560 



Mr. A. R. McLeod on 



should tend to the corresponding astronomical refractions as 

 limits, when hi increases indefinitely. 



The refraction correction for an observer's instrument is 

 the angle between the tangent to the ray at his position, and 

 the chord of the rav ioinino its extremities. The value of 



^ v 'J o 



this angle lies between ^A</> ar| d A^ an( l should tend 

 to the corresponding astronomical refraction as a limit when 

 l»i increases indefinitely. Denote its value by e;A$i f°r a ra J 

 whose zenith distance, O , is given, and whose upper extremity 

 is at height hi. The values of e; may be calculated in the 

 following manner. Consider a ray A B C D . . . . (fig. 4), 

 the observer being at A and the points B, C, 1), . . . . being at 



Fig. 4. 



heights 1, 2, 3, ... . km. above him. The observer is supposed 

 to be on the ground (sea-level). Let AT,, BT 2 , CT S , .... be 



the tangents to the ray at A, B, C, The lengths, k, of 



the successive arcs are given by (32). We suppose each arc 

 to be part of a circle, so that the angles made by the tangents 

 at the extremities with the chord are equal. Let 6i denote 

 this angle for the iih arc, which lies between the heights 

 ft»-_i = (t— 3) km. and hi — i km. Let L; be the length of that 

 chord of the rav which is drawn from A to the upper extremity 



