theory, and showed why Newton's calculation was not exact.

Newton proceeded to explain the other inequalities recognised by Tycho
Brahe and older observers, and to calculate their maximum amounts as
indicated by his theory. He further discovered from his calculations
two new inequalities, one of the apogee, the other of the nodes, and
assigned the maximum value. Grant has shown the values of some of
these as given by observation in the tables of Meyer and more modern
tables, and has compared them with the values assigned by Newton from
his theory; and the comparison is very remarkable.

Newton. Modern Tables.
degrees ' " degrees ' "
Mean monthly motion of Apses 1.31.28 3.4.0
Mean annual motion of nodes 19.18.1,23 19.21.22,50
Mean value of "variation" 36.10 35.47
Annual equation 11.51 11.14
Inequality of mean motion of apogee 19.43 22.17
Inequality of mean motion of nodes 9.24 9.0

The only serious discrepancy is the first, which has been already
mentioned. Considering that some of these perturbations had never been
discovered, that the cause of none of them had ever been known, and
that he exhibited his results, if he did not also make the
discoveries, by the synthetic methods of geometry, it is simply
marvellous that he reached to such a degree of accuracy. He invented
the infinitesimal calculus which is more suited for such calculations,
but had he expressed his results in that language he would have been
unintelligible to many.