26o 



NA TURE 



[January 12, 1899 



always presents the concavity towards the denser layers ; and 

 there is another principle, that the amount of curvature of the 

 ray, i.e. the total bending that there is in the ray over a given 

 length of ray, is directly proportional to the rate at which the 

 density changes along the normal to the direction of the ray. 

 For instance, if we take a vertical line, the normal to the 

 direction of the ray is horizontal, and there is no change of 

 density in that horizontal direction, and accordingly there is no 

 bending of the ray ; if, on the other hand, the general direction 

 of the ray is horizontal, the normal to the ray is vertical, and 

 that is the direction along which there is maximum change of 

 density, and therefore in that case you will get maximum bend- 

 ing. We get, then, the two cases : when the ray is vertical 

 there is no bending, no curvature ; when the ray is horizontal 

 you get maximum curvature ; and for intermediate directions 

 you get intermediate amounts of curv.iture. 



I was first led to look into this subject by considerations which 

 arise in discussing certain questions respecting artillery firing, 

 and I propose to give you some results which I have obtained in 

 order to show the effect of refraction upon artillery fire. .\ 

 mile on the earth's surface subtends at the centre of the earth 

 an angle of about 52" ; the refraction will have a mean angle of 

 about 4', a minimum value of about 2V', and a maximum value 

 of about S' ; and taking a range of three miles these values of 

 the refraction would become 12", about 8", and about 24" re- 

 spectively ; and very exceptionally the refraction would amount 

 to about I' 1 8". The meaning of this, in regard to artillery 

 fire, is that (taking this exceptional amount of refraction), if the 

 tangent sights of the gun were laid upon an object at that 

 distance they would be really laid at an elevation l' 18" too 

 much, and correction for terrestrial refraction would consist in 

 depressing the gun through an angle of i' 18". That is not a 

 very important matter from an artillerist's point of view, because 

 guns can only be laid properly to within about 5'. 



There is also the question of determining the range. That can 

 be done from an elevation by an instrument called the depres- 

 sion range-finder. If we take the range of an object by means 

 of this instrument the terrestrial refraction would give a longer 

 range than we ought to have, and the necessary correction would 

 diminish the found range. 



I now come to other cases that may present themselves in the 

 density of the air. The case that we have considered already is 

 that of the temperature diminishing gradu illy upwards at the 

 rate of 1/300' !•'. for every foot of ascent ; in (">reat Biitain the 

 diminution is seldom more than about 1/130° or less than 

 1/400' 1'., but in other climates it is different. If the temper- 

 ature were to fall at a n-ore rapid rale the air would be very 

 much more nearly of uniform density, and that would result in 

 a smaller curvature of the ray. If the fall were at the rate of 

 about 1/30" Y. for every foot of ascent it would result in the 

 density of the air being uniform, and there would be no ter- 

 restrial refraction at all. A more rapid fall of temperature still 

 would cause a rise of air density upwards, and that would cause 

 a curved ray with the concavity presented upwards. In such a 

 case the refraction is said to be negative, whereas in the case 

 that we had formerly the refr.action is said to be positive. On 

 the other hand, a rise of temperature upwards causes a rapid 

 diminution in air density in ascending, and the ray with the 

 concavity presented downwards is then more curved ; and in 

 the extreme case in which the rise of temperature upwards is 

 at the rate of l/l6^ F. for every foot, the curvature of the 

 ray would be the same as that of the earth, and ir 

 that case — which, of course, would never actually present 

 itself — we should be able to see completely round the globe, 

 simply because the ray would encircle it. .\gain, climatic con- 

 ditions may le.id to another distribution of the density. There 

 might be a gradual rise in density upwards to a certain stratum 

 of maximum density, and then a diminution of density upwards, 

 in which case the ray of light would pass in a curious sinuous 

 path with the concavities presented towards the denser layers. 



[Major MacMahon here enumerated conclusions, relating to 

 terrestrial refraction in the plains of India, drawn from the 

 experiments and observations of the late dencral J. T. Walker, 

 K.E., formerly Superintendent of the (Jreat Trigonometrical 

 Survey of India, from which it appeared that the circumstances 

 mainly affecting terrestrial refraction were in order of import- 

 ance as follows : (l) The time of the day, (2) the temperature, 

 (3) the aspect of the .sky — whether cloudy or sunshine, and (4) 

 the humidity of the air.) 



