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.

In approximate coincidence with the Renaissance movement and the accompanying awakening of the intellect of Europe, there began a conflict between the sovereigns and the Pope. The Popes had gradually acquired great power, because of their prestige as the successors of St. Peter, to whom it was declared our Savior had given the keys of heaven. Coincidentally, the multitudinous barons had gradually built up the Feudal System. This was a loose-jointed contrivance, under which Europe was virtually divided into little geographical sections, ruled over by hereditary feudal lords, who in each country owed allegiance to a sovereign. By reason of the slowness and uncertainty of transportation and communication, the various feudal lords were extremely independent, and each one did substantially as he willed in his little domain.

The situation was a miserable one for every person, except the Pope, the sovereigns, the feudal lords and their hangers-on; not only because of the various petty tyrannies, but because of the continual little wars and the general absence of good government. Gradually, the sovereigns got more and more power (except in England) and the conditions improved so much that the people realized that it was better to be ruled by one king, or emperor, than by a multitude of barons. The sovereigns finally acquired so much power that they dared to oppose the Pope in many of his aggressions; but no very important situations were developed until the Reformation caused the existence of protestant or heretic sovereigns, and the occasional excommunication of one of them by the Pope, with its attendant exhortation to his subjects to take up arms against him. To meet this situation, the theory of the Divine Right of Kings was invented.

This was a very important invention; for it offset the Divine authority of the Pope as Pope, and gave a theme for the bishops and priests in their discourses to the people, and a slogan for the soldiers. It was extremely successful for three centuries, and its influence was in the main beneficent. It worked for the establishment of stable governments and great nations, tended to prevent the excessive domination of a religious organization, and, by recognizing the fact that every sovereign's power comes from the Almighty, it suggested the sovereign's responsibility to Him. At first this suggestion evidently bore little fruit; for the seventeenth and eighteenth centuries were characterized by general oppression of the people, and filled with dynastic wars, waged merely in behalf of monarchical ambitions. But gradually the kings and the peoples came to realize the duties of sovereigns, as well as their privileges and powers. Gradually then, the view came to be held that kings were bound to exercise their power for the benefit of their people.

Even the doctrine of the Divine Right of Kings, now condemned and obsolete, had a great influence and a good influence during the time it was in vogue; and it supplies a clear illustration of the power of a good idea, skillfully developed, to fulfill a given purpose, so long as its existence is necessary.

Most men have a considerable amount of energy, but do not know what to do with it. Children are in the same category, except that toys have been invented for them, and parents give these toys to their children. Without toys, children find the days very long, and parents find their children very trying. The usefulness of toys seems to be mainly, not so much in giving children pleasure directly, as in supplying an outlet for their energies, both physical and mental. For what greater pleasure is there than in expending one's natural energies under pleasant conditions?