Dip and Variation of the Magnetic Needle. 95 



These equations solved by the method of minimum squares give 

 5=1.0801, a;= + 0.00987, y = -}- 0,00303, and the direction of the 

 isoclinal lines is from N. 72° 56' W. to S. 72° 56' E. Computing 

 from these data the dip at the several stations, we obtain the differ- 

 ences given in the sixth column above. At Cote sans Dessein, the 

 difference between the observed and computed dip amounts to 63'.9. 

 An error of one degree may perhaps have been committed in re- 

 cording or transcribing this observation. At all events this ob- 

 servation seems entitled to less weight than the others, and we 

 shall perhaps do best to reject it altogether. The remaining 

 equations solved as before, furnish us <^ = . 97301, a; = + 0.0 1301, 

 2/,= +0.00397. Computing again the dip at the several stations, 

 we obtain the differences given in the last column above. The 

 mean dip at St. Louis for 1819 was then, according to these ob- 

 servations, 69° 59'.8. The dip in 1840, according to p. 102, was 

 69° 20'. 7. Decrease 39'. 1 in twenty one years, that is, 1'.9 per 

 year. This result would be deserving of confidence if the ob- 

 servations of 1819 could be depended upon. For information on 

 this point, I wrote to Major Graham, who made the observations 

 in question, from whom I learned that the poles of the needle 

 employed were never reversed ; and that he knew of no data 

 for determining the correction necessary for this omission. Here 

 then is a constant error of unknown amount, which renders the 

 observations quite useless for our present purpose. This is a re- 

 sult much to be regretted ; yet if no observations were made at 

 the time with the polarity of the needle reversed, the loss seems 

 irreparable ; for if the instrument were still preserved and in good 

 condition, we obviously could not assume the inequality of the 

 arms of the needle to be the same as in 1819. I do not find then 

 any observations of dip made in this country before 1822, which 

 are capable of informing us whether the dip has been increasing 

 or diminishing. 



The next observations in respect of age were made at New 

 York city. Here we have five observations. In order to deduce 

 from them the most probable results, let us put <J for the mean 

 dip, Jan. 1, 1822, and ^ for the annual motion ; we thus obtain 

 five equations of condition. 



