The greatest single exploit of Archimedes was his discovery and demonstration of the hydrostatic principle that the weight of liquid displaced by a body floating in it is equal to that of the body. The story is that the king gave him the apparently impossible task of determining the quantity of gold and the quantity of silver in a certain gold coin, in making which the king suspected the workmen of stealing part of the gold and substituting silver. Pondering this subject later while lying in his bath, Archimedes suddenly realized that his body displaced a bulk of water equal to that part of his body that was immersed, and conceived the consequent law; and the conception was so startling and so vivid that he rushed unclad out into the street crying, "I have found it, I have found it." The story as a story may not be exactly true; but if Archimedes had realized the full purport and the never-ending result of his conception, he would probably have done something even more eccentric than he did. * * * * * Archimedes esteemed mechanical inventions as greatly inferior in value to those speculations and demonstrations that convince the mind, and considered that his chief single work was discovering the mathematical relation between a sphere and a cylinder just containing it. Whether this discovery and the discovery of the hydrostatic principle just mentioned were inventions or not, depends, of course, on the meaning of the word invention. Within the meaning of the word as employed heretofore in this book, both seem to have been inventions. Each made a definite creation and each caused something to exist, the like of which had never existed before. Furthermore, the mental processes followed resemble very closely the conception and formulation of a religion or a theory, the conception and composing of a new piece of music, story or poem, the conception and developing of any new plan or scheme; the conception and embodying in material form of any mechanical device. It is not asserted, of course, that all inventions are on a dead level of equality, simply because they are inventions. Evidently there are degrees of excellence among inventions as among all other things. CHAPTER IV INVENTION IN ROME: ITS RISE AND FALL We have noted, up to a time approximately that of Archimedes, a continual succession of inventions of many kinds, that formed stepping-stones to civilization so large and plain, that we can see them even from this distance. We now come to a period lasting more than a thousand years, in the first half of which there was a gradually decreasing lack of inventiveness shown, and in the latter half a cessation almost complete.