118 KIGHTH REPORT — 1838. 



The foregoing observations having been made with different 

 needles in the same circle, it becomes necessary, in estimating 

 tlie probable error, to separate those due to the limb from those 

 which arise from irregularities in the axle. From the mode in 

 which the observations were taken, — namely (in all but one in- 

 stance) a single observation with each needle, — the axle error 

 and the error of observation are combined ; and the beautiful 

 accordance of the partial observations shows that their com- 

 bined result is inconsiderable. There seems reason, however, 

 for believing that the circle itself is not free from error. The 

 mean result obtained with these needles, in this circle, at West- 

 bourne Green, is S'^O less than the mean of the other needles 

 employed at the same place (see Table III.) ; while on the other 

 hand, they give a result 3''8 in excess of the mean dip, as shown 

 by Gambey's needles in Dublin, — the latter being observed by 

 the method of ai'bitrary azimuths. 



Now the total probable error at each station, in this series, 

 (as deduced from a comparison of the computed and observed 

 results) is found to be 4'"0, — a result scarcely differing from 

 that of the former series. Of this, the part which is reduced 

 by repetition is (as has been already stated) exceedingly small ; 

 and, consequently, the remainder (the combined result of the 

 station and circle errors) is considerable. Under these cir- 

 cumstances, it will be readily seen, no disproportion in the 

 number of observations can materially alter the weights ; and 

 as, in addition to this, the observations have been distributed 

 with some attention to uniformity, it is manifest that we must 

 regard the weights of all the stations as equal. 



The results of calculation are 



L = 710 22''0, M = +-270, N = + -550 

 M = -63^ 49', r='QlS. 



Hence the dip at the central station, on the 1st November, 

 1838, was 71° 2^''0, the central station being the same as 

 before ; consequently, the probable dip at that station, on the 

 1st January, 1837, was 71° 26''4. 



Finally, if we combine these results with those of the former 

 series, allowing weights in proportion to the number of stations, 

 we find 



L = 71° 23'-7, M = +-292, N = + -517 

 u= -60° 32', r =-594; 



L denoting the mean dip at the central station, on the 1st 

 January, 1837. 