Before proceeding to the next part of my subject, I will 



NO. 1524, VOL. 59] 



mention the well-known case of astronomical refraction — the 

 circumstance that during a total eclipse of the moon the whole 

 disc of the moon is not obscured, the fact being that the rays of 

 the sun in p.assing through the atmosphere of the earth are 

 refracted towards the normal, and in that way some light does 

 get upon the surface of the moon. 



I come now to that effect of extraordinary refraction which is 

 more especially termed mirage, and which was first noticed, so 

 far as we know, by the French army under Napoleon. "The 

 conditions favourable to mirage are generally a very hot sun 

 and a sandy soil, which becomes very hot under the influence of 

 the sun, and an almost total absence of wind. Under these 

 circumstances there is an extraordinary amount of negative 

 refraction, the rays are very much curved, and the concavity is 

 presented upwards. An illustration which is familiar to eveiy- 

 body. because it occurs in many books on physics, is that in 

 which the observer sees the top of a tree by means of a nega- 

 tively-curved ray, and it accordingly appears to him to be in the 

 direction of the tangent to the ray where it enters the eye ; the 

 other points in the tree he sees in other directions, and alto- 

 gether the tree appears with an inverted image below it. Not 

 only so, but where there is a very clear sky that also is refracted 

 down, so that the tree appears in the midst of an inverted 

 image of the sky, w hich has very much the appearance of water. 

 This phenomenon is very common in Egypt. In Egypt there 

 is very often a great quantity of sand with villages dotted about, 

 these being somewhat raised in order to escape the periodical 

 inundations of the Nile, and the effect to an observer is that of 

 a nuinber of raised villages in the midst of what appears to be 

 an enormous lake. The illusion is increased by two circum- 

 stances : first, that by reason of the great heat of the sand 

 there is a considerable convection of heated air upwards, which 

 gives the air that peculiar rippling appeanance, causing the re- 

 fracted sky to look like ruffled water ; and second, that the 

 general direction of the ray is very similar to that of a ray- 

 reflected by a horizontal mirror placed upon the ground. This 

 phenomenon is also common in Australia and in the plains of 

 India, in the low-lying fen districts of England, and on the 

 shingle ranges at Lydd. 



One very curious thing about niiraee is that it depends very 

 much upon the position of the eye ; a few inches in the height 

 of the eye may make all the difierence. I remember myself, on 

 the plains of India, observing a mirage which was only evident 

 when I was at a particular height ; there was only a vertical 

 space of two or three inches in which the effect could be seen, 

 so that these phenomena may easily escape notice. .\ singular 

 effect may sometimes be observed at a particular spot on the 

 south coast, and very likely at other places ; when the waves 

 come in on to a very hot beach, if you place the eye within 

 about a foot from the ground and look parallel to the wave- 

 fronts, you can see an image of the wave two or three feet above 

 the real wave. This may conceivably arise in this way : the 

 wave may bring in some cold air, and if the wind were blowing 

 a little off the heated beach there might be soine heated air 

 brought in as a layer above that cold air ; that wnuld give that 

 rapidly diminishing density upwards which gives a ray with 

 considerable curvature and with concavity presented downwards, 

 and would certainly result in an image of the wave above the 

 real wave. 



I should like to mention a case of refraction observed on the 

 artillery ranges at Lydd, which has given rise to some contro- 

 versy. .'\n officer was firing on a hot .sultry day, from an 

 ordinary Maxim machine gun at a target about 600 yards 

 distant, and as the firing went on he saw a great wedge-shaped 

 gap in the top of the target, and he thought that the hail of 

 bullets had beaten down a part of the target. To his astonish- 

 ment, however, when the firing ceased the gap disappeared, 

 and the target appeared intact and undamaged. I imagine this 

 to be an effect of mir;ige. I conclude that he was looking over 

 the gun through the heated gases rising from the muzzle, which 

 formed a medium of gradually increasing density upwards ; he 

 was observing the upper portion of the target through this 

 medium, and I have no doubt that that caused negative refrac- 

 tion, bending the rays so that the sky above the target was 

 seen in the shape of a wedge, something like the shape of the 

 vertical section of the rising gases. I have discussed the matter 

 with physicists, and some agree with me, but other physicists of 

 note do not accept the explanation which I have given. 



I now pass on to another part of the subject, which is called 

 "looming." Distant objects are said to "loom" when they 



