122 Observations relating to the Operations undertaken 
fectual, it behoved these great bodies to have been originally 
fluid. He tock them then as in that state, and showed how to 
calculate the flattening of a planct, according to the intensity of 
the gravity at its surface and the quickness of its rotation, sup- 
posing its mass to be homogeneous. This theory, applied to the 
earth, gave a variation of gravity but little different from that 
observed by Richer, though somewhat slighter, indicating that 
the earth is composed of strata of which the density goes on in- 
creasing from the surface to the centre, as Clairault has sinee 
demonstrated. 
For some time the calculations of Newton were the only in- 
ductions for believing the earta to be flattened at the poles. The 
are of the ’meridian measured by Picard was sufficient to give 
the length of the semidiameter of the earth at the place where 
it was observed; but that arc was much too small even for 
showing imperfectly the effect of the flattening. More accurate 
knowledge was expected to be procured from the measurement 
of the complete arc which traverses France from Perpignan to 
Dunkirk, which was intended to serve as the axis of a general 
map of France, with the exeeution of which Colbert had in- 
trusted the Academy. But in the imperfect state of the instru- 
ments and astronomical methods of that period, this are itself 
was too short to make the influence of the flattening distinctly 
perceptible ; and the small variations which thence result in the 
length of the consecutive degrees, might very easily be lost in 
the errors of the observations, as was indeed actually the ease. 
The differences which the degrees presented, were found from 
the effects of these errors, in such a direction as would have led 
to the result of elongation at the poles, in place of flattening. 
The Academy was not intimidated. It perceived that the ques- 
tion could not be accurately decided without measuring two 
ares. of the meridian, the one near the equator and the other 
near the pole. In the year 1735, Bouguer, Godin, and La 
Condainine were sent to America, where they joined the Spanish 
commissioners. Clairault, Maupertuis and Le Monnier de- 
parted for the Noith. The results of these expeditions com- 
pletely ascertained the flattening of the earth, but its absolute 
amount still remained uncertain. The degree of Peru compared 
with that of France, gave a slighter flattening than if the earth 
was homogeneous ; the sphere of Lapland indicated a greater. 
In this uncertainty the lengths of the pendulum which they were 
careful to measure, agreed with the flattening deduced from the 
operation at the equator; but the exactness of these measure~ 
ments, especially in the sphere of Lapland, was not such as 
could enable them to solve the difficulty. 
Matters remained in this state for fifty years, Meanwhile Bou- 
guer, 
-_—" 
