272 TERRESTRIAL REFRACTION AND MIRAGE. 
be the path of the ray of light passing from A to B. A T'and B Tare 
Fie. 3. 
Refraction =} (180°+ Z ACB—ZZAT— Z Z'BT) 
K ZACB 
Mean value of K for Great Britain = :078 
Minimum valuein summer ,., =:05 
Maximum value in winter coo | SS ONS 
tangents to this curve at A and B respectively ; ZAC and Z' BC are 
the verticals at the two places. The point B, as seen by the eye at A, 
is seen in the direction of the tangent of the curved ray A PB at A— 
that is to say, in the direction A 7, the point B appears in the direction 
AT. The angle 7A B, the angle between the true direction and the 
apparent direction, is termed the refraction or the angle of refraction ; 
similarly the angle 7’B A would be termed the refraction or the angle 
of refraction from Bto 4. Theangles ZA and Z'B 7 are the apparent 
zenith distances of Band A from A and B respectively. In order to 
determine this angle of refraction at the point A the apparent zenith 
distance of the point B is taken; that is to say, Z being the zenith at 
A,the angle ZA T' is measured by an astronomical instrument; the 
angle Z' B Tis also measured, and then by a formula, which is attached 
to the figure, the refraction is computed. We merely wanta knowledge 
of those two zenith distances and of the angle subtended by the line 
AB atthe centre of the earth in order to express this angle of refraction. 
This angle of refraction is found, as the result of a great many ex- 
periments, to be expressible as a simple multiple of this angle 4C B; 
that is to say of the arc between the points 4 and B; we may represent 
the refraction as K times the angle 4C B. This coefficient, which 
multiplies the angle 4 CB, has in Great Britain a mean value of 078 
which is very nearly +5; it has a minimum value in summer of about 
zy, and a maximum value in winter of about 35. According to one 
authority, exceptionally in Great Britain, this coefficient may be as large 
as 4; thatis to say the refraction may, exceptionally, be half as large 
as the arc between the two points. Taking a mean value of the co- 
efficient K say z's, this means that the curvature of the ray of hight 
between the points 4 and B is only about 3% or from 3% to +; of the 
curvature of the earth. This fact may also be expressed by saying 
that the curved ray isa portion of a circle whose radius is 54 or 64 
times the radius of the earth. Its effect in the normal /atmosphere 
in Great Britain is very small. 
I propose now to examine into the effect this refraction would be 
likely to have upon artillery fire. A mile on the earth’s surface subtends 
at the centre of the earth an angle of about 52”. Accordingly, per 
mile, the refraction will have a mean value of about 4", a minimum 
