serve a great number of juices of different natures, viz. the blood,lyrnpha, saliva, stomach-liquor, intestinal juices, pancreatic juice,bile, urine, &c. and the blood is the general source of all. SeePhysiology.

SECTION, in general denotes a part of a divided thing, or thedivision itself. Such, particularly, are the subdivisions oi a chap-ter; called also paragraphs and articles: the mark of a sectionis §.

Section, in geometry, denotes a side or surface of a body orfigure cut off by another; or the place where lines, planes, &c.cut each other.

Sections, Conic. See Conic Sections.

SECTOR, in geometry, is a part of a circle comprehended be-tween two radii and the arch ; or it is a mixed triangle, formed bytwo radii and the arch of a circle.

Sector of an Ellipse, or, of an Hyperbola , &c. is a partresembling the circular sector, being contained by three lines, twoof which are radii, or lines drawn from the centre of the figure tothe curve, and the intercepted arc or part of that curve.

Sector of a Sphere, is the solid generated by the revolutionof the sector of a circle about one of its radii; the other radius de-scribing the surface of a cone, and the circular 3rc a circular por-tion of the surface of the sphere of the same radius. So that thespherical sector consists of a right cone, anti of a segment of thesphere having the same common base with the cone. And hencetlie solid content of it will be found by multiplying the base orspherical surface by the radius of the sphere, and taking a third partof the product.

Sector is also a mathematical instrument, of great use in find-ing the proportion between quantities of the same kind ; as betw eenlines and lines, surfaces and surfaces, &c. whence the French callit the compass of proportion. The great advantage of the sectorabove the common scales, &c. is, that it is made so as to fit all radiiand all scales. By the lines of chords, sines, &c. on the sector,we have lines of chords, sines, &c. to any radius betwixt the lengthand breadth of the sector when open. The real inventor of thisvaluable instrument is unknown : yet of so much merit has the in-vention appeared, that it was claimed by Galileo, and disputed bynations. The sector is founded on the fourth proposition of thesixth book of Euclid : where it is demonstrated, that similar tri-angles have their homologous sides proportional. An idea ,of thetheory of its construction may be conceived thus. Let the linesAB, AC, (Tlate CLVI. fig. 1,) represent the legs of the sector;and AD, and AE, twoequal sections from the centre: if, now thepoints CB and DE be connected, the lines CB and DEvvill be pa-rallel ; therefore the triangles AD E, ACB, will be similar; and con-sequently the sides AD, DE, AB, and BC, proportional: that is,as AD ; DE: : AB : BC: whence, if AD be the half, third, orfourth part of AB ; DE will be a half, third, or fourth part of CB:ai id the same holds of all the rest. If, therefore, AD lie the chord,s: oe, or tangent, of any number of degrees to the radius AB ; DEw dl be same to the radius BC.

Sector, Description of the. The instrument (fig. 2, 3,)consists of two rulers or legs, of brass or ivory, or any other matter,re presenting the radii, moveable round an axis or joint, the middleof which expresses the centre ; whence are drawn on the faces ofthe rulers several scales, which may be distinguished into singlear >d double. Tlie double scales, or lines graduated upon the facesof the instrument, and which are to be used at sectoral lines, proceedtrom the centre ; and are, I. Two scales of equal parts, one oneach leg, marked lin, or l. each of these scales, from the greatextensiveness of its use, is calltfd the line of lines. 2. Two lines ofchords marked cho. or c. 3. Two lines of secants marked sec.

s - A line of polygons marked pol. Upon the other facethe sectoral lines are, 1. Two lines of sines marked sin. or s.

