SOLAR ECLIPSE, MAY 6, 1883. 1 2i> 



The uiiusiKil tliickuess of the spider thread is the cause of the large probable error of 

 observation. The latitude is deduced from forty measures ou 15 pairs. The tables show the 

 reductiou of one pair observed ou several uigbts, aud the general summary of all the results. 

 The last table gives the result for the individual pairs, the number of observations on a pair, and 

 the weight assigned to each result. 



The probable error of observation (e) deduced by comparing each individual result with the 

 mean result for the pair is ± 0".69. 



Probable error of resulting latitude from any one pair depending on the probable error of 

 observation aud the probable error of the mean of two declinations is e = ± 0".58. 



Weight of result by a pair = ^ "■ 



ne^i+ e^ • 10 n + • 48 

 where n is the number of observations and e'^ the prob. error of the mean of two declinations. 



Value of latitude from all the pairs = <»« = :^J''- ''- = 10° 00' 00".59. 



Probable error of latitude from all the pairs =J '^^^ ^^^"f' ?! = 0".13 



V {p — 1) 2 to 



where p is the nuadier of i)airs and w = weight. 



The latitude of station is then 



— 10° 00' 00".59 ± 00".13 



DETEKMINATION OF TIME. 



Whenever it was possible to adhere to it the following plan was followed : The inclination of 

 the telescope axis was determined, then a low north star, a low south star, and several stars within 

 15° of the zenith were observed, after which the inclination was again determined. The telescope 

 was then reversed and the same programme repeated. Circumstances, however, did not always 

 admit of this scheme being literally carried out. The inclination was always taken at least every 

 fifteen minutes, and stars low enough for azimuth were observed, except in one position on one 

 night, when it was not possible. The preliminary reduction of the transits was made on the island 

 by Mr. W. Upton, of the Signal Service, and the final reduction by me in part at sea during the 

 voyage from Caroline Island to Honolulu aud in part at the latter i)lace. 



In the final reduction the method of least squares was applied. Each star gave a conditional 

 equation of the form 



ST + aA = a — T— AT 



after having corrected the observed transit for rate of chronometer, inclination of axis, and collima- 

 tion and observation. Each conditional equation is multiplied bj' the square root of the weight of 

 the observation depending on the star's declination, and the number of threads observed, and then 

 the normal equations are formed in the usual way. The reductiim for May 7 is given in full. 

 S. Mis. 110 17 



