100 EIGHTH REPORT — 1838. 



We have, therefore, from the preceding formula, e^^ = 2"78, and 



e.= l'-7. 

 > 



It appears, then, that the instrumental error is somewhat less 

 than the error of observation. The difference, however, is 

 probably less than the error of our result ; and we shall as- 

 sume, in round numbers, two minutes as the amount of each 

 error in the Irish series. 



Taking, then, e . = e^ = 2, we have (15) (13) 



E2 = l = 4(- + -V (16) 



From this formula we learn how useless it is to multiply obser- 

 vations with the same instrument, in order to obtain the dip at 

 a given station : When ??,• = 1, we have 



i-=4(- -f l), - = 4x2; 

 W \n / w 



tv denoting the weight of a single observation ; so that 



W _ ^% _ 



w ~" «„ + 1 ' 



and, however the observations be multiplied, the weight of the 

 result can never amount to double the weight of a single ob- 

 servation. 



In what precedes, we have considered only the actual dip at 

 a given station. But in deducing the position of the isoclinal 

 lines from observations of dip made at several stations, it is 

 necessary to consider likewise the probable difference between 

 this dip and that due to the geographical position of the sta- 

 tion : or, in other words, the probable mean local error. 



Let €i denote this error ; then it is manifest, from what has 

 been already said, that the actual resulting error will be ex- 

 pressed by the formula 



«„ n, '• 



(17) 



The mean local eri'or will, of course, be very different in dif- 

 ferent countries, the differences depending chiefly on the re- 

 lative proportion of the igneous and sedimentary rocks. In 

 Scotland, as appears from Major Sabine's excellent report (Sixth 

 Report, p. 102), the local error is considerable ; in England it 

 is probably small. We may estimate its amount in any district, 

 by computing the dip due to the geographical position of each 

 station, by the formula (2), and taking the sum of the squares 



