ALTAZIMUTH SOLAR OBSERVATIONS. 359 
assumed polar distance, may be thus ascertained :—Let, as in § 4, 
I denote the angle of intersection between the direction of the 
sun’s path and the vertical through its centre at any moment. 
Then similarly to (g) in that section, we have for the parallactic 
angle g, which is the complement of J, 
cot g = tan J = sin (=£ sin ¢ (61) 
After g is obtained, ¢ may be found for any value of p, by the 
following formule, in which @ is merely an auxiliary angle :— 
tan 6 = tan (cos q ) 
: 2O8 F 80S p— )) wee ece one 62 
ain. os oo ee! : 
cos @ / 
If we make (= 80°, and & successively 1, ?, 3, and 4, the corres- 
ponding values of g will be 45 26’, 53% 34’, 63° 47’ and 71° 50’. 
The curves shewn in Fig. 5 are obtained by (61) and (62) for that 
zenith distance ; the abscissze being the polar distances measured 
from the elevated pole, and the ordinates the latitudes measured 
north or south from the equator. From the figure the latitude 
