144 < Dr. Robertson's demonstrations of the late 
When the longitude is in the third or fourth quadrant, then 
A^O=SAH= B, if the latitude is north, but A+ 0 =SAH=B, 
if the latitude is south. 
If S be on Etf, as represented in Fig. 3, and 6, then 90° — O 
= SAH = B. 
To find the right ascension , 
We have the following proportions, cos. SAF:R::tan.AF:tan.Sx\ 
and R:cos. SAH::tan.SA:tan.AH 
Hence, cos. SAF : cos. SAH : : tan. AF : tan. AH= — " H s ^p AF » 
That is tan. M = c ° s ^ . ^ 0 "g itude . 
COS* 1 1 
S* A 
But tan. A : R : : sin. A : cos. A = , and this being put 
for the cos. A in the preceding expression, we have also 
rr , 7T9 tan. A cos. B tan. longitude 
Tan.at= rm • 
If S be on Ee, then R : cos. SAH : : tan. SA : tan. AH 
CO, SAH .an . SA. Tha , j, tan . M = cos. (9 o°-0)^n. latitude _ 
To find the declination. 
By trigonometry sin. AH : R :: tan. SH : tan. SAH, and tan. SH 
= sih. ah tan.SA H tan# declination = B . But tan 
AH : R : : sin. AH : cos . AH, and sin . AH = tan and this 
being put for sin. AH in the preceding expression, we have 
, . .. tan. JR cos. At tan. B 
also tan, decimation = — ^ • . 
Rules for ascertaining the right ascension from the preceding 
formula. 
1 . The right ascension falls in the first, second, th#rd or 
fourth quadrant, according as the longitude is in the first, 
second, third or fourth quadrant, unless the auxiliary angle B 
be equal to, or greater than 90°. 
