visible. Absolutely to determine whether the divisibility of mat-ter may r proceed without limits, or that there are ultimate"primarycorpuscles not admitting of further division, does not appear asyet to be within the reach of philosophy'. That all bodies con-tain an infinity of parts is exceedingly obvious, thus any bodywhich can be proposed has for instance ten parts, each of the tenpurls has also ten parts, and again each of these has ten parts, andso on without limit. The same would appear by supposing anyother number of parts as well as ten, and it would be absurd tosuppose that the smallest particle has fewer halls, quarters, lentlrsparts, &c. than the largest mountain. That any given extensionis divisible ad inlinilum in a mathematical point of view may bethus demonstrated. See Plate LIV. tig. Id. Suppose the lineAC perpendicular to BP ; anil another, as GII, at a small dis-tance from it, also perpendicular to the same line. With the centresCCC, &c. describe circles cutting the line Gil in the points ece,Sc c. Now the greater the radius AC is, the less is the part cG.But the radius may be augmented in infinitum; so long*, there-fore, the part eG may be divided into still less portions ; conse-quently it may be divided in infinitum. Or thus, suppose theline AB, (fig. 12,) be required to lie divided, through its extremepoints A and B draw EP and CD parallel to each other ; in one ofthese lines take a point as L, and from L draw lines LD to theline CD, cutting AB in e: it is evident that the further D is takenfrom 15, the part A e will be the less, and since BD may be continuedwithout limits, the part A c may be lessened without limits, or it isdivisible ad infinitum. 'Thus far we have shewn that exten-sion, and consequently that an extended body, contains an unli-mited number of parts ; but with respect to the limits of the divi-sibility of matter itself, we are perfectly in the dark. We can in-deed divide certain bodies into surprisingly fine and numerousparticles, and the works of nature offer many fluids and solids ofwonderful tenuity ; but both our efforts, and those naturally smallobjects, advance a very short way towards infinity. Ignorant ofthe intimate nature ol matter, we cannot assert whether it may hecapable of infinite division, or whether it ultimately consists ofparticles of a certain size, and of perfect hardness. However, theuniformity and constancy of the qualities of the same bodies wouldlead us to conclude that there are ultimate invariable, indivisibleparticles which are their true constituents, and which do not admitof a separation of their parts by any powerless than that of Ilimwho formed them. But even these are amazingly small, as willappear from the following instances of the wonderful tenuity ofcertain bodies, which have been produced either by art, or disco-vered by means of microscopical observations amongst the stu-pendous works of nature. The spinning of wool, silk, cotton, andsuch-like substances, aflord no bad specimens; since the threadwhich has been produced by this means, has often been so veryfine as almost to exceed the bounds of credibility, had it not beensufficiently well authenticated. Mr. Boyle mentions that twograins and a half of silk was spun into a thread 300 yards long. Afew years ago, a lady of Lincolnshire spun a single pound of wool-len yarn into a thread of 168,000 yards long, which is equal to 95English miles. Also a single pound weight of fine cotton-yarnwas lately spun, in the neighbourhood of Manchester, into a thread134,400 yards long. The ductility of gold likewise furnishes astriking example of the great tenuity of matter amongst the pro-ductions of human ingenuity. A single grain weight of gold hasbeen often extended into a surface equal to 50 square indies. Itevery square inch of it is divided into square particles of the hun-dredth part of an inch, which will be plainly visible to the nakedeye, the number of those particles in one inch square, will be10,000; and multiplying this number by the 50 inches, the pro-duct is 500,000 ; that is, the grain of gold may lie actually dividedinto at least half a million of particles, each of which isperfecllvapparent to the naked eye.- i et, if those particles are viewed ina good microscope, they will appear like a large surface, the tenthousandth part of which might by this means lie easily discerned.An ingenious artist in London has been able to draw parallel linesupon a glass plate, as also upon silver, so near one another, that10,000 of them occupy the space of one inch. Those lines canhe seen only by the assistance of a very good microscope. Ano-ther workman has drawn a silver wire, the diameter of which doesnot exceed the 750th part of an inch. But those prodigies of humaningenuity will appear extremely gross and rude, if they are com-voi.. u.— so. 66.

