A 



AT THE OBSERVATORY AT PARAMATTA. 31 



" 49'.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 ..; .li.. 



I should prefer, however, to take a mean of 5 1"93, 5 1".98 and 49".6 = 50".88, 

 which being added to lO** 4™ 6^.26, the longitude of the observatory at Paramatta, 

 give for longitude of Sydney 10'' 4'" 57M3. 



Remark. — The conjunction O*' 6™ 52'.2 deduced from the inner contact of the 

 immersion of Sydney, is probably written wrong by Professor Wurm. I sus- 

 pect he meant it O** 6™ 24^78. 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 insufiiciency 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, imder 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 thei'efore 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 I. I take also out these parts A' A" A"' . . . and 5' I" S'" 



for each individual time ^ f f and call their means . . . — = S 



g* + 8" 4- 8"' J. -I- .. •< 



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 



lat. X cos declin., t = — /m + Z\ ' P ~ 



r 



i^y 



sin 



*;• 



-^^ 



't*r 



