January 29, 1920J 



NATURE 



563 



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 anonymous communications.} 



The Deflection of Light during a Solar Eclipse. 



It may be worth while to give my endeavour to 

 obtain a rough value for the refraction effect of the 

 atmosphere during a total eclipse of the sun. The 

 simplest case possible is when the sun is in the zenith. 



I will assume that the air density of the normal 

 atmosphere has been removed, and that there is left 

 the atmosphere which produces the abnormal effects 

 in question. This is not necessary, but it makes the 

 calculation somewhat simpler. 



If O be the place on the earth's surface of maximum 

 air density, the density p. of the residual atmosphere 

 there will be one-seventieth of the density of the normal 

 atmosphere if we assume that it corresponds to a fall 

 of 4° C. in the atmosphere when in equilibrium. Take 

 Ox in the direction opposite to that of the motion of 

 the shadow, and Oy the vertical passing through the 

 centre of the moon's disc. This assumes that the 

 density is greatest at the centre of the shadow, which 

 is almost certainly incorrect. I will take the density 

 at any point of the residual atmosphere in the plane of 

 xy to be given by 



where /3, although it varies with temf>erature, is 

 assumed to be constant and equal to 1-3x10-", dis- 

 tances being measured in centimetres. If we assume 

 that the density of the atmosphere becomes normal at 

 150 miles distance from O, k will be 4-17x10-'. 



With these values of the two constants, the above 

 formula expresses that the horizontal density gradient 

 is uniform and independent of height, and that the 

 atmosphere has its normal density at a distance of 

 150 miles. None of these statements is correct. The 

 shadow-cone in the earth's atmosphere acts like a down- 

 draught chimney or a kind of thermal air-compression 

 pump, increasing the density in the central region of 

 the shadow and diminishing it in surrounding regions. 

 Thus K may have a very much greater value than that 

 given above, and, indeed, the factor i-kx may be 

 quite incorrect in form. 



However, taking this formula for the density, the 

 index of refraction of the residual atmosphere at any 

 point is 



M=i+(Mo-i)(i-«-^->-^^, 



where ju,= 1-000004. 



The path of any ray in the plane of xy might be 

 got by solving the usual differential equation for this 

 case, but I have not succeeded in getting a solution. 

 However, the amount of the deviation can be obtained 

 without knowing the actual path. 



If ^ be the angle which the tangent to a curve of 

 equal refractive index makes with the a.xis of x, we 

 have 



tan 



9/i /3/i 



^ 9-f/i 



It can easily be shown that the radius of curvature 

 of the lines of equal density or refractive index in 

 the neighbourhood of the axis of y is much greater 

 than the radius of the earth. Thus, as we have 

 assumed the earth's surface to be plane, we can 

 assume these lines to be straight in the portion of 

 the atmosphere concerned. On the axis of y, 

 tan If =0032, and for an observer at O the refraction 

 of the light coming from a star near the edge of the 

 NO. 2622, VOL. 104] 



sun's disc will be the same as if he were looking 

 through an atmosphere stratified in parallel planes, 

 making an angle (p with the horizon. A ray coming 

 from such a star will make an angle of ^— 15' with the 

 normal to these planes, and the refraction will be 



(/<o-i) tan (0-15') 



= 0000004 ^ 0-0277 



= 1108x10-"' or 0023". 



If the ray come from a star the angular distance of 

 which from the sun's centre is 45^, the result is 

 00082", which is a little more than one-third of 

 0023'. But if, as I believe, k has been greatly under- 

 estimated, the possible values of these refractions are 

 much greater. 



If the observer be hot at the origin, but at a dis- 

 tance along the positive direction of the 3c-axis, the 

 refraction of the light from stars on the other side 

 of the sun's disc will not be away from the sun's 

 centre, but towards it, and vice-versa, if he be on 

 the other side of the origin. But no difficulty of this 

 kind occurs for refraction in planes perpendicular to 

 Ox if the position of the observer be on the x-axis. 

 Perhaps it is worth mentioning that, from the only 

 account of the observations I have seen, it appears 

 that, with the exception of one star, all the changes 

 in right ascension were of the same sign, whereas the 

 changes in declination were all in the right direction. 



I ought to mention in reference to Sir Arthur 

 Schuster's letter (Nature, January 8, p. 468) that 

 I never thought of a ray that, in its passage through 

 the earth's atmosphere, lay partly inside and partly 

 outside the umbra. And I thank him for correcting 

 the slip that I made in- the angular radius of the 

 sun's disc. In these days of relativity, an error of 

 fifteen minutes either of arc or of time is, perhaps, 

 excusable. Alexr. Anderson. 



University College, Galway, January 14. 



" The White Water." 



It is possible that some readers of Nature can en- 

 lighten me on the cause and nature of what the Arabs 

 call " The White Water." This phenomenon was wit- 

 nessed by me on two occasions at the entrance to 

 the Persian Gulf in the vicinity of the Quoin. On 

 both occasions the time was about 8 p.m. There was 

 no moon on the first occasion, but a moon on the 

 second. 



I first observed what appeared to be a line of 

 breakers ahead of the ship; this was not possible be- 

 cause we were in deep water and the position of the 

 ship was known. As we approached, it seemed that 

 these supposed breakers were a succession of phos- 

 phorescent waves of a period of about sixty to the 

 minute. The waves extended, so far as could be seen, 

 for about two miles. 



In addition to these waves there were also phos- 

 phorescent Catherine-wheels, both right- and left- 

 handed, also phosphorescent light apparently coming 

 to the surface and radiating out in all directions. 



The phenomena lasted for about half an hour, gradu- 

 ally fading away, apparently sinking. There were 

 strong atmospheric disturbances at the time. Both 

 nights were clear and the sea was calm. I could 

 obtain no local information. I may add, in con- 

 clusion, that I was not the only person who witnessed 

 this display. A. R. Palmer. 



Portsmouth, January 13. 



I HOPE that Capt. Palmer's letter will induce officers 

 of the Indian Marine to investigate any cases of 

 " White Water " that coxne under their notice. I am 



