figure of the earth. 
571 
16,88164 x n°.of seconds inL' — L — 935 8 x (sin 2 L'— sin2 L) 
-f- 267 x (sin 4 L'— sin 4 L). 
The lengths of the several arcs found from this expression 
differ from those above by — 4, +4, — 19, + 35, and + 63 
fathoms respectively. The largest of these errors falls (as 
will generally be the case when the method of least squares 
is used) on that length in which the coefficients of M, N, and 
P, are smallest ; but in a mountainous country, I conceive 
that an error of less than 4" in the difference of latitudes is by 
no means inadmissible. And I am the more inclined to 
allow this error, because, upon applying the formula to the 
arc measured in Sweden by the French Academicians, the 
error, which is much greater than this, has a different sign. 
I may here perhaps without impropriety, make some re- 
marks on the credit which appears to be due to the French 
measure in Sweden. That measure has often been men- 
tioned with contempt ; but more particularly since the late 
measure by Svanberg. I have not however been able to 
discover any reason for this contempt, except the disagree- 
ment of its results from those of other operations. The last 
part of the process, it is well known, was the measure of the 
base ; and the Academicians themselves were so much asto- 
nished at the result, that they immediately proceeded to 
verify every part of the measure, particularly the latitudes. 
And the general accuracy of the measure has been confirmed 
by the late measure. The triangles were admirably chosen ; 
the length of the arc agrees within a few fathoms with that 
found by Svanberg; the latitude. of the southern extremity 
at Tornea is precisely the same as that calculated by Svan- 
berg from the observations at Mallorn ; the latitude of Kittis, 
