INTRODUCTION AND RESULTS. 
251 
From these equations the values of the constants were obtained by elimination as 
follows : — 
a= — -01138 d=+ 0-5633 
b= — -02522 e— + 0'4485 
c— — *0356 /= +7254. 
With these constants we obtain 
5=79-9 ; and the Force at the point of maximum =(l-798 + -0799 = )l-878 : 
x= +29"38 ; whence the difference of longitude between the origin of coordinates 
and the point of maximum = ( + 293-8 miles X sec 52°T 9'= +481' = ) + 8°-01' : 
j/= — 4-07 ; whence the difference of latitude between the origin and the point 
of maximum = — 40'*7. 
The geographical position of the maximum therefore is 52° 19' N., and 268° 01' E. 
The angle which the major axes make with the parallel of geographical latitude is 
jgO 4g° j(/ 
=66° 55'; and the values of the semi-axes of the ellipse of T875 are 
223 and 85 geographical miles respectively. 
The line of 1*875 has been drawn first on a map on a plane projection, and then 
transferred to the map on the polar projection which accompanies this memoir. The 
lines more distant from the maximum, viz. those of 1*850 and T800, have been 
drawn by the hand without the employment of calculation, and in such accordance 
with the observations as could be judged by the eye. The intensities entered in the 
map, and by which the lines have been drawn, are those of 192 stations. They in- 
clude all the stations at which the total Force has been computed in the arbitrary scale, 
and inserted in the general table, No. XLVIII., except at 15 stations, where there is 
reason to believe that local disturbance prevailed to a considerable amount. The 
values of the total Force are derived from horizontal and statical ratios in the United 
States, and from statical ratios only in the countries to the north, where the Inclina- 
tion became so great as to introduce an element of much uncertainty in the deduction 
of the total Force from its horizontal component. The intensities at four stations on 
the western side of the continent, on the shores of the Pacific, are introduced from the 
observations of Sir Edward Belcher, discussed in the IVth number of these Contri- 
butions. The line of 1*7, distinguished by a different character from that in which the 
other lines are drawn, is taken from the map (already referred to) in the Reports of the 
British Association for 1837, and is introduced into the present map for the purpose 
of affording a more ready means of comparing the form and geographical position of 
this line, with those of the lines inclosed within it, which are now for the first time de- 
lineated from observations, all of which have been made subsequently to the period 
when the map from which the line of 1*7 is taken was published. The accordance of 
the earlier and more recent observations is thus distinctly brought into view ; and it 
will be perceived that the modifications, if any, which the line of 1‘7 will require, will 
be very slight. With respect to the geographical position of the point of maximum 
