248 
MAGNETIC SURVEY IN NORTH AMERICA. 
from observations distributed in the space included by those lines, appears to be that 
of concentric and similar ellipses. The representation will not be strictly just, 
because the curves which include the two points of maximum in a hemisphere are 
of the nature of lemniscates, and not of true ellipses, and the curves of higher inten- 
sity inclosed within them partake of the same form. I have taken for a calculation 
of this nature all the observations by the statical methods of Lloyd and Fox in 
which the resulting value of the Force equals or exceeds 1*838 ; with the exception of 
two stations, viz. the Little Rock Portage and Pierre au Calumet, where a compari- 
son of the values, both of the Inclination and Force, with those at adjacent stations, 
shows that a great disturbing influence prevailed : and I have included the three 
stations at the foot of the Rocky Mountains, viz. Forts Vermilion, Dunvegan and 
Edmonton, where the intensity is less than 1*838, but the position important; as 
well as Toronto, where the value of the force is just beyond the limit (being 1*836), 
but has the advantage of having been remarkably well determined. The number of 
stations in this combination is seventy-eight, and double weight has been given to 
four, viz. Norway House, Cumberland House, Shamatawa and York Factory, on 
account of the repetition of the observations. These stations furnish therefore eighty- 
two equations of condition of the form described in the following Note, for which I 
am indebted to Archibald Smith, Esq., of Lincoln’s-Inn, Fellow of Trinity College, 
Cambridge. 
“ Note on the calculation of the Isodynamic Curves and the Focus of greatest intensity 
in North America. 
“These isodynamic curves consist of a series of ovals surrounding the point of 
greatest intensity. 
“ The method of combining the observations at different stations which was used in 
the Magnetic Survey of Great Britain*, and which proceeded on the assumption that 
the isodynamic lines were nearly straight, cannot therefore be applied. The most 
simple assumption which will give an approximate result, and admit of all the obser- 
vations within a given limited space being combined in the calculation, appears to be 
the following *. — 
“ Let a place near the centre of the region which is to be included in the calcula- 
tions, be taken as the central station and origin of coordinates. Let y 1 and y 2 , &c. 
be the differences of the latitudes of the several stations (which may be called s l3 s 2 , 
See.), and that of the central station : 
“Letx 1: x 2 , Sec. be the differences, multiplied respectively by the cosines of the lati- 
tudes of s l5 s 2 , &c., of the longitudes of s 13 s 2 , Sec., and that of the central station. 
* See Reports of the British Association for 1838. 
