318 G. H. KNIBBS. 
will facilitate the computations. It may be remarked that the 
_ bracketed factor in (12) is generally very small and consequently 
a very rough calculation of its value is all that is required. 
TasBLe I.—Values of } t? sin? p. 
Semi- Polar Distances. 
oan. ae. «80° 40" .. 50°. 60°70". 80°. ee 
t 170° 160 150 140 130 120 110 100. 9% 
fmm.) 02. 00 O8t. 12 16! 1:7". 10. oe 
2 63. 00. 20 . 39 £6: 69. 69 75.48 
3 G6... 91. 44. 73 104 133 156 .17-1 fee 
4 Oy. S179 130° 164 936 (97-7. 30:5: Sim 
5 ib 657 123 203 288 $63 48:3 476 40% 
6 21 83 J7-7 2992 41:5 53-0 62-4 686 704 
7 2:9 11:3 24:1 393 56-5 72-2. 85:0 93:3 96:2 
8 38 147 31-4 51-9 73-7 94-2 111-0 121-9 1257 
TasLe II.—Values of } B? coté~ 
True Zenith Distances. 
30°. 3B’ 40’ 4.” GO” a 
10’ Lh oe 10" 6 07" 06" 06". O83". Oe 
162 S428 88 Oe ee 1 Oe 
20 60 “60. £3. 35. 99 94° 90 13.798 
$0. .488 412.94 79, 66 55 46. 29. oe 
40-242 199 166 140 117 98 81 OSB1 29 
50 378 312 260 21:8 183 15:3 126 79 38 
60 544 449 37-4 314 264 2290 181 114 55 
75 850 70-1 58:5 49-1 41:2 344 28:3 179 87 
90 122-4 1009 84:2 70-7 59:3 49:5 408 257 125 
The application of the tables, by means of which the values of 
the corrections may be interpolated by inspection, does not require 
illustration, and it is only necessary to remember that a, f or 4 
are one-half of the observed differences between the azimuths, of 
the zenith distances corrected for refraction, or of the times. 
6. Refraction Error of the mean of observed altitudes.—In the 
case discussed in the preceding section, the error of employing the 
mean of the true altitudes of a star has been investigated. 4 
