THE TRANSCONTINENTAL ARC. 
215 
Ten years ago no one would have thought of giving the lati¬ 
tude as a function of the time. Thanks, however, to inter¬ 
national work in which the Coast and Geodetic Survey has 
taken a very creditable part, we are now able to state the 
law according to which the latitude changes, and all our 
latitudes are consequently corrected and reduced to what 
they were at a certain definite epoch. It will no longer suf¬ 
fice to write unconditionally the latitude of Washington. 
Modern exigency requires that the time be given at which it 
had this particular value. 
So with the correction for height. Before the subject of 
potential had attracted much attention and before latitudes 
of precision were observed at great altitudes no one thought 
of correcting these results for elevation; but Gauss showed, in 
1853, that the plumb-line changes its direction as we recede 
from the earth’s surface, and the same fact has been devel¬ 
oped from the theory of potential by more recent writers. 
We must therefore take into account what is called the curva¬ 
ture of the vertical and apply a correction to every latitude 
that is observed at a considerable distance above the level of 
the sea. 
It is an established fact that the surfaces of two confocal 
ellipsoids subject to the influences of attraction and rotation 
are not parallel. It follows from this that the surface of a 
lake on a mountain top converges toward the surface of the 
sea. Moreover, it is known that the convergence varies with 
the latitude, and that the angle is measured approximately 
by the difference of height for stations situated near the same 
parallel. The convergence of two corresponding meridians 
in the two surfaces will be identical with the inclination of 
the plumb-lines, and we therefore have a value for the devia¬ 
tion of the vertical in passing from the sea-level to greater 
elevation. 
It may be roughly stated that for the transcontinental arc 
there is a correction of one-twentieth of a second for each 
1,000 feet of height, and since many of our stations are above 
10,000 feet and some are beyond 14,000, it is evident that 
