Mr Harvey cm the Method of Minimum Squares* ^97 
and, by making this sum equal to a minirrium^ we shall have 
0 — (a'— 4- (a— . t) -t- a?) 4- &c. > 
and from which results, 
__ a' 4- a" -h a'*' 4 &c. 
X ^ ^ r— , 
n ■ .. 
n being the number of observations. 
In like manner, if, in order to determine the position of a point 
in space, we have found by a first experiment the co-ordinates 
a', 6', c/ ; by a second, the co-ordinates 5", c", &c., and so 
on, and that we regard as the true co-ordinates of the 
same point; then the error of the first experiment will be the 
distance of the point (a', d') from the point (a?, z ) ; the 
square of this distance is 
and the sum of the like squares being equal, to a minimum^ we 
deduce from it three equations, which give 
n being the number of points given by experiment. These for- 
mulae are the same as those by which we find the common centre 
of gravity of several equal masses, given in position ; and from 
which we perceive that the centre of gravity of any body what- 
ever possesses this general property : 
If we divide the mass of a body into equal molecules ^ and so 
small that they may he considered as points^ the sum of the 
squares erf the distances of these molecules from, ike centre of 
gravity will he a minimum. 
We perceive, therefore, that the method of minimum squares 
discloses a kind of centre around which the results furnished by 
experiment arrange themselves, so that they may be removed 
from it in the least possible degree. The application we are 
about to make of it to the measurement of the meridian, will 
unfold its simplicity and fertility in a clear point of view. 
Application to the Measurement qf Degrees of the Meridian. 
Let us suppose the terrestrial meridian to be any ellipsis whose 
^xes are related to each other as 1 to l-p«; that D designates 
the length of the 45th degree, and S that of the arc contained 
between the two latitudes L and L' ; then by known formulae, 
