MAGNETIC SURVEY OF GREAT BRITAIN". 



99 



have undergone in this respect, subsequently to the year 

 1835*. The mean error, for any set of needles, may be ob- 

 tained from (15), when we have made a series of observations 

 with these needles at any one station. Let e denote the pro- 

 bable error of the result given by any set of observations with 

 a single needle, as inferred from comparison with the others ; 

 Then e* = n. E% and substituting in (15), we have 



eU = e 



n. 



-el 

 n„ 



in which the value of e^ is deduced from the observations by 

 means of (12). 



To deduce, according to these principles, the value of e^ for 

 the needles employed in the Irish survey, we must compare 

 the results obtained at Limerick, — that being the only station 

 where all the needles were employed. These results are con- 

 tained in the following table. The first column contains the 

 names of the needles employed; the second, the dips obtained, 

 reduced to the 1st of January, 1837, of which the mean value 

 is 71° 0''5 ; in the 3rd column are the differences of the par- 

 tial results and the mean; and in the 4th, the squares of these 

 differences. 



Table XXIX. 



From the last column of the preceding table we find 



t {a; — aY = 41-07; and substituting in (12), e^ = 3-70. 



n. 

 Again, w,- = 6, n = 26, and, assuming e^ = 2, — i e^ = 0*92. 



o 



* The probable instrumental error of the needles employed at Westbourne 

 Green in 1835, as deduced from the observations recorded in the Irish Report 

 (Fifth Report, p. 142), amounts to 8'-3. The mean probable error of the 

 needles employed at the same place in 1837 and 1838, as deduced from the 

 observations contained in Table III. of the present memoir, is ahout one minute 

 only. 



t_The needle S. 1 had undergone a change in the disposition of its axle in 

 the interval between the two observations recorded in this table. These obser- 

 vations must therefore (as far at least as the axle is concerned) be regarded as 

 the results of different instruments. 



h2 



