98 



EIGHTH REPORT. — 1838. 



Table XXVIII. Needle L. 4. 



From the former of these tables we find 



w = 13, a = 70° 51'-6, S (^ - df = 121-09 ; 

 and from the latter 



« = 20, a = 70° 50'- 1, %{x - of = 389-69. 

 Substituting these numbers in (12), the probable error of ob- 

 servation in the former series is found to be 2''1 ; and in the 

 latter 3'-0. 



It is remarkable that the squares of these errors (the inverse 

 of which are the measures of the weights) are, almost exactly, 

 in the ratio of 1 to 2 ; that is, in the inverse ratio of the num- 

 ber of readings with each needle. This is a curious confirma- 

 tion of the accuracy of the conclusion. 



From the preceding it follows, that in combining the results 

 of the two needles, L. 1 and L. 4, (when used together) double 

 weight must be allowed to the former. It appears from (14) 

 that the probable error of the mean, thus deduced, is l'*8. We 

 may therefore consider two minutes as the probable error of 

 observation in the present series, whether the result be that 

 of a single needle with the usual number of readings, or the 

 mean of the two needles L. 1 and L. 4. 



The probable instrumental error, e,, varies, of course, within 

 very wide limits, depending on the perfection of workmanship. 

 In a former part of this memoir. Major Sabine has pointed out 

 the very great improvement which our English dipping needles 



