ALTAZIMUTH SOLAR OBSERVATIONS. 349 
‘be usually quite accurate enough to calculate the parallactic angle 
q by either of the formule 
sin Y sin A’ _ 
sin ¥ sin 7” 
sin 
though strictly the zenith and polar distances for the afternoon 
observation, together with the colatitude should be used to calculate 
that quantity ; ic. it should be determined from the three sides 
Pas Ca, Poe . 
The equation of equal altitudes may be derived by writing the 
value of cos (p + 4 dp)—in which 3 dp denotes the half difference 
between the polar distances at the two observations—in terms of 
¥, (and A, and taking the difference of the results. This procedure 
gives 
; sin 3 dp sin 
sin $(A4,-—A,) = ive as Bay Te a eee (50) 
But the azimuth of the sun’s centre is not directly observed, and 
the time must be recorded in order to compute the change of polar 
distance, hence, since 
sin g = 
vesssees(49) 
sin A = sin 7 sin p cosec ¢ 
and the quantity (50) is small, the equation may with advantage 
be written in the simpler, approximate, but sufficiently accurate 
form 
A,-A, = (50a) 
si eel 
cos ¢ sin 7” 
$ the latitude being considered positive, and 7” as before, half 
the elapsed time between the observations. The azimuthal angle 
A is reckoned east or west from the elevated pole. When the 
polar distance is increasing, the azimuthal angle from pole to sun 
is less for the first observation than for the second, whether the 
former be a morning or an afternoon observation. 
For great precision, second differences should be taken into 
account in computing dp, especially at the solstices, being then 
considerable, although the change of declination is itself small. 
A nna i oie its 
1 We write yy, because hereafter the case is considered where the 
Second observation is made at a locality the latitude of which is slightly 
different, 
