236 Coast Survey of the United States. 
The nicety of this result rivals both the English and French 
surveys. It is not necessary to carry comparisons (which may 
appear invidious) any farther at present; but they need not be 
shunned, whatever the source or standard by which they are 
challenged. It is only necessary to add that the calculations were 
not made by Dr. Bache himself. 
This subject leads to the mention of the formule used upon 
the survey for the calculation of L. M. Z. which depend upon 
the figure of the earth. The value of e?, the expression by 
which the ellipticity enters into these equations, has been variously 
decided by the most distinguished geometers, and has resulted 
differently from the comparison of different meridional measure- 
ments; from experiments with the pendulum by different ob- 
servers, and from calculations of it from the moon’s motion by 
La Place and Buckhardt. The history of these facts will be fa- 
miliar to the reader. Among the comparatively modern deter- 
minations, the linear measure of Mason and Dixon in 1764 has 
given a result in one extreme, and the magnificent triangulation 
of Méchain et Delambre in the other. This is precisely one of - 
those questions in which the purely practical depends upon the 
purely theoretical, and that of the highest order. The direction 
hitherto taken by the main triangulation of the coast survey 
does not enable it to supply the, measurement of an are of me- 
ridian, that is, an element for deducing the figure of the earth 
satisfactorily. But it is now approaching this point. The tri- 
angulation from Nantucket, (which will be one of the points of 
the first order during the present season,) to Portland, will qualify 
the survey to take its place in this respect also amongst the per- 
manent scientific works of the world. 
From the head to the mouth of the Chesapeake will be formed 
another series, favorably situated for this purpose, and here the 
line of Mason and Dixon will be included and its accuracy tested. 
The tables for the reduction of triangles, and for projection, were 
first calculated by Mr. Hassler in 1818, but in 1834 he found it 
necessary to repeat all the calculations,—the knowledge of the 
dimensions and figure of the earth having been much improved 
and more strictly defined. Since then, however, has appeared 
the determination of Bessel, founded upon a comparison of all 
the authentic measures, to each of which is assigned its just 
weight as determined by the theory of probabilities, or the method 
