Dr. Maskelyn es form idee for finding the longitude , &c. 147 
than 90°. The consequences therefore with respect to its 
right ascension, must be as stated in the third rule. 
In Dn Maskelyne's XIVth Problem, it is said, “ right 
ascension will be of the same kind, or in the same quadrant 
of the circle as the longitude is, unless B exceeds 90°, which 
can only happen when long . is in 1st semicircle * Then if long, 
be in 1st. quadrant ; M will be in 4th quadrant ; and the ope- 
ration will give log. cot. excess of M above 9*. Or if long, 
be in 2d. quadrant, M will be in 3d. quadrant, and the opera- 
tion will give L. t. excess of -M above 6 \ 
In each of the two Problems the quantity which comes out 
by calculation, either for the longitude or right ascension, is 
the distance from the nearest equinoctial point. In the first 
quadrant this quantity itself is the longitude or right ascension. 
In the second quadrant this quantity must be subtracted from 
i8o°, but in the third quadrant it must be added to 180°, and 
the difference or sum will be the longitude or right ascension 
sought. In the fourth quadrant this quantity must be sub- 
tracted from 360°, and the remainder will be the longitude or 
right ascension required. 
M. Delambre has duly appreciated the value of Dr. 
Maskelyne's method, while comparing it with that of M. 
Lalande. Lalande uses the four following proportions for 
finding the longitude and latitude.^ 
R : cos. AH : : cos. SH : cos. SA. 
R : sin. AH : : cot. SH : cot. SAH. 
R : cos. SAF : : tan. SA : tan. AF. 
R : sin. SA : : sin. SAF: sin. SF. 
* These words printed in italics also contain a mistake, similar to that pointed out 
in the preceding Problem. In consequence of these mistakes, in each of the two 
instances, the remarks after the words in italics in the quotations are incomplete, 
f Page 304.. Vol. I. 
