And yet if one realizes his method of work, and the calm, uninterrupted flow of all his earlier life, perhaps his achievements become more intelligible. When asked how he made his discoveries, he replied: "By always thinking unto them. I keep the subject constantly before me, and wait till the first dawnings open slowly by little and little into a full and clear light." That is the way--quiet, steady, continuous thinking, uninterrupted and unharassed brooding. Much may be done under those conditions. Much ought to be sacrificed to obtain those conditions. All the best thinking work of the world has been thus done.[18] Buffon said: "Genius is patience." So says Newton: "If I have done the public any service this way, it is due to nothing but industry and patient thought." Genius patience? No, it is not quite that, or, rather, it is much more than that; but genius without patience is like fire without fuel--it will soon burn itself out. NOTES FOR LECTURE IX The _Principia_ published 1687. Newton died 1727. THE LAW OF GRAVITATION.--Every particle of matter attracts every other particle of matter with a force proportional to the mass of each and to the inverse square of the distance between them. SOME OF NEWTON'S DEDUCTIONS. 1. Kepler's second law (equable description of areas) proves that each planet is acted on by a force directed towards the sun as a centre of force. 2. Kepler's first law proves that this central force diminishes in the same proportion as the square of the distance increases. 3. Kepler's third law proves that all the planets are acted on by the same kind of force; of an intensity depending on the mass of the sun.[19] 4. So by knowing the length of year and distance of any planet from the sun, the sun's mass can be calculated, in terms of that of the earth. 5. For the satellites, the force acting depends on the mass of _their_ central body, a planet. Hence the mass of any planet possessing a satellite becomes known. 6. The force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles. [Because, while a stone drops 16 feet in a second, the moon, which is 60 times as far from the centre of the earth, drops 16 feet in a minute.] * * * * * 7. The moon is attracted not only by the earth, but by the sun also; hence its orbit is perturbed, and Newton calculated out the chief of these perturbations, viz.:-- (The equation of the centre, discovered by Hipparchus.) (_a_) The evection, discovered by Hipparchus and Ptolemy. (_b_) The variation, discovered by Tycho Brahé. (_c_) The annual equation, discovered by Tycho Brahé. (_d_) The retrogression of the nodes, then being observed at Greenwich by Flamsteed. (_e_) The variation of inclination, then being observed at Greenwich by Flamsteed. (_f_) The progression of the apses (with an error of one-half).