59 
Captain Hall’s comet seen at Valparaiso. 
dv = 3299 dt — 977400 dp 
dv — 1510 dt — 768635 dp 
dv"= 947 dt — 667980 dp 
x — 8353 dt — 220500 dp 
x' = 4768 dt — 172700 dp 
x"= 3390 dt — 138150 dp 
dn= — ,4543# • d$ = — 1 ,1466 x 
d-n ■=■ — ,3 599 °°' • d$ = — 4756 x ' 
^7r"=: — ,3053a;" . <//5" = — ,2252 a?" 
We may now use the equations (10) and (11) for finding dV 
and dY 
dV sin V= sin ( V — 7r') (^tt— ^7t) -f- a 
</H=H sin i"(tan^ (/3 — /3 r ) (dj8 — d'/S') — dn' tan tt' — tan tt) 
The expressions for dY and d H' are had by changing 
H, /S’ and nr into H', j6" and tt". 
Then, by substituting the above values for ^tt", &c. &c. 
dY = — 3858 dt -J- 80110 dp 
d\'=: — 4888 dt -f- 112190 dp 
and the equations 
U + d\J = Y + dV 
U'+ d\J'= V'-f dY 
become 
— 20 6gdt — 128650^ = 111 — (14) 
— 2536 dt— 197230 dp = 80 — (15) 
which give 
dp= -f ,001425 and dt= — ,1423 
Consequently, the new approximate values of p and t are 
P — ,092925 and t = 17, 9315 
