260 
JPRESTON. 
rectly referred to the mean surface of the earth. When we 
assume that the difference of longitude between Cape May 
and San Francisco is correctly measured, as far as our instru¬ 
mental means permit, we may be several seconds in error, 
owing to the attraction exerted on our plumb bob by the 
mountains or the sea. Just here the equations of Laplace 
bring us a precious aid, in that they make it possible for us 
to treat these anomalous features so as to arrive at a result 
less affected by the influence of the form and density of the 
earth’s crust; the real significance of Laplace’s equations 
being that with our present refined methods in the tele¬ 
graphic determination of longitude it is possible to establish 
for a geodetic line that has been completely determined in 
latitude, longitude, and azimuth a conditional equation which 
is independent of the deflection of the plumb line. Gener¬ 
ally speaking, it may be said that the dimensions of our mean 
ellipsoid of revolution can be determined with great precision 
by measurements on the geoid which approximately coincides 
with the ellipsoid. One word about the best reference for 
the deflections of the vertical. It is now—indeed, has been 
for some time—most emphatically brought out that some 
standard must be adopted. Of course, relative deflections 
may be treated without making any assumption as to the 
absolute direction of the vertical line; but when it is a ques¬ 
tion of considering all such determinations, it has been pro¬ 
posed to refer them to a mean ellipsoid of revolution whose 
center is identical with the center of gravity of the actual 
earth, whose smaller axis coincides with the earth’s axis of 
revolution, and whose surface most nearly agrees with its 
actual form. All deflections can thus be referred to a stand¬ 
ard direction. 
While we are on the question of the earth’s figure we may 
take time to notice some peculiar conditions consequent upon 
its actual shape. When we speak of the earth as being flat¬ 
tened at the poles, the idea usually conveyed is that were the 
earth small enough to be seen at one view its ellipsoidal 
shape would be quite apparent. Many facts have been cited 
