564 PROFESSOR TAIT ON MIRAGE. 
c c 
b=10¢e b=c b=59 j= 00 
U/] 
7 ff © Sf G § 6 Hei to 
0:0 co — ] for — 10 oe) —1:0 o — 10 
O01 517 — 2°63 23:24 — 1:16 20:40 —1:02 20711 — 1:0 
0:2 42:4 — 4:99 13°39 — 1:34 10:49 —1:03 10:20 — 1:0 
0:3 40:2; —14°‘73 10°25 — 1:58 725 —1:05 695 — 1:01 
0-4 402 +11°95 8:83 — 1:97 569 —1:08 5°38 — 1:01 
0°5 415 + 3:32 815 — 2:97 481 —113 448 — 1:01 
0°6 441 + 1°51 791 —13°91 4:29 —1:21 3°92 — 1:02 
0°7 484 + 0°73 801 + 2:31 397 —1°41 3°57 — 1:03 
0°8 553 + 0:32 850 + 0°58 3°82 —2:52 3:36 — 1:07 
0:9 68:3 + 0:09 969 + 013 383 +0°83 3:25 —: 1°35 
0°95 81:9 + 0:026 11:02 + 0:03 394 +014 3°23 +60°59 
0:975 956 + 0:007 12:39 + .0:01 407 +0:03 3°24 + 0°33 
1:0 re) 0:0 ore) + 0:0 fo) +0:0 ao + 00 
16. We must now consider, so far as is necessary, the physical properties of 
air :—and observations which have been made as to actual changes of temper- 
ature at different elevations above the earth’s surface. There is no necessity 
for dealing with very exact physical data, because we must make assumptions 
as to distribution of temperature which cannot, at the best, be more than rough 
approximations. All that we can attempt to show is, that the observed pheno- 
mena are of a character and ona scale compatible with the known properties 
of air, with observed changes of temperature in the atmosphere, and with the 
arrangement we have suggested for the production of these phenomena. 
Thus, although aqueous vapour diminishes the refractive index of air, the 
practical effect is so minute at its utmost that we neglect it :—a very slight 
change in our assumption as to temperature would be sufficient to make up for 
it. 
Assume, then, for air at 0°C. and 760 mm., 
1 
f= 1.000294— 1 +3700 . 
Assume farther, what is only approximately true, that the refractive power 
depends on the density alone, and is proportional to it :—-2¢., 
1 
nae (pera ee 2 
tl 3400%pi! 
The next assumption :—that the air is practically in hydrostatic equilibrium, 
when such phenomena are observed :—is probably not far from the truth, except 
in the case of the mirage of the desert. It gives 
dp _ 
dy —J9JP; 
