RECENT PROGRESS IN GEODESY. 
259 
of differential equations involving our available data the 
length of the line joining the points in question is regarded 
as a constant. This means simply that, in comparison with 
the other variable quantities, an error in the length of the 
measured line has little or no influence in the adjustment of 
discrepancies. 
In fact, the inherent nature of the observations must always 
be considered, and we are often restrained and hampered in 
striving after a certain limit of accuracy for the reason that 
geometrical conditions render one result much more accurate 
than another. Consider the equations of Laplace already 
cited. We are able to get the deflection of the plumb line in 
an east and west direction in two ways, by determination of 
longitude and azimuth; but while an error of one second in 
the geodetic longitude of a place is not admissible, it is quite 
within the limit of possibility that the geodetic azimuth 
should be erroneous by such amount. Since both of these 
data can be applied to determine the deflection of the plumb 
line, it is evident that they furnish results entitled to very 
different degrees of consideration. In general, it may be said 
that the accuracy attainable in the result by the two methods 
(longitude and azimuth) have about the same relation that 
the earth’s radius has to the distance between the two points. 
The principal meridian, parallel and oblique arcs, measured, 
in progress and projected, to the present time are shown in 
Plate 11. 
These are the principal steps in the work, but in the exe¬ 
cution of the necessary detail we meet many modifying con¬ 
siderations. Prominent among these is the question of the 
deflection of the plumb line. It is well known that the so- 
called vertical lines, as defined by a freely suspended weight, 
are not perpendicular to the surface of our ellipsoid of revo¬ 
lution. Every change in the density of the underlying 
strata, every elevation and depression on the earth’s surface, 
has its effect on the plumb bob, and when we make astronom¬ 
ical and geodetic observations based on a certain assumed 
vertical we are by no means sure that our measures are cor- 
38—Bull. Phil. Soc., Wash., Vol. 13. 
