Terrestrial Refraction. 553 



If 7*0 = 0, (24) becomes 



A*-JL(, + *)>.^ 



b ,-, 



-- 4 V« 



2 9 * 



^[•a + 2^ + 6'V-V«] (25) 



Substituting the values 



p = -00002646, q = -000000696, 

 n = 1-0002839, li = 6370 km., 

 we find the following values for the constants involved : 



T=(p + — )= -0000207186; —. --= 702-861 ; 

 v c V c J sjc 



x/'c = 7-5401; 2b = 10599'28 ; 



c = 56-8530 ; ^ - -0000000244842. 



c 



The values k and a involve the zenith distance, <£ , of the 

 ray at the ground. With these numerical values, the values 

 of /\cj)i have been determined for the 8 values of hi given by 

 hi = i km. (i=l, 2, .... 8) ; and for a series of values of </> 

 ranging from 0° to 90° inclusive. These values are given in 

 Table II. They were obtained with the aid of seven-figure 

 logarithms, and are correct to the nearest second. They 

 have been checked by taking successive differences, and in 

 other ways. 



To show that the values of A</>i given by (23) represent 

 the corresponding values of (19) to the nearest second, 

 we have calculated the coefficients of h 2, and h 4 under the 

 radical sign, when (20) is substituted in (19). These are, 

 respectively; d and e, where 



d = 2{qRn Q f (qR,-p)(n --pR)} = '0162005, 

 e = (qn-p) 2 + 2q(n -pR) = -0000206. 



Taking h=S in the biquadratic under the radical, we find 

 that the terms of the third and fourth degrees contribute 

 only 1 part in 11,000 to its value, and this in the case most 

 favourable to them, when <£ = 90° and a=0. 



