444 



NATURE 



[April 8, 1922 



Letters to the Editor. 



The Editor does not hold himself responsible^ for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of NATURE. No notice is 

 taken of ationymous communications^ 



Atmospheric Refraction. 



I PERCEIVE on further consideration that my sug- 

 gestion (Nature, January 5, p. 8) of a spherical 

 wave-front in place of a plane one to account for 

 the discrepancy between the coefficient of terrestrial 

 refraction as derived by Dr. Hunter from Mr. 

 Mallock's proposition and the coefficient deduced from 

 trigonometric levelling operations under ordinary 

 conditions is inapplicable, for the reason that in 

 practice we have to deal, not with a single point- 

 source of light, but with an assemblage of point- 

 sources the wave-front from which is sensibly plane. 

 There must, therefore, be some other explanation 

 for the disagreement between the two values of the 

 coefficient. I find on examining Dr. Hunter's figures 

 (Nature, August 11, 1921, p. 745) that the almost 

 exact two-to-one ratio between the values, which 

 was suggestive of a simple geometrical explanation, 

 is illusory owing to an unfortunate slip of Dr. Hunter 

 in confusing sea miles with statute miles. The 

 earth's radius in sea miles is not 3960, but 3437, and 

 the resulting value of k from Mr. Mallock's proposi- 

 tion is not 0-133, 3.S Dr. Hunter states, but o-ii6. 

 Using the Continental definition of k, this gives 

 k =0-232, which agrees with the value found by 

 Jordan's formula (quoted in my former letter) for 

 isothermal conditions at 0° C. As to the remaining 

 discrepancy between o-ii6 or 0-232 and the values of k 

 (on the two definitions of it) which are usually found 

 to hold in practice, it is clear both from Comdr. 

 Baker's letter (Nature, January 5, p. 9) and from 

 Jordan's formula that this is readily accounted for 

 by temperature considerations. It is only under 

 isothermal conditions, such as seldom or never occur 

 in practice, that Mr. Mallock's result can be even 

 approximately true ; it was evidently incorrect to 

 consider, as Mr. Mallock did in his reply to Dr. 

 Hunter, that temperature effects could produce 

 merely a difference in the result of i or 2 per cent, per 

 1000 ft. The mistake of assigning an insignificant 

 part to temperature considerations is one which is 

 very easily fallen into by any one who first considers 

 the isothermal condition with its accompanying re- 

 lation between density and pressure, because of the 

 small effect which the existence of a temperature- 

 gradient has on the rate of decrement of pressure as 

 distinguished from density. 



The great interest of Mr. Mallock's demonstration 

 lies in its deriving the refractional radius under cer- 

 tain conditions in a very simple and elegant manner 

 from the velocities of light in air and in vacuo and 

 the height of the homogeneous atmosphere. What 

 has led to some confusion is the omission from the 

 enunciation of the proposition of the qualification 

 that it holds true only for isothermal conditions and 

 for air at 0° C. 



Putting p for pressure, p for density, and h for 

 height, we may take the refractional radius as de- 

 pending only on dpjdh, as Mr. Mallock does, so 

 long as we keep to isothermal conditions. But once 

 we depart from these conditions, as is inevitably the 

 case in practice, we must take it as depending on 

 dpjdh, which no longer corresponds to dpjdh. We 

 can, however, extend the simplicity of Mr. Mallock's 

 reasoning to the condition of a linear temperature- 



NO. 2736, VOL. 109] 



gradient provided we replace the height of the homo- 

 geneous atmosphere, -pdhjdp (or " pressure height," 

 as Prof. Everett preferred to call it in his " C.G.S, 

 System of Units "), by the " density height," -pdhjdp, 

 which latter may be much greater than the " pressure 

 height " under ordinary conditions. 



Comdr. Baker lays great stress on the fact that 

 the path of the refracted ray cannot be a circular arc 

 unless the temperature-gradient is linear. This stress 

 is justifiable, especially from the seaman's point of 

 view of the problem ; for the temperature-gradient 

 in the air immediately over the sea is frequently far 

 from linear, and in navigation horizontal sights must 

 always be taken fairly close to the surface of the sea ; 

 moreover, it will seldom happen that the most 

 favourable time of day can be chosen for observations 

 at sea. 



The moral is that in navigation too much reliance 

 should never be placed on the results of observations 

 made on a single bearing whenever the accuracy of 

 the tabular value of the dip has to be assumed. But 

 the land-surveyor is much less limited by conditions 

 than the seaman ; he can generally keep his lines well 

 above the ground by observing between points of 

 considerable elevation, he can choose that time for 

 his observations when refraction is least likely to be 

 abnormal, and -he can usually get an adequate check 

 on his results for the elevation of a point by observ-" 

 ing it from a number of others at different distances 

 and comparing the results. As a matter of experi- 

 ence, it is found by surveyors in many countries that 

 during the afternoon hours, when refraction is 

 steadiest, the assumption that the temperature- 

 gradient is linear and the path of a nearly horizontal 

 ray consequently a circular arc is tolerably near to 

 the truth, at any rate for lines which do not run 

 very close to the ground for any considerable part 

 of their length. This follows from the close con- 

 cordance between the trigonometric levels obtainable 

 for the same point from stations at very different 

 distances, when the observations have been taken 

 under proper conditions and worked out by the usual 

 formulae. John Ball. 



Survey of Egypt, Cairo, February 1 1 . 



Diffraction by Molecular Clusters and the 

 Quantum Structure of Light. 



The investigations on the molecular scattering of 

 light now in progress under the writer's direction 

 (regarding which previous communications have been 

 published in Nature) have brought to light some 

 very remarkable cases in which the observed facts 

 are in sharp contradiction with the theories of light- 

 scattering based upon Maxwell's electromagnetic 

 equations. According to the Einstein-Smoluchowski 

 formula for the scattering power of a fluid, viz. 



-^ If „._„.(,.,,), 



the intensity of the diffracted beam should be pro- 

 portional to the compressibility /S of the fluid and 

 should thus be very large near the critical tempera- 

 ture as the compressibility is there great. Experi- 

 ments by Keesom and Kammerlingh Onnes have 

 confirmed this result in the case of ethylene vapour 

 over a range of a few degrees above the critical 

 temperature. The scattering powers of liquid carbon 

 di-oxide and vapour for a considerable range of 

 temperatures below the critical point have been 

 determined in the writer's laboratory by Mr. K. R. 

 Ramanathan, who has discovered that the formula 

 is approximately valid only for a range of a few 

 degrees below the critical temperature, and then 



