134 
FIFTH REPORT- 1835. 
These three equations are to be combined by the method of least 
squares ; that is* each equation is to be multiplied by its weight* 
and by the coefficient of each unknown quantity separately* and 
the two sets of results added together will be the final equations 
from which the values of the two unknown quantities are to he 
determined. We find in this manner 
A S x — C c { a~ l (a~ l %y — c l a~ l S x + c t — c) = 0 
B£y -j- C « _1 ( a~ l cy — c i cr x Sx + c i — c) = 0* 
from which we obtain* by elimination* 
B , 
-r-ac, (e, — c) 
d x = — A-- 
B a B q 
C “ + A C +1 
a (c, - c) 
Zy = - B 
c flS+ f c8 + 1 
If the weights of the three results be regarded as equal* that 
is* if 
A = B = C, 
the preceding values become 
*... - M c i - c L s ,, _ «( c i - c) 
' a* + cf + 1’ y ~ a* + (f + 1 ’ 
To apply these results to the present case* we have 
a = *9380* h — *9460, c - 1*0038 
h 
Cy = — = 1*0085* c t - c = -0047 * 
and introducing these values into the preceding expressions* we 
find 
8 # = — 83 / = *0015* 
so that the corrected values of x and y are 
# = -9395* y = *9445. 