I wo lines of tangents marked tan. or t. 3. Between the linee. tangents and sines there is another line of tangents to a less ra-I lus > o to supply the defect of the former, and extending from 45°0 73°, marked t. Each pair of these lines (except the line ofPolygons ) is so adjusted as to make equal angles at the centre;a "^ cons cquently at whatever distance the sector be opened, theng es will be always respectively equal. That is, the distanceOn anc * 011 *be bne Ihies, will be equal to 60 and 60

on tl"' !- ne . r ' 10n * s > 91* an d 90 on the line of sines, and 43 and 45'e hue of tangents. Besides the sectoral scales, there are

vol. iv.-— no. 194 . , ,

others on each face, placed parallel to the outward edges, andused as those of the common plane scale. 1. These are a line ofinches. 2. A line of latitudes. 3. A line of hours. A line ofinclination of meridians. 5. A line of chords. Three logarithmicscales, namely, one of numbers, one of sines, and one of tangents ;these are used when tlie sector is fully opened, the legs formingone line. The value of the divisions on most of the lines are de-termined by the figures adjacent to them ; these proceed by tens,which constitute the divisions of the first order, and are numberedaccordingly ; but the value of the divisions of the line of lines,that are distinguished by figures, is entirely arbitrary, and mayrepresent any value that is given to them ; lienee the figures 1, 2,3, 4, &c. may denote either 10, 20, 30, 40, or 100, 200, 300, 400,and so on. 'I he line of lines is divided into ten equal parts, num-bered 1, 2, 3, to 10; these may he called divisions of the first or-der; each of these are again subdivided into 10 other equal parts,which may be called divisions of the second order; each of theseis divided into two equal parts, forming-divisions of the third or-der. The divisions on all the scales are contained between foul-parallel lines; those of the first order extend to the most distant:those of the third to the least; those of the second to the interme-diate parallel. When the whole line of lines represents 100, thedivisions of the first order, or those to which the figures are an-nexed, represent tens; those of the second order units ; those ofthe third order the halves of these units. If the whole line repre-sent ten, then the division of the first order are units ; those ot thesecond tenths; the third twentieths. In the line of tangents, thedivisions to which the numbers are affixed, are the degrees ex-pressed by those numbers. Every fifth degree is denoted by aline somewhat longer than the rest; between every number andeach fifth degree, there are four divisions, longer then the inter-mediate adjacent one 5 , these are whole degrees; the shorter ones,or those of the third order, are 30 minutes. From the centre, to60° the line of sines is divided like the line of tangents, from 60 to70; it is divided only to every degree, from 70 to SO, to everytwo degrees, from 80 to 90; the division must be estimated bythe eye. The divisions on the line of chords are to be cstimateilin the same manner as the tangents. The less line of tangents isgraduated to every two degrees, from 45 to 50 ; but from 50 to 60to every degree; from 60 to the end, to half-degrees. The lineof secants from 0 to 10 is to be estimated by the eye; from 20 to50, it is divided to every two degrees; front 50 to 60, to everydegree ; from 60 to the end, to every half-degree.

Sector, Use of the Line of Chords on the. 1. Toopen the sector so as the two lines of chords may make an angleor number of degrees, suppose 40. Take the distance from thejoint to 40, the number of the degrees proposed, on the line ofchords ; open the sector till the distance ftom 60 to 60, on eachleg, be equal to the given distance of 40; then will the two lineson the sector form an angle of 40 degrees, as was required. 2.The sector being opened, to find the degrees of its aperture.

I ake the extent from 60 to 60, and lay it off on the line of chordsfrom the centre; the number whereon it terminates will shew thedegrees, &c. required, 3. r I o lay oft any number of degrees uponthe circumference of a circle. Open the sector till the distancebetween 60 and 60 be equal to the radiits of the given circle ; thentake the parallel extent of the chord of the number of degrees oneach leg-of the sector, and lay it off on the circumference of thegiven circle. Hence any regular polygon may be easily inscribedin a given circle.

Sector, Use of the Line of equal Parts on the. i.To divide a given line into any number of equal parts, supposeseven. Take the given, line in your compasses; and setting onefoot in a division of equal parts, that may be divided by seven,for example 70, whose seventh part is 10, open the sector till theother point fall exactly on 70, in the same line on the other leg.In this disposition, applying one point of the compasses to 10 fnthe same line ; shut them ti l the other fall in 10 in the same lineon the other leg, and this opening will be the seventh part of thegiven line. Note, if the line to be divided be too long to be ap-plied to the legs of the sector, divide only one-half or one-fourthby seven, and the double or quadruple thereof will be the seventhpart of the whole. 2. To measure the lines of the perimeter of apolygon, one of which contains a given number of equal parts.'Take the given line in your compasses, and set it parallel, upon,7 A- tire