vanced project of a piston, driven by steam-pressure on one side, assisted by a vacuum produced on the other; and he can only be regarded, therefore, as an ingenious and intelligent though unfortunate projector, and not as a successful inventor, notwithstanding his acknowledged ability and learning.
WHEN the details of knowledge had in modern times accumulated to so great an extent as to demand some organization of them into principles, thoughtful men cast about for some law which might serve to relate and connect together, in part at least, the multitude of facts and theories which were in an isolated and incoherent state.
At this important stage of scientific development, Galileo was the first to recognize the value of Plato's thought as to the continuous action of natural forces. By arranging in serial order the cases of a law, he showed that phenomena which might be supposed to be radically distinct were really due to one cause; and he said that, where links of connection were unknown, they should be sought for diligently.
Galileo, however, was too busy a man to work out many of the suggestions of the law of continuity, and it remained for Leibnitz to be the first to apply it extensively in the test of physical theories, and in the reduction of fragmentary knowledge to order and intelligibility. He affirmed that nothing passes from one state to another without passing through all intermediate states, and established the truth of his proposition by showing the absurdity of the contrary. If a change were to happen without the lapse of time, the thing changed must be in two different conditions at the same instant, which is manifestly impossible.
From this principle, for example, if it be known that a body at one moment had a temperature of 20°, and at another moment a temperature of 40°, it is certain that at some intervening moment its temperature was 30°. Although this law is so simple when stated as to seem almost axiomatic, yet its cases are frequently so obscure as to have caused much hesitation in its acceptance as a universal or even a widely-operating law. Some of its illustrations, lately discovered, are among the hardest-won triumphs of experimental skill, and have demanded the aid of the most refined modern apparatus.
A typical example of continuity has long been familiar to students of geometry; figures which may differ so much in graphic delineation