January 26, 1922] 



NATURE 



105 



I 



trary meanings. Biologists say they understand one 

 another, and therefore I suppose they do; but I wish, 

 in pity, they would enlighten me. Why do 

 Lamarckians and neo-Darwinians say "inherit" 

 when they mean "vary"? Why do Mendelians and 

 biometrici'ans say "inherit " when they mean "repro- 

 duce "? Meanwhile, I cannot help suspecting that 

 something is wrong. Consider what has happened — 

 Lamarck's theory and half a century of stasis; 

 Darwin's brilliant lucidity and twenty years of pro- 

 gress, with biology in its splendour, a great intel- 

 lectual force; Weismann's effort, and nearly half a 

 century of controversy, with interest in the subject 

 limited to some (not all) zoologists and botanists, and 

 of these few a majority resentful of trespassers. 



I propose in two or three letters to adopt the physio- 

 logical classification when dealing with'three or four 

 biological subjects. Biologists, I hope, will be tolerant 

 towards one who uses this classification because, 

 admittedly, he does not understand the difficult 

 language they speak. G. Archdall Reid. 



9 Victoria Road South, Southsea, January i6. 



Atmospheric Refraction. 



Dr. Ball is surely wrong in suggesting in Nature 

 of January 5, p. 8, that the difference between Mr. 

 Mallock's figure for the radius of curvature of a nearly 

 horizontal ray and that given by Dr. de Graaff Hunter 

 is accounted for by any consideration of the curvature 

 of the wave-front. If such were the case, then an 

 observer looking towards the sea horizon would see a 

 ray of light in different, directions for different initial 

 curvatures of the wave-front. Suppose an observer 

 from the bridge of a ship were looking at a search- 

 light placed at sea-level at the extreme limit of visi- 

 bility. The rays of the searchlight beam would be 

 ►lane waves, those coming from the barrel of the 

 -( archlight spherical. Does Dr. Ball wish us to infer 

 that in such circumstances the visible beam would 

 appear to the observer to issue from a point above the 

 ]>rojector ?— for that is what his suggestion leads to. 



To my mind, a great deal of the confusion between 

 refraction figures given by different authorities Jies in 

 their attempt to connect refraction with variations 

 of temperature before they have properly considered 

 the subject from the point of view of variations in 

 refractive Index. If we assume that, over the sea at 

 all events, the refractive index stratification is one 

 which is spherical and concentric with the earth, then 

 the general equation of any ray of light is 



^n = constant, 

 where n is the refractive index and ^ the perpendicular 

 upon the tangent to the ray from the earth's centre 

 (see Herman, "Geometrical Optics," p. 305, or Heath, 

 "Geometrical Optics," p. 329). 



If r is the distance of any point upon the ray from 

 the earth's centre, h. the height of the point above the 

 earth's surface, and R the earth's radius, then 

 r = R + /i. 



Now n must be some function of the height = /(^) = 

 /(r-R), and hence the "^, r " equation of the ray is 



^/(r— ■R) = constant = C. 

 The radius of curvature of the ray is thus 



C \ dY 



^ _ vvC'' jdn 



c/'t 



zontal, variations in r artd n^ cannot haVfe large effects 

 upon 0-. The variations in r might amount to i part 

 in 200,000. if the ray never gets above 100 ft. above the 

 surface of the sea ; the refractive index, which at the 

 sea-level is 1-00029, could scarcely be reduced below 

 100027 in the same height, so that variations in n' 

 could not exceed 4 parts in 100,000. It follows that 

 the curvature of such rays is essentially proportional 

 to the refractive index gradient. Since by Dale and 

 Gladstone's law n— i is proportional to p, the density, 

 the curvature of the ray-path becomes immediately 

 proportional to the density-gradient. If we attempt 

 to translate density-gradient into temperature-gradient, 

 I see no means of doing so other than by making 

 the assumption that the atmosphere Is statically in 

 equilibrium, in which case the formulae given in my 

 letter in Nature of January 5 result immediately. But 

 I have the gravest doubts of the legitimacy of such 

 an assumption for the lower levels of the air. A 

 steady motion leading to a dynamical relationship 

 between pressure, density, and temperature is much 

 more likely, but is, from the mathematician's point of 

 view, a hopeless thing to try to set down owing to 

 the impossibility of dealing with all the factors of 

 the problem, such as rate of radiation of heat-energy 

 from the earth or sea, rate of thermal conduction in 

 the air, nature of the upward air-currents, and so on. 



If however, we leave all such considerations aside 

 and deal only with the established connections between 

 curvature of the ray-path and the density-gradient, 

 then we can only admit uniform curvature if we are 

 prepared to admit that the density of the air in Its 

 lower levels is a linear function of the height. To 

 such an admission I take the strongest exception. It 

 Is quite Insufficient to account for a refraction of the 

 visible sea horizon above the true horizontal — a pheno- 

 menon which, as every seaman knows, is by no means 

 uncommon. T. Y. Baker. 



Admiralty Research Laboratory, Teddlngton, 

 Middlesex, January 7. 



Cf dh 



As we are dealing with a rav which is nearly hori- 

 NO. 2726, VOL. 109] 



The Colours of Tempered Steel. ^ 



The well-known and characteristic tints that 

 appear on the surface of a tarnishable metal when 

 it is heated in contact with air have been usually 

 regarded as interference colours due to the formation 

 of a thin film of oxide on the surface of the metal. 

 The correctness of this explanation has, however, 

 recently been questioned (A. Mallock, Proc. Roy. 

 Soc, 1918), and rightly so, as a continuous film on 

 a strongly reflected surface cannot on optical prin- 

 ciples be expected to exhibit such vivid colours as 

 those observed. 



I have recently made some observations which shed 

 a new light on this subject. It is found that the 

 missing colours complementary to the tints seen by 

 reflected light appear as light scattered or diffracted 

 from the surface of the metal. In other words, if a 

 plate of blue-tempered steel be held in a beam of 

 light and viewed in such a direction that the regularly 

 reflected light does not reach the eye, the metal shows 

 a straw-yellow colour, and not the usual blue. It 

 will be understood that the scattered light, being dis- 

 tributed over a large solid angle, appears much feebler 

 than the regularly reflected colour, and in order to 

 observe the effect satisfactorily the metal should have 

 a smoothly polished surface before being lieated up. 

 Scratches and other irregularities show the ordinary 

 colour of the film, and not the complementary tint. 

 The most attractive effects are those, exhibited^ by a 

 heated copper plate, both on account of the vividness 



