INF 



INF 



though infinitely greater than the other, 

 are yet infinitely less than any of those 

 wherein all the three dimensions are in- 

 finite. Such are the spaces intercepted 

 between two inclined planes infinitely ex- 

 tended ; the space intercepted by the sur- 

 face of a cone, or the sides of a pyramid, 

 likewise infinitely continued, 8cc. of all 

 which, notwithstanding the proportions 

 one to another, and to the T srav, or vast 

 abyss of infinite space (wherein is the lo- 

 eus of all things that are or can be ; or to 

 the solid of infinite length, breadth and 

 thickness, taken all manner of ways) are 

 easily -assignable ; for the space between 

 two planes is to the whole as the angle of 

 those planes to the three hundred and 

 sixty degrees of the circle. As for cones 

 and pyramids, they are as the spherical 

 surface intercepted by them is to the sur- 

 face of the sphere, and therefore cones 

 are as the versed sines of half their angles 

 to the diameter of the circle : these three 

 sorts of infinite quantity are analogous to 

 a line, surface, and solid ; and, after the 

 same manner, cannot be compared, or 

 have no proportion the one to the 

 other. 



INFINITESIMALS, among mathema- 

 ticians, are defined to be infinitely smull 

 quantities. In the method of infinitesi- 

 mals, the element, by which any quantity 

 increases or decreases, is supposed to be 

 infinitely small, and is generally express- 

 ed by two or more terms, some of which 

 are infinitely less than the rest, which be- 

 ing neglected as of no importance, the re- 

 maining terms form what is called the dif- 

 ference of the proposed quantity. The 

 terms that are neglected in this manner, 

 as infinitely less than the other terms of 

 the element, are the very same which 

 arise in consequence of the acceleration, 

 or retardation, of the generating motion, 

 during the infinitely small time in which 

 the element is generated : so that the re- 

 maining terms express the elements that 

 would have been produced in that time, 

 if the generating motion had continued 

 uniform : therefore those differences are 

 accurately in the same ratio to each other 

 as the generating motions or fluxions. 

 And hence, though in this method infini- 

 tesimal parts of the elements are neglect- 

 ed, the conclusions are accurately true, 

 without even an infinitely small error, and 

 agree precisely with those that are de- 

 duced by the method by fluxions. 



In order to render the application of 

 this method easy, some analogous princi- 

 ples are admitted, as that the infinitely 

 small elements of a curve are right lines, 

 or that a curve is a polygon of an infinite 

 number of sides, which, being produced, 



give the tangents of the curve ; and by 

 their inclination to each other measure 

 the curvature. This is as if we should sup- 

 pose, when the base flows uniformly, the 

 ordinate flows with a motion which is uni- 

 form for every infinitely small part of 

 time, and increases or decreases by' infi- 

 nitely small differences at the end of every 

 such time. 



But however convenient this principle 

 may be, it must be applied with caution 

 and art on various occasions. It is usual, 

 therefore, in many cases, to resolve the 

 element of the curve into two or more in- 

 finitely small right lines ; and sometimes 

 it is necessary, if we would avoid error, 

 to resolve it into an infinite number of 

 such right lines, which are infinitesimals 

 of the second order. In general, it is a 

 postulatum in this method, that we may 

 descend to the infinitesimals of any order 

 whatever, as we find it necessary ; by 

 which means, any error that might arise in, 

 the application of it may be discovered and 

 corrected by a proper use of this method 

 itself. See Maclaurin's Fluxions. 



INFLAMMATION. See MEDICINE 

 and SuRGEur. 



INFLAMMATION, in chemistry, is combus- 

 tion attended with flame : under the arti- 

 cle COMBUSTION, we have referred to the 

 spontaneous inflammation of certain bo- 

 dies, in peculiar circumstances, and like- 

 wise to the combustion of living individu- 

 als in the human species. We shall in this 

 place mention some of the causes of spon- 

 taneous inflammation. The heat produced 

 by friction ; the slacking of lime when in 

 contact with combustible matter ; the fer- 

 mentation of hay, dunghills, &c. are well 

 known. Many vegetable substances, high- 

 ly dried and heaped together, will heat, 

 scorch, and at last burst in a flame. A mix- 

 ture of linseed, or rape oil, with almost 

 any dry vegetable fibre, as hemp, cotton, 

 matting, &c. and still more if united to 

 certain carbonaceous matters, will in time, 

 if in a warm place, burst out into a flame. 

 To this circumstance many alarming and 

 destructive fires are to be imputed, which 

 at the time were supposed to have been 

 occasioned by wilful crime. In 1781 a 

 large magazine of hemp was destroyed, in 

 this way, at Constradt : and in the summer 

 of 1794 an accident of this sort happened 

 at Gainsborough, with a bale of yarn ac- 

 cidentally soaked in rape oil, which, after 

 remaining in the warehouse for several 

 days, began to smoke, and finally to burst 

 out into a most violent flame. A similar 

 accident happened at Bombay. A bottle 

 of linseed oil had been thrown down in 

 the night, the oil had penetrated into a 

 chest of coarse cotton cloth, and in the 



