250 
MAGNETIC SURVEY IN NORTH AMERICA. 
“If 0 be the angle which either axis of the ellipses makes with the parallels of lati- 
tude, we have 
tan 2Q=-^— (4.) 
a — c 
“This expression is ambiguous, giving two directions at right angles to each other, 
and does not determine which of these directions is that of the major axis. This will 
generally be apparent from the observations themselves ; and it may be determined 
by this consideration, that if the numerical value of a be greater than that of c, the 
inclination of the major axis to the parallel of latitude is greater than 45° ; if less, 
less. 
“ The values of the semi-axes of the isodynamic ellipse for which the intensity has 
the value z, are given by the two values of the expression 
semi-axis 
W- 
2(z—z) 
a + c + V {a— c) 2 + 6 2 
(5.) 
“ The proportions of the semi-axes are 
a + c+\/(a— c) 2 +6 2 : 4ac— b 2 (6.) 
“The simplest method of drawing the isodynamic ellipses will be to lay down the 
parallels of latitude and meridians in the manner above described ; the isodynamic 
curves are true ellipses on that projection and may be easily constructed, and the 
points at which they intersect the meridians and parallels of latitude may then be 
laid down on any other map.” A. S. 
Lincoln’s Inn. 
I have taken the intersection of the latitude of 53° with the meridian of 260° as the 
origin of coordinates ; the values of x l3 x 2 , &c., yi,y 2 > See., were taken in units each of 
ten geographical miles ; and, for convenience in calculation, the excess above 1'798 has 
been taken at the value of z, the observed force at each station, and the decimals 
regarded as integers ; the eighty-two equations thus furnished of the form described 
in Mr. Smith’s Note have been combined by the method of least squares, to obtain 
the most probable values of the constants a, b, c, d, e and f, the calculations having 
been performed by Sergeant M c Grath and Corporal Hendley of the Royal Artillery, 
independently of each other, and agreeing; the six final equations were: — 
+ 5081 = + 134394a 
- 69949 6 
+ 
48449c 
+ 1632c? 
— 660e 
+ 
82/ 
- 37298=- 3779899a 
+ 21985236 
— 
1142033c 
- 69949 d 
+ 48449e 
— 
66 V 
+ 98527=+ 7136612a 
— 377989 96 
+ 
2198523c 
+ 134394c? 
- 69949e 
+ 
1632/ 
+ 2603880= + 177659938a 
- 967019766 
+ 
57677688c 
+ 2198523 d 
— 1142033e 
+ 48449/ 
-3570819= — 323660394a 
+ 1776599386 
— 
96701976c 
-3779899c? 
+ 2198523e 
— 
6994 9/ 
+ 6822989= +6227l8413a 
-3236603946 
+ 177659938c 
+ 71366l2c? 
— 3779899c 
+ 134394/. 
