TERRESTRIAL REFRACTION AND MIRAGE. 277 
fraction in the plains of India as bearing upon artillery fire :-— 
(a) That the best time for shooting is between the hours of 1 
and 8 o’clock p.m. when the refraction whether positive or 
negative is small. 
(b) Taking the extreme decimals of the contained are to be 
+1°5 and —-2, and a range of 2’ of arc, say 24 miles, the 
angular refractions will range from +3' to —24'. In these 
two cases it would be necessary to depress the gun 3’ and 
elevate it 24”, in regard to the line of sight, respectively. 
(c) Therefore I gather thirdly, as my last conclusion, that the 
consideration of terrestrial refraction in the plains of India is 
not of urgent importance, because 3’ is not a very serious 
matter in artillery fire. 
Greater complication and uncertainty arises when we have to fire out 
to sea from a high cliff ina tropical climate. We might well there have 
a state of affairs such as is depicted in fig. 6 with the stratum of max- 
imum density at some distance above the surface of the ground, and 
the observer himself above the stratum. In such a case the path 
of the ray: would be somewhat sinuous, and the effect might be 
rather serious. JI have had great difficulty in obtaining data in 
regard to tropical climates or indeed in regard to the Mediterranean, 
Gibraltar, Malta, and such places. I have no satisfactory data to work 
upon, and it is greatly to be wished that one had more facts to speak 
about; but it seems to me that in cases where the refraction is 
likely to be serious, it would be desirable to abandon the vertical 
base depression range-finder or any vertical base range-finder, and to 
adopt a horizontal base range-finder, and then to lay the gun, not by 
tangent sights, but by means of straight-edged sights and quadrant 
elevation. 
I pass on now to consider other effects of extraordinary refraction. 
We have the effect which is termed mirage. 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 we have a state of affairs such as is 
depicted in Fig. 5 and we get quite an extraordinary amount of negative 
refraction ; that is to say, the rays are very much curved and the con- 
cavity is presented upwards. We may take Fig. 7 which is no doubt 
Fie. 7, 
very familiar to everybody because it occurs in nearly every book 
