110 EIGHTH REPORT — 1838. 



vations. Hence, if e^ = Cg, that is, if the reading power be 

 the same in the two cases, and the same pains be bestowed on 

 the observations, 



l=i+i, (18) 



n denoting the value of the ratio ^f^, or the equivalent num- 

 ber of observations of the difference sought, supposing it to be 

 the immediate subject of observation. 



But when we desire to compare the result of the uncor- 

 rected needle with the actual dip, we must also take into ac- 

 count the probable instrumental error of the results with 

 which it has been compared ; and we have (15) 



And in place of equation (18), we have the following: 



11 1 eM 



-= - + - + -J_-. (19) 



n «i n^ e% n. 



To apply this, we shall assume, as before, the instrumental 

 error to be equal to the error of observation, the latter inclu- 

 ding the error of epoch ; and we obtain 



Needle L. 1, n^ = 13, n = 6-1, 



— L. 3, 6, 3-9, 



— L. 4, 20, - - 7-3. 



We shall adopt the nearest whole numbers, 6, 4, 7. 



The correction of needle S. 2 has been determined with 

 great care by Major Sabine *, by a comparison, at various sta- 

 tions, of its results with those of the needles M and G. 2, 

 needles which may be regarded as almost free from all instru- 

 mental error. The amount of this correction is — 9'*6 ; and 

 its weight 16. This amount is almost identical with that pre- 

 viously employed in the calculation of the Irish observations. 



The other needle employed by Major Sabine in Ireland, S. 1, 

 is constructed on a plan suggested by Mr. Dollond. The 

 middle of the needle has the form of a cube, and is perforated 

 so as to receive the axle in different directions, the intention 

 being, that the position of the axle should be varied in the 



• Table XIX, 



