Swift Used Kepler's Third Law

Jonathan Swift didn't pluck random figures out of the air, he applied Kepler's Third Law. In the case of Phobos the ratio is 10²/3³=3.704 and for Diemos it is 21.5²/5³=3.698. Swift wrote "...the squares of their periodical times are very near in the same proportion with the cubes of their distance from the centre of Mars". But that still doesn't explain how his figures came so close to the actual figures.