MAGNETICAL OBSERVATIONS IN IRELAND. 
132 
II. Horizontal intensity in Limerick, the horizontal intensity 
in London being unity. 
July, Aug., Sept. 1834 ... Cyl. S (b) . Int. = '9396 
July, 1835 . — — — -9470 
July, August 1835. — R ( c ). — -9461 
■ * ......... ■“* R ( f/j. ...... 1 9o 13 
Mean = '9460 
III. Horizontal intensity in Limerick, the horizontal intensity 
in Dublin being unity. 
Sept., Oct., 1834 _ 
. Cyl. 
July, Aug. 1835 .... 
Aug., Sept. 1835 .... 
Nov., Dec., 1835 
L (a) . Int. = 1 0064 
L (6). — 1-0044 
R (c). — 1-0005 
R (d) . - 1 0098 
L (a ) . — 1-0027 
L (b) . — 1-0047 
L (a) . — 1-0001 
L (b) . — 1-0021 
Mean = 1*0038 
If then x and y denote the horizontal intensities in Dublin and 
Limerick, that in London being unity, observation gives 
x = -9380, y = -9460, ^ = 1-0038, 
and it is required to determine the most probable values of x 
and y. To generalize this problem, let the mean results of 
-observation be a, b , c , and let their weights be A, B, C respec¬ 
tively ; so that we have 
x — a = 0, weight = A, 
y - h = 0,-B, 
- c = 0,-C : 
X 
a and b being approximate values of x and y , let their true va¬ 
lues be 
x = a + 8 x, y = b + 8 y, 
and let — — c lf then — = — 
a 1 x a + S x 
c i + 
a 1 {Zy - Cj Sx), 
the squares and higher powers of the quantities S x and hy being 
neglected; so that the preceding equations may be written 
l x = 0, 5^ — 0, 
a~ l (Zy — c t $i r) + c t — c = Ch 
