AT THE OBSERVATORY AT PARAMATTA. 
31 
“ 49 s .6 may therefore be adopted for difference of longitude between Sydney 
and Paramatta with the more confidence, as inner and outer contact give 
almost the same result, which is at the same time a proof of the exactness of 
the observations made at Sydney as well as Paramatta.” 
I should prefer, however, to take a mean of 5 l"93, 51".98 and 49".6 = 50",88, 
which being added to 10 h 4 m 6 9 .25, the longitude of the observatory at Paramatta, 
give for longitude of Sydney 10 h 4 m 57 s -13. 
Remark . — The conjunction 0 h 6 m 52 s .2 deduced from the inner contact of the 
immersion of Sydney, is probably written wrong by Professor Wurm. I sus- 
pect he meant it 0 h 6 m 24 s ./8. I have, however, not ventured to alter it. 
II. Solar Observations. 
1.) Solstices. 
a.) Observed with Reichenbach’s repeating Circle. 
I shall first state the methods employed in the Reductions of the Observa- 
tions, and begin with, 
The Reduction to the Meridian. 
Already, on occasion of the first southern solstice observed in this colony, I 
remarked the insufficiency of Delambre’s method for the reduction to the 
meridian when the sun culminates near the zenith, on account of the slow 
convergency of the series employed by him, under such circumstances : when 
the hour angle is about 25', the second term of his formula will in a set of four 
observations amount to 100", the third to 60", and even the fourth to 12" ; and 
the work of Delambre’s third and fourth term is very laborious. 
I have therefore substituted another series, the very first term of which 
comes as near the truth as the four terms of that of Delambre. 
I find the middle of the times of observation for which I take out Delambre’s 
first and second part A and c$. I take also out these parts A' A" A'" . . . and h' h" l ! " 
for each individual time t 1 1" t'" and call their means . . . — — = S 
n 
8 ' + 8 " + 8 "' + + 
and 
- = S, n being the number of observations, M the meridi- 
onal zenith distance, z the observed zenith distance or mean arc, and r — cos 
T 
lat. X cos declin., % — — /m _l 7 .\ ? P 
r 
sin 
(M + Z)> 
smz. 
