RECENT PROGRESS IN GEODESY. 
261 
by writers to show that no difference would be noticeable 
between the length of its polar and equatorial dimensions. 
Let us compare the length of the shortest line joining two 
points on the earth’s surface and the path actually traced by 
the line of sight of a theodolite. These lines have essen¬ 
tially different characters, the latter being a plane curve, 
while the former is of double curvature. The Coast and 
Geodetic Survey is now tracing the boundary betwean Cali¬ 
fornia and Nevada, running from a point in Lake Tahoe in 
a southeasterly direction to Fort Mohave. This line is sev¬ 
eral hundred miles long and will furnish material to bring 
out the points in question. It may appear paradoxical, but 
such is nevertheless the case, that if it were possible to set 
up an instrument at one end of this line and sight to the 
other, and if a man were required to pass over this line of 
sight he would not follow the same path that he would had 
he started from the other end and complied with the same 
conditions. This is due to the earth not being a perfect 
sphere. It is understood, of course, that the instrument is 
in both cases set up vertically at the two stations. What 
difference in length is there, then, between either of these 
lines and the shortest line joining the two points? for in 
neither case would our traveler traverse the shortest path. 
The difference is not great, and in this we realize how nearly 
equal, even for great distances, the lines on our planet are to 
those on the surface of a sphere. The shortest line between 
Washington and Eastport, Maine, is about T oVir °f an inch 
less than a plane curve joining the two points. Between 
Lake Tahoe and Fort Mohave the distance is 404.5 miles. 
The azimuth of the line is about 45° and its middle latitude 
not far from 37° north. The difference of length between 
the shortest line on our ellipsoid and a line traced under the 
conditions stated is* not quite 4 microns (or about of an 
inch) and the lines of sight observed from either end to¬ 
wards the other would differ by only 2".2 of arc. If two 
observers, having adjusted their instruments in the usual 
manner, one at each end of the line, should sight to the 
