1 
56 Dr. Brinkley’s elements of 
d\—d 11 = 2084/' - - (8) 
dV'—dU = 2480" - - (9) 
By the formulae above given 
dv = 2751 dt — 950060 dp 
dv'= 1336 dt — 762080 dp 
dv°= 861 dt — 669980 dp 
x = 7512 dt — 209300 dp 
x 7 =±= 4459 dt — 158300 dp 
x"= 3235 <*—13345° dp 
dn= — ,4390 x . . d(. 3 = — ,9345 x 
dir — — ,3446 x' . . d [ 3 = — ,43 6 7*' 
<*r 77 = — ,2954 x" . . d( 3 " = — ,2130 x" 
From these values it is necessary to compute d V, d V 7 . 
Let H = 2 sin* i ( jG — jG 7 ) cos 7/ cos tt 
H = 2 sin* ^ ( |Q — jG' 7 ) cos 7r #/ cos 7r 
then equations (5) and (6) become 
cos V = cos (7 r — 7T 7 ) — H — (10) 
COS V' = COS ( 7 T — 7 T 7/ ) — H' - (.,) 
It is obvious from the smallness of /3 — j 3 ' and (3 — / 3 ", and the 
magnitude of the errors of U — V and U 7 — V /7 that the errors 
of jG — / 3 # and jG — fi" may bear a considerable proportion to 
the quantities themselves, or be even greater. Therefore the 
coefficients of the differentials dp and dt in d¥L will be quite 
incorrect, if the differential of H be computed in the common 
way. 
It is the smallness of G— / 3 7 and / 3 7 — jG 77 in this case that 
renders M. Laplace’s method of computing V, V' inconve- 
nient, in consequence of its being necessary to use the tangent 
of an angle nearly = 90°. 
But the variations of V and V # may be obtained with suffi* 
cient accuracy in the following manner. 
