On the Secular Change in the Magnetic Dip in London. 233 



Hence on the 1st of July the mean clip at Toronto would be derived 

 as follows, viz. : — 



o / 



From the four winter months, November to February . . 75 18*97 

 From the four summer months, May to August 75 17*47 



Showing an excess of V'5 in the winter months above the summer 

 months. 



The annual variation at Kew, as it may be derived from the 282 

 determinations in Tables I., II. and III., does not differ materially 

 from this conclusion. There are in these Tables 87 results obtained 

 in the four winter months of the different years, and 93 results 

 obtained in the four summer months of those years. If we collect 

 into separate means the results in the winter months of 1857-58, 

 1858-59, and 1859-60, numbering them (1), (3), and (5), — and into 

 separate means the results in the summer months of 1858, 185°- and 

 1860, numbering them (2), (4), and (6), — and if we compare (1) 

 and (3) with (2), (3) and (5) with (4), (2) and (4) with (3), and 

 (4) and (6) with (5), (by which comparisons the effects of secular 

 change are eliminated), we find an excess of l'*7 in the mean dip of 

 the winter months over that obtained from the summer months. The 

 mean of the two corrections, thus separately obtained at Toronto and 

 Kew, is l'*6 ; of which the half, or 0'*8, has been applied in the 

 Tables with the — sign to the results in the winter months, and with 

 the 4- sign to the results in the summer months. 



Probable error of a single determination of the Dip. — It may be 

 desirable to state the probable error of a single determination as it may 

 be derived from the observations in the Tables, before and after the 

 application of the correction for annual variation. It will be seen 

 that the probable error is diminished by the application that has 

 been made of a correction on this account, 



When uncorrected When corrected 

 for annual variation, for annual variation. 



From the 1 15 Results in Table I. . . +1*50 ±1*49 



From the 96 Results in Table II. ±1*44 ±1*39 



From the 71 Results in Table III. +1*57 ±1*46 



±1*50 ±1*45 



The probable error thus obtained represents all the diversities 

 ascribable to the employment of different instruments (all of the one 

 construction), — to the supposed peculiarities of different observers, 

 — to the occasional presence of magnetic disturbance (for which no 

 correction has been attempted), — and to differences due to different 

 hours of observation ; — in addition to what may be more strictly 

 viewed as "observational errors." It may thus serve in some mea- 

 sure as a guide to those engaged in similar researches, as to the degree 

 of accuracy which is attainable in such experimental inquiries, when 

 proper care is taken in the procurement of a reliable inclinometer 

 and in its manipulation. 

 For the purpose of comparing the probable error thus obtained 



