat M. Gouy liad an- 

 ticipated me (Enc. Brit. xxiv. p. 425) in the remark that the production 

 of a large number of interference-bands from originally white light is a 

 proof of the resolving power of the spectroscope, and not of the regularity 

 of the white light. It would be instructive if some one of the contrary 

 opinion would explain what he means by regular white light. The 

 phrase certainly appears to me to be without meaning — what Clifford 

 would have called noiisense. 



t Phil. Trans. 1801. 



t Enc. Metrop., Light, § 703 (1830). 



§ The following may serve as an illustration. Out of a very large 

 number of men (say an army) let a regiment of 1000 be chosen by lot, 

 and let the deviation of the mean height of the regiment from that of 

 the army be exhibited as the ordinate of a curve. If a second set of 1000 

 be chosen by lot, the new ordinate will bear no relation to the old. But 

 if at each step but one man of the regiment be eliminated by lot, and 

 one successor be chosen in the same way, the new oi dinate will be almost 

 the sauie as the old one, and not until after a large number of steps (of 

 the order of 1000) will the new ordinate become sensibly independent. 

 If the abscissa be taken proportional to the number of steps (each hually 



2 12 



