forced to hand over his calculations to a friend, to be completed by
him.



8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.


Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
1721. Although he did not contribute directly to the mathematical
proofs of Newton's theory, yet his name is closely associated with
some of its greatest successes.

He was the first to detect the acceleration of the moon's mean
motion. Hipparchus, having compared his own observations with those of
more ancient astronomers, supplied an accurate value of the moon's
mean motion in his time. Halley similarly deduced a value for modern
times, and found it sensibly greater. He announced this in 1693, but
it was not until 1749 that Dunthorne used modern lunar tables to
compute a lunar eclipse observed in Babylon 721 B.C., another at
Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
two later ones up to the tenth century. He found that to explain
these eclipses Halley's suggestion must be adopted, the acceleration
being 10" in one century. In 1757 Lalande again fixed it at 10."

The Paris Academy, in 1770, offered their prize for an investigation
to see if this could be explained by the theory of gravitation. Euler
won the prize, but failed to explain the effect, and said: "It appears
to be established by indisputable evidence that the secular inequality
of the moon's mean motion cannot be produced by the forces of