40 



RESULTS AND DISCUSSION OF THE 



The annual inequality in the dip need not here be considered, as the index error 

 of the various needles and the observing error are much greater than the maximum 

 amount of that inequality which, according to the Toronto observations, hardly 

 exceeds ±1'. 



Collecting the mean dips and mean epoch, and adopting the expression 

 e = 0, + a> + 7/ (t—Q + z {t—t,f 

 where 



Q ^resulting dip at any time between 1830 and 1860 

 0j= assumed dip at epoch, x its corrigction, 6j = 72^00 

 ^0= epoch or 1840.0 



t = any other time between the above limits. 

 We obtain from the following combination of the observations by the method of 

 least squares, the- values of x, y, and z. 







Mean dip. 



Mean year. 



Group I . . . . 

 II ... . 

 Ill ... . 



3 results 

 5 " 

 2. " 



72.000 

 72.00 

 72.20 



1838.3 

 1843.5 

 1859.2 



whence 6 = +72.^00—0.00011 (#—1840) + 0.00060 (<— 1840)^ 



The observed and computed dips compare as follows : — 



Epoch. 



Observed dip. 



Computed dip. 



Obs'd— comp'd. 



1834.5 



72.000 



72.002 



— 0.O02 



1839.7 



72.12 



72.00 



+0.12 



1840.7 



71.88 



72.00 



—0.12 



1841.5 



71.97 



72.00 



—0.03 



1842.5 



72.00 



72.00 



0.00 



1843.6 



71.97 



72.01 



—0.04 



1844.3 



72.03 



72.01 



+0.02 



184(5.4 



72.02 



72.03 



—0.01 



1855.7 



72.29 



72.15 



+0.14 



1862.6 



72.10 



72.31 



—0.21 



The probable error of .any one representation is ±4. '8. 



The minimum dip, according to the above formula, occurred in January, 1840; 

 at Toronto this minimum occurred in 1843. 



By means of the formula we find the dip for the middle of each year : — 



Tear. 



Computed dip. 



Obeerved dip. 



Adopted dip. 



1840.5 



72.000 





710 59' 



1841.5 



72.00 





71 59 



1842.5 



72.00 



72.000 



72 00 



1843.5 



72.01 



71.97 



71 58 



1844.5 



72.01 



71.97 



71 58 



1845.5 



72.02 





72 01' 



