1818.] Mr. Herapatk on the Law of Continuity. 20i* 



bility of the reasoning upon which it is founded, will not, perhaps, 

 readily allow them to perceive where the error lies. This seems 

 to have been the case with Maclaurin and some others ; who, 

 notwithstanding they were thoroughly satisfied of the incompa- 

 tibility of some of the results of continuity with sound philosophy, 

 have not, I believe, pointed out the cause of the errors, or 

 attempted to show wherein the reasoning of Leibnitz is fallacious . 



The following ideas respecting this law are what occurred to 

 me at the commencement of my researches on the subject of my 

 paper, published in your number for July, 1816, and which I 

 have now a little extended for the purpose of rendering them 

 more easy to be understood. 



Conceive time divided into what I apprehend Leibnitz means 

 by indivisible instants ; namely, into such parts as have the 

 same relation to a given portion of time which a mathematical 

 point has to a given line. Then if we admit, with Leibnitz, that 

 a body cannot be in two different states in one of such instants, 

 it must however be acknowledged, that it may be in one state in 

 one of them, and in a different in the next ; for if not, it would 

 be no great difficulty to show that a body could never be in 

 different states, and that eternity itself would be insufficient for 

 the production of the slightest change. Now there is no more 

 time between two such moments than there is length between 

 two contiguous points in the same line, and yet in the two 

 instants the states are different. In this manner it is, I conceive, 

 that changes may take place. It is not in the same, but in 

 different contiguous, or successive points of time, that a body 

 is in different states. Thus, with respect to motion, is it not 

 universally allowed that a body may move uniformly throughout 

 one portion of time, a minute for instance, with one degree of 

 motion, and uniformly throughout the subsequent with a 

 different? and, nevertheless, there is no lapse of time between 

 the end of one and the beginning of the other ; nor can it be 

 strictly said that the end of one minute is the beginning of the 

 following. For if each minute be divided into infinitely small, 

 parts, there is evidently one of these parts to terminate the pre- 

 ceding, and one to begin the subsequent minute. These final 

 and incipient moments are not, however, one and the same 

 moment ; they do not coincide, nor have they any interval 

 between them. They are consecutive, contiguous, and, if I 

 may so term them, touching, but not coinciding points in the 

 same line of time. Let, for example, A B and C D be two 

 straight lines, extending towards opposite parts, and touching at 

 their extremes B, C. Now although the two lines thus united 



same nature and texture in all ages; but should they wear away, or break in 

 pieces, the nature of things depending on them would be changed. Water and 

 earth, composed of old worn particles and fragments of particles, would not be 

 of the same nature and texture now, with water and earth composed of entire par- 

 ticles in the beginning, &c." 



Vol. XI. N°III. O 



