CXXXVlll 
APPENDIX. 
Having thus detailed the Observations on the Intensity of the Magnetic 
Force, it may not be uninteresting briefly to examine, how far the results are 
consistent with the ratio in which it was expected that the magnetic force 
would be found to vary under diflerent Dips of the Needle. 
In the Rules and Tables for clearing the Compass from the regular Effect of 
the Ship’s Attraction, printed in 1819 by order of the Commissioners of 
Longitude, and published, with some alterations and additions, in the 
Journal of the Roi/al Institution for October, 1820, the Magnetic Force in the 
direction of the Dipping Needle is considered to vary, inversely, as the 
square root of four diminished by three times the square of the sine of the 
dip ; and the force acting on a needle limited to a horizontal motion, inversely^ 
as the square root of three increased by the square of the secant of the Dip, 
The Observations at Melville Island are entitled to principal consider- 
ation, as having been made under more favourable circumstances than were 
presented by the other opportunities of the voyage ; they are therefore, to be 
compared with those which were made in England. 
The Dip in London being 70° 33'.3, and at Winter Harbour 88° 43'.5, the 
force in the direction of the Dipping Needle should increase by calculation in 
the ratio of 1.153 to 1. 
The time of vibration of Mr. Browne’s Dipping Needle, decreased between 
London and Winter Harbour in the proportion of 481 to 446, and conse- 
quently the force appeared to have increased in the ratio of 1.163 to 1. 
The Dip at Sheerness being 69° 55', and at Winter Harbour 88° 43'.5, the 
Magnetic Force should increase by calculation as 1.163 to 1 ; but the force 
acting on the horizontal needle should be diminished in the proportion of 
13.275 to 1. 
The times of vibration of the three horizontal needles increased between 
Sheerness and Winter Harbour, in arcs from 7 to 1 4 degrees, respectively, as 
follow ; No. 1 as 339.7 to 94.5 ; No. 2 as 327,4 to 90 ; and No. 3 as 316.1 to 
85 ; consequently, the force acting on them appeared to have diminished by 
No. 1 as 12.93 to I ; by No. 2 as 13.23 to 1 ; and by No. 3 as 13.83 to 1 ; the 
mean being as 13.33 to 1 ; differing but from the result of the calculation. 
This is, perhaps, a nearer agreement with the theory than there was reason 
to have expected, considering how much the unavoidable causes of uncertainty 
in such experiments are augmented in high magnetic latitudes. 
