Only one farther step had to be taken, and this the most complicated of all: he must make all the bodies of the sky conform to his third law of motion. This is: Action and reaction are equal, or the mutual actions of any two bodies are always equal and oppositely directed. There must be mutual attractions everywhere: earth for sun as well as sun for earth, moon for sun and sun for moon, earth for Venus and Venus for earth, Jupiter for Saturn and Saturn for Jupiter, and so on. The motions of the planets in the undisturbed ellipses of Kepler must be impossible. As observations of the planets became more accurate, it was found that they really did fail to move in exact accord with Kepler's laws unmodified. Newton was unable, with the imperfect processes of the mathematics of his day to ascertain whether the deviations then known could be accounted for by his law of gravitation; but he nevertheless formulated the law with entire precision, as follows: Every particle of matter in the universe attracts every other particle with a force exactly proportioned to the product of their masses, and inversely as the square of the distance between their centers. The centuries of astronomical research since Newton's day, however, have verified the great law with the utmost exactness. Practically every irregularity of lunar and planetary motion is accounted for; indeed, the intricacies of the problems involved, and the nicety of their solution, have led to the invention of new mathematical processes adequate to the difficulties encountered. And about the middle of the last century, when Uranus departed from the path laid out for it by the mathematical astronomers, its orbital deviations were made the basis of an investigation which soon led to the assignment of the position where a great planet could be found that would account for the unexplained irregularities of the motion of Uranus. And the immediate discovery of this planet, Neptune, became the most striking verification of the Newtonian law that the solar system could possibly afford. The astronomers of still later days investigating the statelier motions of stellar systems find the Newtonian law regnant everywhere among the stars where our most powerful telescopes have as yet reached. So that Newton's law is known as the law of Universal Gravitation, and its author is everywhere held as the greatest scientist of the ages.