[ H8 ] 



XXI. On an Apparent Violation of the Law of Continuity. 

 By P. M. Roget, ilf.Z). F.R.S.* 



FT cannot fail to strike every philosophical observer of na- 

 ■■• ture, that the greater number of changes which take place 

 in the universe are effected only in a gradual manner ; that 

 each event is connected by insensible differences, both with 

 the one which immediately precedes, and the one which im- 

 mediately follows it; and that we may hence infer that the 

 whole series of mutations which constitute any observed 

 change, is perfectly uninterrupted and continuous. With re- 

 gard to those changes which appear at first sight to be more 

 suddenly effected, a careful analysis of the whole of the pheno- 

 mena, and a more minute subdivision of the time during which 

 they occur, will enable us to perceive the operations of the same 

 general principle of successive and intermediate gradation of 

 condition necessarily existing between opposite states of being. 

 Thus, the apparently sudden impulse communicated to a ball 

 by the explosion of gunpowder is, in reality, as much the re- 

 sult of a gradual communication of motion, during which the 

 ball passes successively, though with great rapidity, through 

 every intermediate degree of velocity, as in the case of the 

 slowest increase of motion, which it might acquire by the con- 

 stant operations of the greatest accelerating force. It was by 

 extending these views to a variety of subjects of physical sci- 

 ence, that Leibnitz was led to the conclusion, that the same 

 principle pervaded every department of nature, and that the 

 Law of Continuity^ as he called it, was the law of the universe. 

 Natura non operatur per saltum was his motto ; implying that 

 every thing that is executed in nature is done by indefinitely 

 small degrees. Boscovich has assumed this principle as the 

 foundation of his ingenious and profound theory of natural 

 philosophy, and deduced from it a variety of important corol- 

 laries and conclusions. The law of continuity, says that phi- 

 losopher, consists in this, that any quantity, whilst passing 

 from one magnitude to another, must pass through all the in- 

 termediate magnitudes of the same kind : or, according to the 

 law of continuity, all changes in nature are produced by in- 

 sensible and infinitely small degrees ; so that no body can in 

 any case pass from motion to rest, or from rest to motion, 

 without passing through all possible intermediate degrees of 

 motion* 



* From the Scientific Gazette, Nos. 19 and 20, for November 5 and 12, 

 1825. — As this work has long since been discontinued, and was of confined 

 circulation, we think Dr. Roget's interesting paper will be acceptable to the 

 readers of the Philosophical Magazine. — Edit. 



The 



