558 PROFESSOR TAIT ON MIRAGE. 
fall to a nearly stationary state) secures the upper erect image, the latter the 
inverted image. When the former is not present, we have the phenomenon so 
often observed and figured by Scorespy. This requires merely a change from 
a slowly diminishing refractive index to a more quickly diminishing one, and 
may occur simultaneously in more than one horizontal layer. Turned upside 
down, this arrangement gives the ordinary mirage of the desert. When this 
condition is not present, but only the stationary state, we have VINCE’s upper 
erect image without the inverted one. This is figured several times by 
SCORESBY. 
9. If, instead of a plane of minimum, we have a plane of maximum, refrac- 
tive index, we may assume 
pw2=a?—y?, 
An investigation precisely similar to the preceding gives for a ray passing 
through 0, 6 the equation 
—1 y -1 b 
a= J/a?—7? (sin “—sin -) : 
” ” 
Each ray therefore is a harmonic curve, whose level line is in the maximum 
stratum, and which passes through that stratum an infinite number of times. 
The locus of vertices is 
si 
e= Ja—n? (cos ~+n7) : 
Here 7 is to be taken positive when m (any integer) is even, and negative when 
it is odd. 
The following rough table suffices to determine the general form of this 
curve in the particular case a=6d. It is shown in fig. 6; and it has been 
foreshortened for convenience of representation. 
-1 
i. —cos 2 £ 
7 o) b 
n=0 n=1 
iow aa | 
1:0 0:0 +0:°0 98 9°8 
0°95 0:2 +0:98 8:8 10°76 
0:9 0:29 +1°39 8°35 1113 
0°8 0°41 +1:98 7:70 11°66 
0-7 0°51 +2°42 716 12:0 
0°6 0°59 +2°78 6°64 UA 
0°5 0°67 +3°05 6:11 be 2a 
0°4 0°74 +3:'20 5°46 11°86 
03 0:80 +2:97 4-47 10°41 
0°25 0°84 +1°9 2°5 63 
0:2 0°87 0:0 0:0 0:0 
01 0:93 oe 
