J. M. Schacherle—Lateral Astronomical Refraction. 467 
Ah Pere aor 
Let D be the inclination of the plane of equal density to the 
horizon, and let ¢ be the angle which a vertical plane, perpen- 
dicular to the line of intersection of the inclined and horizontal 
planes, makes with the meridian, reckoned from the south 
.point toward the west through 860°; the angle ¢ always being 
in that quadrant in which the préssure is greatest. 
_ Now a ray of light from a star lyingin the plane whose azimuth 
is ¢, and making with the normal to the horizontal plane the 
angle ¢, will make the angle C+ with a normal to the in- 
clined plane. For a homogeneous atmosphere the refractions for 
the first and second cases would then be given by the equations 
2% 
‘ m ails: 
S10 2-2 and. sis 
sin 
C : Ah 
sin (: + 3) 
ra=t—z di 8 Esa 
D.. 
; Ah 
: or goca@. tan:2 ? =a tan ( a Fy very nearly. 
The error in the computed refraction due to the inclination of 
the strata will therefore be 
play 
r=a (tan 2— an satel 
which, if we neglect terms of the second order, can be written . 
Ah 
Ar=a —- sec*z. 
D 
_ The ref sacdhion 4r will moreover be wholly in zenith distance, 
and all rays, lying in the vertical plane whose azimuth is %, 
will be refracted in a vertical plane. If ¥’ denotes the angle 
which any other vertical plane makes with the meridian, all 
rays of light in this plane will, after refraction, lie in a plane 
which is inclined to the horizon by the angle 
90° —a = sin (W— ¥”) 
The vertical and lateral components of refraction due to the 
Inclination will then be respectively 
j ah . A ad 
a sec? 2 COS (W'-W") and ay os z2sin (V-¥"). 
The second expression giving, for the zenith distance z, the 
angular distance of a star from the vertical circle in which it 
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