PROFESSOR TAIT ON MIRAGE. 561 
The headings explain themselves. The last column is required, as will 
soon be seen, for the determination of the magnitudes of the images, as 
compared with that of the object when seen (at its true distance) through 
uniform air. 
11. Let us now extend the formule of § 4 to the case of a stratum of depth 
ec, in which the refractive index is constant (=,//(c) ); surmounted by 
another of thickness 6, in which the index is .//(y). 
The equation of a ray, passing from the origin, which we now take in the 
lower surface of the inferior stratum, is 
While y is not greater than c, this is the straight line 
Pt ae 
~ NF) a 
But when y is greater than c, we have 
1 
Sapa ORT ats ain 2 oS OD 
Also; for the branch of the curve of vertices which is in the upper stratum 
(the other branch being, of course, the axis of 2), 
_ el fm) _ ” 
Oa J fc) —Kn) + Raf Toa = - oo? cal 
Fig. 5 has been roughly traced from this formula and the curve of fig. 2. 
12. In the next following equations, recurring to the form 
w=a+ ecos se ; 
we will simplify matters by making a=1, and altogether neglecting the terms 
in é when they are added to others not containing e. This will be fully 
justified, so far as air is concerned, in a subsequent section. 
By § 11 the equation of the curve of vertices is 
b,/2 
ef = —jacoseesg + oe 
1s = sine sint 
If we write 
where @ is the inclination of the straight part of the ray, this becomes 
7 4 2 hy \ = jaad 
C= 5. 7 
