304 
MAGNETIC SURVEY IN NORTH AMERICA. 
the year the most simple hypothesis of an uniform loss in equal intervals of time, 
without incurring the risk of any material error. If x be the magnetic moment at 
Toronto on January 29, 1845, a the interval of time in days between the date of the 
observations at any anterior station and the 29th of January, and y the change of m 
corresponding to a single day, each of the stations where observations of deflection 
were made will furnish an equation of the form, 
observed value of m=x-\-ay ; 
and by the method of least squares we shall obtain the most probable values of m 
on the hypothesis of uniform loss. There are fifteen such equations furnished by 
No. 30, between June 12, 1844, and January 29, 1845 ; from these we obtain m='3928, 
and ?/ ='00003 17- Hence we have m at Toronto on January 29 ='3928 ; and on any 
earlier day between June 12, 1844, and January 29, 1845, m=*3928 +'00003 IJa. 
By the experiments with Dr. Lamont’s rings, p. 293, the values of w 2 K, or the 
moment of inertia of each of the magnets 30, 31 and 17, multiplied by the square of 
the ratio of the circumference of a circle to its diameter, were determined as follows, 
viz. — 
No. 30. 21-581. 
No. 31. 21'853. 
No. 17. 43'272. 
The absolute horizontal force at the stations where the observations of vibration 
only were made, are then deducible from the following expression, 
v— 
mT 2 ’ 
in which T is the time of vibration and m computed as above. 
The values of m with magnet No. 31 at the stations where the deflections were 
observed were as follows : — 
Athabasca, March 2, 1844 . . 
'3763. 
Fort Simpson, May 2, 1844 . . 
•3721. 
Fort Good Hope, May 29, 1844. 
•3641. 
Fort Norman, June 2, 1844 . . 
•3616. 
Fort Simpson, June 12, 1844 . 
'3587. 
Fort Resolution, June 24, 1844. 
'3592. 
Athabasca, July 2, 1844 . . . 
'3568. 
Fort Vermilion, July 11, 1844 . 
'3592. 
Fort Dunvegan, July 24, 1844 . 
•3528. 
Fort Edmonton, Aug. 18, 1844. -3507. 
Carlton House, Aug. 26, 1844 . '3499. 
Norway House, Sept. 4, 1844 . *3512. 
Fort Alexander, Sept. 20, 1844 . '3517- 
Rat Portage, Sept. 25, 1844 . . '3515. 
Fort Francis, Sept. 29, 1844 . . '3506. 
Fort William, October 10 , 1844. '3522. 
Toronto(with stirrup), Feb. 5, 1845. '3494. 
Toronto (without stirrup), Feb. 5. '3494. 
In this case also the twenty-five stations at which the times of vibration only were 
observed, were all comprised in the interval between the 24th of July 1844 at 
Dunvegan, and the 5th of February 1845 at Toronto. The loss of magnetism of j 
No. 31 in this interval appears to have been very small ; and to have been progressive, 1 
