I have looked at several sources, and Newton was right about the fact that the Earth is not a perfect sphere, but an ellipsoid caused the precession of equinoxes, as the Moon's gravitational attraction of the Earth causes torque, if the Earth is not a perfect sphere.
However, I looked at the English translation of Principia
 "And since the mean semi-diameter of the earth, according to Picart's mensuration, is 19615800 Paris feet, or 3923,16 miles (reckoning 5000 feet to a mile), the earth will be higher at the equator than at the poles by 85472 feet, or 17 1⁄10 miles. And its height at the equator will be about 19658600 feet, and at the poles 19573000 feet."
I also looked at the Latin edition, even though I don't know Latin: http://www.gutenberg.org/files/28233/28233-h/28233-h.htm
The value was slightly different, but not that much
"Ideoque cùm Terræ semidiameter mediocris, juxta nuperam Gallorum mensuram, sit pedum Parisiensium 19615800 seu milliarium 3923 (posito quod milliare sit mensura pedum 5000;) Terra altior erit ad æquatorem quàm ad polos, excessu pedum 85200 seu milliarium 17."
I searched the Internet and found out that the actual difference is neither 17.1 miles nor 17 miles but 13.3 miles. So, Newton got the radius difference quite wrong. I thought about the possibility that the miles then and now were different, but this was not the case. Internet says that the radius of the earth is 3950~3963 miles, which almostly agrees with Newton's value 3923.16 miles or 3923 miles.
So, if Newton got wrong about the radius difference, how did he end up getting the right value? (50 arcseconds per a year)
https://en.wikipedia.org/wiki/Axial_precession Wikipedia says
"Over a century later precession was explained in Isaac Newton's Philosophiae Naturalis Principia Mathematica (1687), to be a consequence of gravitation (Evans 1998, p. 246). Newton's original precession equations did not work, however, and were revised considerably by Jean le Rond d'Alembert and subsequent scientists."
Does anyone know what actually happened?