Page:Scientific Memoirs, Vol. 2 (1841).djvu/221

 Rh of the degree of uncertainty which still attaches to the fundamental members.

From the equations the total number of which is double the number of the parallels, we have to obtain, by the method of least squares, (after substituting in $$\frac$$, &c., and in $$P^{1 \centerdot 0}$$, &c. the corresponding numerical values of $$u$$,) as many of the co-efficients $$g^{1 \centerdot 0}$$, $$g^{2 \centerdot 0}$$, $$g^{3 \centerdot 0}$$, &c. as require to be taken into account.

In like manner the equations the number of which is three times as great as the number of parallels, serve to determine the co-efficients $$g^{1 \centerdot 1}$$, $$g^{2 \centerdot 1}$$, $$g^{3 \centerdot 1}$$, &c. And the following, determine the coefficients $$h^{1\centerdot 1}$$, $$h^{2 \centerdot 1}$$, $$h^{3 \centerdot 1}$$, &c. Further, the equations determine the co-efficients $$g^{2 \centerdot 2}$$, $$g^{3 \centerdot 2}$$, $$g^{4\centerdot 2}$$, &c.; and we obtain the co-efficients of the succeeding higher numbers in a similar manner.

The chief advantage which this method possesses over that