208 Mr. Herapath on the Laiv of Continuity. [March, 



Article VIII. 



On the Law of Continuity. By J. Herapath, Esq. 



(To Dr. Thomson.) 



DEAR SIR, 



It was an opinion of Leibnitz, the celebrated contemporary 

 and rival of Newton, that all changes are made gradually and 

 with time. " If," says this philosopher, " a change can be 

 effected without the lapse of time, then the body on which this 

 change is made is in two different states at one and the same 

 instant, which is impossible. If, for instance, it be a change of 

 motion, and the saltus be made at the beginning of the motion, 

 then the body is both at rest and in motion in the same indivisible 

 instant." Hence he infers the impossibility of sudden or instant- 

 aneous change, and, therefore, the necessity of continuity as a 

 law. I do not know, having never seen the original work, 

 whether Leibnitz admits any exception to continuity ; but, by 

 what I have read in other authors, he appears to rank it with 

 Nature's invariable and unerring laws. But whatever may have 

 been his opinion of its universality, there is little doubt but that 

 it is an idea which has more embarrassed and perplexed both its 

 partisans and opponents than, perhaps, any other that has 

 hitherto been introduced into philosophy. It is now, I believe, 

 almost universally received as an infallible principle. And 

 indeed the merited celebrity of its author, and the specious 

 arguments with which it may be supported, are well calculated 

 to procure it credit with those who receive it merely as a prin- 

 ciple, without applying it in investigation; but they that are 

 employed in philosophical researches, and that have, therefore, 

 need of sometimes comparing their deductions with its conse- 

 quences, must soon become convinced of the impossibility of 

 its being a universal and an immutable law ; * though the plausi- 



* One of the most singular circumstances that I know of, which the introduc- 

 tion of continuity as a law of nature has occasioned, is the attempt to explode the 

 possibility of absolute hardness ; not because any deductions from the idea of 

 perfect hardness are repugnant to phenomena or reason, but because the commu- 

 nication of motion by the collision of hard bodies must be instantaneous, or with- 

 out the consumption of time ; which is contrary to what the principle of continuity 

 requires. It would not, however, I conceive, be a very difficult matte/ to show, 

 that the primary particles of matter must of necessity be perfectly hard, or that it 

 is impossible for them to be otherwise. The arguments of Sir Isaac Newtpn 

 appear to me to be pretty conclusive on this subject. This excellent philosopher, 

 in enumerating the principles of nature, says : " It seems probable to me, that God 

 in the beginning formed matter in solid, massy, hard, impenetrable, moveable par- 

 ticles, of such sizes and figures, and with such other properties, and in such propor- 

 tion to space, as most conduced to the end for which he formed them ; and that 

 these primitive particles being solids, are. incomparably harder than any porous 

 bodies compounded of them ; even so hard as never to wear or break in pieces ; no 

 ordinary power being able to divide what God himself made one in the first crea- 

 tion. While the particles continue entire they may compose bodies of one and the 



