Chap. 4. PHILOSOPHICAL DISCOVERIES. 87

rid os the insuperable objections against the vortices. To re-move the difficulty a step farther, or to involve the question inobscurity, new vortices are introduced in every infinitely smallparticle of matter. From these, is there be occasion, they willdescend into another order infinitely less ; and so on ; for theyexpresty pretend to take the same benefit from the infinite or-ders of infinitesimals, in philosophy *, that is claimed by somelate geometricians in the resolution os their problems. Thus(as we observed elsewhere -fj an absurd philosophy is the natu-ral product of a vitiated geometry. For tho’ it follows fromour notion of magnitude, that it always consists of parts, andis divisible without end ; yet an actual division in injinitum isabsurd, and an infinitely little quantity (even in Mr. Leibnitz §judgment j) is a mere fiction. Philosophers may allow them-selves to imagine likewise infinite orders of infinitely small par-ticles of matter, and suffer themselves to be transported withthe idea ; but these illusions are not supported by sound geo-metry, nor agreeable to common sense. Aster all that has beensaid for the vortices , there is not one experiment to favourthem ; and some of the most common and simple are againstadmitting such fluids and their motions.

We have another instance of the art by which they supporttheir schemes, in the pretended demonstration they give againstthe possibility of atoms, or of any perfectly hard and inflexiblebodies. According to what they call the law of continuity , allchanges in nature are produced by insensible and infinitely smalldegrees ; so that no body can, in any case, pass from motion torest, or from rest to motion, without passing through all pos-sible intermediate degrees of motion ; from which they coir-

* Mem. de l'Academie Royale des Sciences, 1729.-f- Treatise of Fluxions Introd. p. 47.

X Essay de Fhecdice'e y § 70.