brought into an ecstasy or trance, with the delight he had in the study of geometry, and truly ravished with the love of the Muses. But amongst many notable things he devised, it appeareth, that he most esteemed the demonstration of the proportion between the cylinder (to wit, the round column) and the sphere or globe contained in the same: for he prayed his kinsmen and friends, that after his death they would put a cylinder upon his tomb, containing a massy sphere, with an inscription of the proportion, whereof the continent exceedeth the thing contained."(2) It should be observed that neither Polybius nor Plutarch mentions the use of burning-glasses in connection with the siege of Syracuse, nor indeed are these referred to by any other ancient writer of authority. Nevertheless, a story gained credence down to a late day to the effect that Archimedes had set fire to the fleet of the enemy with the aid of concave mirrors. An experiment was made by Sir Isaac Newton to show the possibility of a phenomenon so well in accord with the genius of Archimedes, but the silence of all the early authorities makes it more than doubtful whether any such expedient was really adopted. It will be observed that the chief principle involved in all these mechanisms was a capacity to transmit great power through levers and pulleys, and this brings us to the most important field of the Syracusan philosopher's activity. It was as a student of the lever and the pulley that Archimedes was led to some of his greatest mechanical discoveries. He is even credited with being the discoverer of the compound pulley. More likely he was its developer only, since the principle of the pulley was known to the old Babylonians, as their sculptures testify. But there is no reason to doubt the general outlines of the story that Archimedes astounded King Hiero by proving that, with the aid of multiple pulleys, the strength of one man could suffice to drag the largest ship from its moorings. The property of the lever, from its fundamental principle, was studied by him, beginning with the self-evident fact that "equal bodies at the ends of the equal arms of a rod, supported on its middle point, will balance each other"; or, what amounts to the same thing stated in another way, a regular cylinder of uniform matter will balance at its middle point. From this starting-point he elaborated the subject on such clear and satisfactory principles that they stand to-day practically unchanged and with few additions. From all his studies and experiments he finally formulated the principle that "bodies will be in equilibrio when their distance from the fulcrum or point of support is inversely as their weight." He is credited with having summed up his estimate of the capabilities of the lever with the well-known expression, "Give me a fulcrum on which to rest or a place on which to stand, and I will move the earth."