566 PROFESSOR TAIT ON MIRAGE. 
y being measured from the surface of the earth. Since we may look on p as 
practically unity, we have by the formule above 
idp__1 t= — sate a) 
pw dy 3400p, dy 3400\ HZ, dy)’ 
Hence, by our assumed law of refractive index, 
1 1 dt_34007e? . a(y—50) | 
Hig = oo 
Hence the greatest rate of change of temperature per foot of ascent (at 
y=75 feet) is 
274 x 342re®—0:0105. 
The whole change of temperature, from the bottom to the top of the 
stratum, is 
274 x 3400e?—0°53. 
Both of these quantities are in degrees centigrade. 
18. To get an idea of the magnitude of e’, we note that, by ScoRESBY’s obser- 
vations, the elevation of the images above the horizon is usually about 10 or 15 
minutes of arc at the utmost. Hence, by the value of = in § 10, we may 
assume as an upper limit, j 
1 
Rc 550 > 
or 
e?=0:000008 . 
With this, the greatest rate of rise of temperature in the assumed stratum is 
0°22 C. per foot of ascent, and the whole rise is about 6°°9 C. These quantities, 
moderate as they are, would be greatly diminished by our relinquishing the 
assumption that the density in the lower stratum is constant. 
But even this indicated rise of temperature with elevation has been actually 
observed. Thus GLAISHER® gives, for July 17th, 1862, 
Time. Altitude. Temperature. By Gridiron Thermometer. 
10.30 A.M. 19,415 feet. 38°1 F. 337-1 B, 
10.35 AM. 19,435 feet. 43°-0 F. 42°-2 F. 
10.39 A.M. 19,380 feet. 37°-0 F. 36°°5 F. 
The greatest difference here observed is as much as 5° F. in 20 feet ; 7.¢., at 
the rate of 12°°5 F. or 7° C. per 50 feet, precisely what is required above. 
* B. A. Report, 1862. 
