MAGNETIC SURVEY OF GREAT BRITAIN. 11«^ 



Now assuming the approximate values 



L = 71° 22'-5, M = +-30, N = +'51 ; 

 the probable dip at each station will be given by the formula 



s! = 7l°22''5 +-30 X +-51y; 

 and the computation gives for the sum of the squares of the 

 differences of the computed and observed results, at the 32 

 stations, 



t{x-ay'= 119209; 

 from which we find (12) 



E2 = 17-48, E = 4-2, 

 E denoting the total probable error at any one station. But if 

 E and E. denote the mean probable errors of observation and 

 of instrument at each station, and E^ the probable local error, 



E' = E^ + E? + Ef. 



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For the observations of this series, E^= ^i~ ^'^* 5 "wherefore 

 E,= 3'-L 

 To deduce the weight of the result of n^ observations, with «,• 

 instruments, at any station, we substitute the values thus ob- 

 tained in (17), and we obtain 



w \n n . I 



When the local error, therefoi-e, bears so great a proportion to 

 the errors of observation and of instrument, as it does in the pre- 

 sent instance, it is manifestly waste of labour (as far as regards 

 the determination of the position of the isoclinal lines) to mul- 

 tiply observations at any one station. In the case under con- 

 sideration, the weight due to the result at any station (however 

 the observations be multiplied, and whatever the number of in- 

 struments employed) can never amount to double the weight of 

 a single observation. 



Substituting the values of n^ and n^ in the preceding formula, 

 we find the weight of the mean dip, in Dublin and Limerick, 

 equal to 1 '8, the weight of a single observation being unity : in 

 no other case throughout this series does the weight amount 

 to more than \'3. Taking the nearest whole numbers for the 

 value of this ratio, we shall assign a weight of 2 to Dublin and 



* Throughout a considerable portion of the series, two needles, T>. 1 and L. 4, 

 were used together. The probable error of observation of the mean is nearly 

 2'; the instrumental error is little less than that of a single needle, being, in this 

 case, due chiefly to the magnetism of the limb. 



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