pared with the immense subtiity of matter which may every wheiebe observed amongst the works of nature. The animal, the vege-table, and even the mineral kingdom, furnish numerous examplesof this sort. What must be the tenuity of the odoriferous carts cfmusk, when we find that a piece of it will scent a whole room in a-short time, and yet it will hardly lose any sensible part of itsweight! But supposing it to have lost one-hundredth part of agrain weight, when this small quantity is divided and disj-ev-ed.through the whole room, it must so expand itself as not to leavean inch square of space where the sense of smell may not he .i-fected by some of its particles! The human eye, unas.-isted by-glasses, can frequently perceive insects so small as to be barelydiscernible. The least reflection must shew, that the limbs, thevessels, and other parts of such animals, must infinitely exceed infineness every endeavour of human art. But the microscope hasdiscovered wonders that are vastly superior, and such indeed aswere utterly unknown to our fore-fathers, befoie the invention ofthat noble instrument. Insects have been discovered so small asnot to exceed the 10,000th part of an inch : so that 1,060,000,000,000,of them might he contained within the space of one cubic incdi; ■yet each animalcule must consist of parts connected with eachother; with vessels, with fluids, and with organs necessary for itsmotions, for its increase, for its propagation, &c. How incon-ceivably small must those organs be ! and yet they are unques-tionably composed of other parts still smaller, and still farther re- ’moved from the perception of our senses.

DIVISION , among logicians, is the explication of a complexidea, by enumerating the simple ideas whereof it is composed ; inwhich sense it is nearly allied to definition, only that tins last re-gards names and things, whereas division is employed wholly aboutideas. When the parts of an idea are divided, in order to a clearerexplication of the whole, this is called a subdivision: thus, a yearis divided into twelve months, a month is subdivided into weeks,weeks into days, days into hours, and so on. The rules for a gooddivision are these, that the members entirely exhaust the whole ;that they be opposite; that subdivisions be not too numerous;that the whole be first divided into Us larger parts, and these intothe more remote and minute parts.

Division, in mathematics. See Algebra and Arithme-tic.

Division, in sea atTairs, a select number of ships in a fleet orsquadron of men of war, distinguished by a particular ling or pen-dant, and usually commanded bv a general officer. A squadronis commonly ranged into three divisions, the commanding officerof which is always stationed in the centre. When a fleet consistsof 60 sail of the line, that is, of ships having at least 60 cannoneach, the admiral divides it into three squadrons, each of whichhas its divisions and commanding officers. Each squadron has itsproper colours, according to the rank of the admiral, and eve.rydivision its proper mast. Thus in'Britain , the first admiral, or theadmiral of the fleet, displays the union flag at the main-top-masthead; next follows the while flag with St. George’s cross; andafterwards the blue. The private ships carry pendants of the samecolour with their respective squadrons at the mast of their particu-lar divisions ; so that the last ship in the division of the blue squa-tiron carries a blue pendant at her mizen-top-mast head.

Division, Mechanical, signifies that separation which is oc-casioned in the parts of a body bv help of mechanical instruments.The mechanical division of bodies does indeed separate them infosmaller, homogeneous, similar parts; but this separation cannotextend to the primary integrant molecules o! any body ; and con-sequently is incapable of breaking what is property called their ag-gregation. No union is formed betwixt the dividend and dividingbodies, in which respect division essentially differs from dissolu-tion. Division is not properly a chemical operation. It is onlyemployed preparatorily to facilitate other operations, and particu-larly solution. For this purpose it is very useful, as it increasesthe quantity of surface, and consequently the points of contact ofany body. Different methods are used to divide bodies accord-ing to their nature, as that of cutting, rasping, fifing, pounding,bruising, grinding, &e.

Division, in music, the dividingof the interval of an octave intoa number of less intervals. The fourth and fifth divide the oc-

I tnve perfectly, though differently : when the fifth is below, and

I serves as a bass to the fourth, the division is called harmonica!;

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