92 
the inaccuracy of the results is increased in a way which it is gener- 
ally quite impossible to determine. 
In 1876, Peirce first perceived one of the most important of these 
defects, viz., the oscillation of the framework of the pendulum ap- 
paratus, and took that in account upon the results he obtained. 
From this time it has been endeavored either to deduce the 
influence of the want of stability of the pendulum framework by 
further measurements, and by these means to correct the results ob- 
tained, or, what is more natural, to remove altogether this injurious 
effect by a better construction of the apparatus. 
We may regard these efforts as the beginning of the really valu- 
able work of the second period, in which ve/ative determinations of 
gravity resumed the first place, which properly belongs to them. 
On the whole, we still pursue the same object as before, viz., the 
investigation of the true figure of the earth, but we have now the 
advantage of much experience which indicates to us the line that 
we should follow for the attainment of the object in view. 
Formerly, we really endeavored to determine the difference be- 
tween the longest and shortest diameters of the earth, which was 
considered to be an ellipsoid. Accordingly the object of the meas- 
urements was to determine the constants of an analytical expression, 
previously defined as the figure of the earth. Theoretically speak- 
ing, two determinations were quite sufficient for this purpose; and 
in any case the problem could -be solved by a relatively limited 
number of observations. 
At the present day it is not only the oblateness that we wish to 
deduce by determinations of gravity, but it is really the shape of the 
geoid which we have set ourselves the task of investigating. The 
geoid is, however, a surface which is very irregular in shape, and 
which we know will not admit of representation by any analytical 
expression. 
Thus we can only ascertain its course by the determination of the 
coérdinates of a very large number of points; and it is therefore 
now necessary, contrary to former efforts, to ascertain the intensity 
of the force of gravity at as great a number of places as possible, 
uniformly and closely arranged over the whole earth. 
It is, again, the relative determinations to which the greatest 
share in the solution of this comprehensive problem falls, and the 
absolute determinations continually recede into the background ; for 
geodesy requires only the comparison of the intensity of the force 
