PROFESSOR TAIT ON MIRAGE. 565 
or, with the laws of BoyLE and CHARLES, 
d(pt 
Now if H=26,000 feet, be the “height of the homogeneous atmosphere,” we 
have 
Po= Rpoto =Jpoll , 
so that the hydrostatic equation becomes 
Instability occurs when f is positive. Hence the greatest rate of fall of 
temperature, per foot of ascent, which is consistent with stability is 
WG. a 274° 
is: 26,000°" , 
dy +H 
or —1°:05 C. per hundred feet. 
GLAISHER,* in a captive balloon, on two occasions out of twenty-seven, . 
observed the fall of temperature in the first hundred feet to be 1°°8 F. and 1°:9 F. 
respectively. On other three of these occasions it was 1°°7 F., 1°°5 F. and 1°°3 F. 
respectively. The first two correspond almost exactly to the 1°°05 C. above 
computed for a stratum of uniform refractiveindex. The temperature near the 
earth’s surface was on these occasions 73°°6 F. and 76°2 F. ; or, roughly 24° C. 
The greatest 77se of temperature per 100 feet of ascent, which he observed on 
any of these twenty-seven occasions was 0°3 F. only. It seems from what 
follows, therefore, that on none of these occasions would Vince's phenomena 
have been possible. 
17. To fix the ideas, let us now assume that the first 50 feet of air is of 
uniform density, and that next there is a stratum of 50 feet thick in which the 
-refractive index is given by 
298 + 68 cos MH 50), | 
pe =a +e cos 50 
* B. A. Report, 1869, p. 37. 
