July io, 1919] 



NATURE 



365 



extensive literature on the subject will be found in 

 Landau's "Handbuch der Primzahlen." 



It would be of interest if Mr. Mallock would con- 

 struct the graph for the function mlof^, m which cor- 

 responds with the j^raph given on p. 305. 



G. N. Watson. 



The University, Birmingham. 



T 



LORD RAYLEIGH, O.M., F.R.S. 

 HOUGH any adequate account of Lord 

 Rayleigh's contributions to science will 

 require time and extend far beyond the limits of 

 a short article, the loss of one who has so 

 longf been their leader cannot be passed over by 

 physicists without some immediate attempt at an 

 appreciation and acknowledgment of the dis- 

 coveries he made and the services he rendered to 

 science. 



For more than fifty years Lord Rayleigh put 

 forth without any interruption and without a 

 trace of diminution in quality or quantity a suc- 

 cession of researches covering almost every 

 branch of the older physics. As the five volumes 

 of the "Collected Papers," which only include 

 those down to 1910, contain 349 papers, he must 

 during his career have published nearly 400 

 papers ; not one of these is commonplace, and 

 there is not one which does not raise the level 

 of our knowledge of its subject. Collected papers 

 are apt to form a kind of memorial tablet in our 

 libraries to men of science, but, if I may judge 

 from my own experience, Rayleigh's are a 

 remarkable exception ; there are few, if any, 

 f)ooks which I consult more frequently than these 

 volumes and from which I derive greater delight 

 and benefit. No small part of this is due to the 

 clearness and finish with which thev are written. 



Rayleigh had, like Kirchhoff, the spirit and 

 feeling of the artist in the preparation and 

 presentation of his papers. His mathematical 

 analysis seemed to flow naturally into the most 

 concise and elegant form, and, whatever might 

 be the difficulty of the subject, it was never 

 increased by any obscurity or ambiguity as to the 

 meaning of the writer. This quality was so in- 

 grained that it could resist the ru.sh and excite- 

 ment of a competition as keen as that of the 

 Mathematical Tripos ; for when he was Senior 

 Wrangler in the Tripos for 1865 one of the 

 examiners said: "Strutt's papers were so good 

 that they could have been sent straight to press 

 without revision." 



.A.nother feature brought out by this collection 

 of papers is their catholicity. The papers are 

 indexed under the headings Mathematics, General 

 Mechanics, Elastic Solids, Capillarity, Hydro- 

 dynamics, Sound, Thermodynamics, Kinetic 

 Theory of Gases, Properties of Gases, Electricity 

 and Magnetism, Optics, Miscellaneous ; and 

 there is such a goodly array under each of the.se 

 headings that it is difficult to decide in which 

 branch of physics his work was the most import- 

 ant. Rayleigh once said to me that he some- 

 times speculated whether he would not have done 

 better to concentrate on a more limited field. 

 NO. 2593, VOL. 103] 



Probably, however, in these matters one's mind 

 takes the bit between its teeth and chooses the 

 path in which it can work to the best advantage. 



Whatever may be the subject of the paper, 

 some characteristics are always apparent. One 

 of these is the quite exceptional power Rayleigh 

 possessed of seeing what was the essence of the 

 question ; he always went straight for the critical 

 spot. Another- — perhaps to a considerable extent 

 the result of the last — was the remarkable gain 

 in clearness any subject acquired after it had 

 passed through his mind, which was like a filter 

 which cleared every subject passing through it 

 from obscurity and error. He seemed to delight 

 in encountering and clearing away difficulties, 

 and had a high opinion of the value of difficulties 

 in helping one to get a better grip of the subject. 

 Once, in speaking to me about one of the extra- 

 ordinarily few cases in which later investigators 

 had arrived at results appreciably different from 

 his, he laid great emphasis on this point, and 

 said that the investigation in question was one 

 of the very few in which from beginning to end 

 he had not been conscious of any difficulty. 

 Another characteristic was the soundness of his 

 judgment. I question if in this respect he has 

 ever been surpassed; his mind was crystalline,^ 

 not affected by any cloud of prejudice ; he did 

 not dislike or shy at an idea because It was new, 

 neither did he think that because it was new it 

 was necessarily better than the old. 



To pass to the discoveries and results con- 

 tained in these papers, there are such a multitude 

 of high peaks that it seems almost invidious to 

 single out any for special mention. In optics we 

 have the series of papers on the scattering of light 

 by small particles, and the proof that the 

 molecules of air are sufficiently large and 

 numerous to account for the colour of the sky. 

 The study of this subject Rayleigh resumed from 

 time to time, and it has of late been taken up 

 from the experimental side with great success by 

 his son. Other noteworthy papers on optics are 

 his researches on the resolving power of optical- 

 instruments and on the nature of white light. His 

 article on light in the " Encyclopaedia Britannica " 

 is remarkable for clearness of exposition and 

 novelty of outlook. The paper on the resultant 

 amplitude of vibrations of the same period and 

 arbitrary phase, though written primarily for its 

 optical application, has proved of great import- 

 ance in connection with the scattering of rapidly 

 moving particles and with the phenomena of 

 viscosity and diffusion. 



In hydrodynamics we owe to Rayleigh the 

 theory of the formation and stability of jets ; 

 researches in capillarity of fundamental import- 

 ance ; the theory of the stability of motion in vis- 

 cous fluids ; the theorv of the resistance experi- 

 enced by a plane when moving through a liquid, 

 with its application to the theory of flight, a 

 subject in which he took great interest, and in 

 which he was a pioneer. His book on the 

 "Theorv of Sound" may be .said to have found 

 the subject bricks and left it marble; it is ideal 



