I 





On the Fundamental Principles of Mathematics. 183 



divided or limited by its bounding or limiting surfaces; or as a 

 line is divided into distinct portions or is terminated by a point. 

 When the one analogy will be the more complete, and when 

 the other, will the more distinctly appear, when the infinities of 

 both space and duration are considered in their proper connection. 

 It will however be observed, that a limit such as the midnight 

 with which one day (according to the ordinary reckoning) ends, 

 and another begins, is not somewhat in duration, but only some- 

 where ; or rather — if such a word were admissible — somewhen : 

 viz., when the one day ends and the other begins. A limit such 

 as this is an instant; and its relations to duration, or to that 

 measured or at least finite portion of it, which we call time, are 

 analogous to the relations of point to space. An instant is the 

 absolute zero of duration, as a point is the absolute zero of space. 

 [An instant is different, therefore, from a moment; which is a 

 small but indefinite portion of duration.] 



(10.) Rest, is, in a manner sufficiently analogous, the zero of 

 motion; and may exist as the effect of an equilibrium ; which is 

 rest compelled. 



This zero occurs, when and where, the body comes to, or is 

 found at, rest ; or when and where, it is prevented from movin 



(11.) An equilibrium is itself one form of the zero of force ; 

 though such a zero may simply imply the absence of all force, 

 from a given place, and at a given time: when and where, there 

 is no force. 



(12.) Perfect shadow is the zero of light; whenever and 

 wherever, it may exist. 

 (13.) Lastly. Empty space is itself the zero of matter ; how- 





space 



, (14) In any and all of such cases as have been specified, zero 

 implies the absence of that to which it is related ; and point being 

 ^> extent in space ; an instant, no time ; rest, no motion ; &e. 

 Yet, an instant seems to be almost as incomparable with a point, 

 as an hour with a mile. Being related to quantities entirely un- 

 like in kind, each alone has place (in its own peculiar sense of 

 the term) in that species of quantity of which it is itself the zero. 

 A point, however, may have place in a line, which itself, as 

 before shown, may be a zero of surface, and this surface, again, 

 a zero of capacity; for the point, the line, the surface, and that 

 ^hich the surface limits, are all to be found in space itself. 

 But the other zeros which have been specified, an instant, rest, 

 equilibrium, shadow, and (with reference to matter) empty space, 

 though any or all of them may exist when, if not where, and 

 s °metimes even, when and where, all the zeros already described 

 ar e found, yet the presence or the absence of one will not, in every 

 cas e, imply, or require the presence or the absence of another; 

 a nd the relations of all, as well as those of other zeros will, when 



