Newton showed from the laws of mechanics which he had discovered that, assuming the first two laws of Kepler to be true, each planet must always be subject to a force directing it toward the sun, that varies inversely as the square of its distance from the sun: otherwise, it would fly away from the sun or toward it. From this, Newton inferred that all masses, great and small, attract each other with a force proportional to their masses, and inversely proportional to the square of the distance between them, and invented what is now called the law of universal gravitation. Another invention of possibly equal value, also published in his _Principia_, but not so generally known, is his three laws of motion. These are "1. Every body continues in its state of rest, or of moving with constant velocity in a straight line, unless acted upon by some external force. "2. Change of momentum is proportional to the force and to the time during which it acts, and is in the same direction as the force. "3. To every action there is an equal and contrary re-action." It is probably impossible for any human mind to conceive any invention of a higher order of originality than either of these two, or to construct any invention more concrete and useful. Certainly no more brilliant inventions have ever yet been made. These two wonderful products of Newton's genius underlie the whole structure of modern astronomy and modern mechanics. The sciences of modern astronomy and modern mechanics could not exist without them, and would not now exist unless Newton (or someone else) had invented them. It may be pointed out that Newton's conception of our solar system is that of a machine in rapid motion, of which the sun and the planets are the principal parts. Another important invention ascribed to Newton is that of the sextant, a small and easily handled instrument, used ever since in ships for purposes of navigation; but whether he should receive the entire credit for this invention seems quite doubtful; for another astronomer, Robert Hooke, is credited by some with the original suggestion, and John Hadley, still another astronomer, with having adapted it to practical sea use. Numerous other scientific inventions, however, that have formed the basis of much of the scientific work of later experimenters and inventors are clearly to be credited to Newton. Among these, his formula for the velocity of a wave of compression, his color-wheel, and his simple apparatus known as "Newton's rings," by which can be measured the wave lengths of light of different colors, are possibly the most important.