560 PROFESSOR TAIT ON MIRAGE. 
With this law it follows that, if the eye be in the plane y=0, the equation 
of the curve of vertices is 
e&= gener f ae ae 2 
™ 
gh cos = eGg—— 
b 
2.0 
— f2-b [2-4 toos™ a +0008" F (sing a) 
The equation of the path of a ray is 
=) Fe as al 
Jeane — cos 
ey 2 TB (sing? } 
7 ore Aa at pt 
where sing? =sing? sing . 
We have also 
TY — ogi 
iy mA Coss" — cos; 
Ge a ra 
; eA a? 4+ cos 
b 
and, for y=0, this takes the value 
x 2h sin 
o, at ecost 
For the application of these formule the following little table has been 
prepared :— 
1 . E,(& 
7 5 =cosecay C3) i a6 - 
T T 
0:0 2 5 5 
01 6°39 1:58 1:60 
0:2 3°24 161 1:69 
0°3 2°20 1:66 1:87 
0°4 70 1°74 2°18 
05 141 1:85 2°70 
0°6 1:24 2°01 3°67 
0°7 1:12 2°24 5°74 
0°8 1:05 2°60 11:53 
0-9 1:012 3:26 42°24 
0°95 1-003 3°94 16417 
0-975 1:00077 4°62 650°85 
1:0 1:000 co oo 
