THE LAW OF CONTINUITY. 29 



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 unfortu- 

 nate projector, and not as a successful inventor, notwithstanding his 

 acknowledged ability and learning. 



-+*+- 



THE LAW OF CONTINUITY. 



By GEOEGE ILES. 



WHEN" the details of knowledge had in modern times accumu- 

 lated 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 incohe- 

 rent 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 tempera- 

 ture of 40, it is certain that at some intervening moment its tempera- 

 ture 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 de- 

 manded 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 



