August ii, 192 i] 



NATURE 



745 



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 manu- 

 scripts intended for this or any other part of NATURE. JV'o 

 notice is taken of anonvmoiis communications.] 



Atmospheric Refraction. 



The proposition that "the course of a nearly hori- 

 zontal ray of light in the lower part of the atmosphere 

 is a circular arc having a radius of 14,900 geographical 

 miles " has been stated by Mr. Mallock in a letter in 

 Nature of June 9, p. 456. Mr. Mallock states later 

 on in the same communication that rays that are 

 pointed a few degrees up or down will still be arcs of 

 a circle of 14,900 miles radius. 



It has been customary for many years in all survey 

 departments to assume that the angle of refraction 

 on a ray bears to the angle subtended at the centre 

 of the earth a ratio denoted by k, which is called the 

 "coefficient of refraction," assumed to be constant at 

 a given point for all rays. It is easy to see from this 

 that the ratio of the curvature of the ray — tacitlv 

 assumed to be circular — to the curvature of the earth 

 is 2fe ; and that if 2fe = i a horizontal ray would circle 

 the earth. According to Mr. Mallock 's result, 2k = 

 3960/14,900, taking the earth's radius as 3960 miles, 

 which leads to fe = oi33. Now this is not a value 

 ordinarily met with in practice. In Clarke's 

 "Geodesy" values of k derived from observations 

 of the Ordnance Survey are given as 00809 ^^^ ''^ys 

 over water and 00750 for rays over land. These 

 values are not far diiferent from values obtained from 

 other surveys. 



Mr. Mallock 's reasoning is based on the equation 



/ H-A\ 



When h — o this becomes z'p(i— 000029), or v„/[x, 

 where /n is the refractive index of air at standard 

 pressure and temperature. While this is correct, it 

 appears to me to be quite erroneous to consider the 

 equation as giving the correct velocity at heights of 

 a few thousand feet. It may not be incorrect to 

 state for a limited range of height that the velocity 

 varies as the height ; but surely it is incorrect to 

 deduce the factor of this variation from an assumed 

 law which gives the velocity at height H (the height 

 of the homogeneous atmosphere = 83 km.) equal to 

 the velocity in vacuo? 



If the refracted ray is circular and of the same 

 radius of curvature for rays deviating several degrees 

 from the horizontal, it would follow that the value 

 of k at two considerably different levels would be the 

 same. Now the refraction depends on /x— i, which 

 varies as the densit}' of the air. It is manifest that 

 k is smaller at a considerable height than at sea- 

 level in the proportion of the densities at the two 

 heights. The value of fe varies not only with the 

 height, but also with the angle of elevation of the 

 ray. The most convenient plan so far evolved is to 

 speak of the "coefficient of horizontal refraction," fe„, 

 and to give values for this quantity at various 

 heights. Under certain average conditions for a 

 ray from A to B, points the heights of which are 

 h^ and hj,, the refraction may be computed by using 

 the coefficient of horizontal refraction appropriate to 

 height 1/3(2^0+^^), while for the reverse rav 

 i/3(fea+2^(,) should be used. The values of k^, which 

 follow from purely theoretical considerations if a 

 temperature gradient of 3° F. per 1000 ft. be assumed, 

 vary from 008 at sea-level to 005 at 19,000 ft. for 

 temperatures and pressures 82°, 30 in., and 25°, 15 in., 

 respectively. These values are found to account vety 

 well for refraction in numerous Indian observations. 



Refraction is not, in general, constant throughout 

 NO. 2702, VOL. 107] 



the twenty-four hours. 'It is usually smallest in the 

 afternoon at about 3 p.m., and the minimum value 

 then reached is approximately the same from day to 

 day. On this account observations are often re- 

 stricted to the hours between 2 and 4 p.m. It mav 

 easily happen that the refraction at 8 a.m. is double 

 that at 2 p.m. The values of fe given above refer to 

 minimum refraction. Recent research has shown that 

 the diurnal change is due mainly to the changes of 

 temperature in, the first 300 ft. of the atmosphere; 

 in that region the form of the ray of light is by no 

 means circular. Beyond a height of 300 ft. tempera- 

 ture changes in the air due to conduction practically 

 disappear. For rays of light which remain most or 

 all of their length within a distance of 300 ft, from 

 the ground, highly anomalous values of fe may, and 

 generally do, exist. In such cases afternoon refrac- 

 tion is smaller than is indicated by values of fe already 

 given, and in some cases is zero, or even negative. 

 Such rays require special consideration. 



Results of a good many observations will be found 

 in my " Formulae for Atmospheric Refraction and 

 their Application to Terrestrial Refraction and Geo- 

 desy " (Professional Paper 14, Survey of India, Dehra 

 Dun, 1913) ; and a more recent article in "The 

 Dictionary of Applied Physics " (Macmillan and Co.), 

 now under publication, may also be consulted. 



J. DE Graaff Hunter, 



Dehra Dun, United Provinces, India, July 13. 



The only points in Dr. Graaff Hunter's letter to 

 which I need refer are (i) the objection raised against 

 taking the refractive-index gradient for the lower 

 levels of the atmosphere as being identical with that 

 which would make fx — i at the height of the homo- 

 geneous atmosphere, and (2) the statement that 

 "conduction " of heat extends to a height of 300 ft, 

 above the ground. 



With regard to (i), the pressure gradient near the 

 ground, and the density and refractive-index gradients 

 also, decrease linearly at such a rate that if the linear 

 relation continues to hold, the pressure and density 

 would be zero and the refractive-index unity at the 

 height H, and this is the gradient which should be 

 used in correction for refraction to such heights, as 

 the linear relation is a sufficient representation of the 

 facts. How far depends on the order of accuracy 

 aimed at. 



Temperature effects may make a difference of i or 

 2 per cent, per 1000 ft., but in such an uncertain cor- 

 rection as that for terrestrial refraction this is scarcely 

 worth notice. 



The presence of water-vapour will have an effect as 

 well as variation of temperature, and it will generally 

 be impossible at any particular time and place to 

 know for certain what the refraction really amounts 

 to, especially if the course of the ray is long. 



(2) It is scarcely correct to. speak of the irregular 

 distribution of temperature near the ground as being 

 due to conduction. True conduction in the air is 

 quite insensible compared with diffusion by eddies and 

 the general instability of flow. A. Mallock. 



The X-ray Structure of Potassium Cyanide. 



Writing in the current number of the Proceedings 

 of the Royal Society, Prof. A. O. Rankine concludes 

 from determinations of the viscosity of cyanogen gas 

 that the cyanogen molecule "behaves in collision like 

 a hard body formed by two overlapping hard spheres, 

 each of which has the kinetic properties of a nitrogen 

 molecule." He gives as the distance between the 

 centres of these overlapping spheres 23 x 10-' cm. 

 Prof. Rankine also remarks : " It is significant that 

 the crystals of potassium cyanide and those of the 

 potassium halides are usually stated to be iso- 



