Mr Harvey on the Method of Minimum Squares. ^99 
ing from the four arcs measured in the operations of the meri- 
dian: 
E' — E” = 0.002923 + € (^.192) — (0.563) 
Eli _j.in _ 0.003100 + € (2.672) — ^ (0.351) 
E«*— -E'^ --0.001096 + € (2.962) -f- ^ (0.047) • 
E»v— -E"^ = —0.001808 + € (1.851) -f- (0.263) 
As it is necessary to consider the errors separately, we shall 
regard the error as a new unknown, and we shall have the 
6ve following equations : 
E' = E^'^ -f- 0.006023 + € (4.864) — ^ (0.914) 
E'' = E“' -}. 0.003100 4- € (2.672) — (0.351) 
E“^ =: E“" . (b) 
E^^ = E”' 4- 0.001096 — € (2.962) — ^ (0.047) 
E^ = E“' 4 0.002904 — g (4.813) — ^ (0.310) 
We must now endeavour to make the sum of the squares of 
these five errors a minimum^ and which condition expressed 
with relation to the unknown function E“\ all of whose co-effi- 
cients are unity, will furnish by the addition of all the equations 
0 = 5 E“‘ 4 0.01 3123 — g (0.239) — ^ (1.622) 
whence 
E“‘ = — 0.002625 4 ^ (0.048) 4 « (0.324). 
By substituting this value in the equations denoted by (5), 
we shall have 
E^ = 0.003398 4g (4.91 2) — (0.590) 
E“ :z 0.000475 4 ^ (^.720) — « (0,027) 
E^^ = — 0.002625 4- € (0.048) 4 ^ (0.324) (c) 
E'^ — 0.001529— g (2.914) 4- ^ (0.277) 
E'^^ 0.000279— g (4.765) 4 ^(0.014) 
In order to express afterwards the condition of the minimum 
with relation to g, it will be requisite to multiply the first equa- 
tion by 4.912 the co-efficient of g ; the second by 2.720 ; the 
third by 0,048 ; the fourth by — 2.914 ; the fifth by — 4.765, 
and make the sum of all the products equal to zero. And, 
by operating similarly with respect to we shall have the two 
following equations : 
0 = 0.020983 4 g (62. 726) — <^(3.830) (d) 
0 = — 0.003287— g (3.830) 4 ^ (0*531) 
