SECTOR. 



The manner m which thefe fcales are difpofed of on the 

 I'eAor, is bell feen in the figure. 



The fcales of lines, chords, fines, tangents, rhumbs, la- 

 titudes, hours, longitude, incl. merid. may be ufed, whether 

 the inllrument is (hut or open, eacli of thefe fcales being 

 contained on one of the legs only. The fcales of inches, 

 decimals, log. numbers, log. fines, log. verfed fines, and 

 log. tangents, are to be ufed with the feftor quite opened, 

 part of each fcale lying oh both legs. 



The double fcales of lines, chords, fines, and lower tan- 

 gents, or tangents under 45 degrees, are all of the fame 

 radius or length : they begin at the centre of the inilrument, 

 and are terminated near the other extremity of each leg ; 

 viz. the lines at the divifion ic, the chords at 60, tlie fines 

 at 90, and the tangents at 45 ; the remainder of the tan- 

 gents, or thofe above 45 degrees, are on other fcales be- 

 ginning at one-fourth of the length of the former, counted 

 from the centre, where they are marked with 45, and run 

 to about 76 degrees. 



The fecants alfo begin at the fame diftance from the 

 centre, where they are marked with 10, and are from 

 thence continued to as many degrees as the length of the 

 feftor will allow, which is about 75 degrees. 



The angles made by the double icales of lines, of chords, 

 of fines, and of tangents, to 45 degrees, are always equal. 

 And the angles made by the fcales of upper tangents, and 

 of fecants, are alfo equal ; and fometimes thefe angles are 

 made equal to thofe made by the other double fcales. The 

 fcales of polygons are put near the inner edge of the legs, 

 their beginning is not fo far removed from the centre, as the 

 60 on the chords is. Where thefe fcales begin, they are 

 marked with 4, and from thence are figured backwards, or 

 towards the centre, to 12. 



From this difpofition of the double fcales, it is plain, 

 that thofe angles which were equal to each other, while 

 the legs of the feAor were clofe, will Itill continue to be 

 equal, although the feftor be opened to any dillance it will 

 admit of. 



The fcale of inches is laid clofe to the edge of the feclor, 

 and fometimes on the edge ; and contains as many inches as 

 the intlniment will receive when opened : each inch being 

 ufually divided into eight, and alfo into ten equal parts. 

 The decimal fcale lies next to this : it is of the length of 

 the fedlor, when opened, and is divided into ten equal parts, 

 or primary divifions, and each of thefe into ten other equal 

 pa. ts ; fo that the whole is divided into a hundred equal 

 parts : and if the fetlor admits of it, each of the fubdivitions 

 is divided into two, four, or five parts ; and by this decimal 

 fcale, all the other fcales, that are t'lken from tables, may 

 be laid do .v;i. The length of a feftor is ufually underftood 

 when it is (liut ; and, therefore, a feftor of fix inches makes 

 a ruler of twelve inches when opened ; and a foot feftor is 

 two feet long, when quite opened. The fcales of chords, 

 rhumbs, fines, tangents, hours, latitudes, longitudes, and 

 inclina: ms of meridians, are fuch as are defcribed under 

 Plane Scale. 



The fca),' of logarithmic or artificial numbers, called 

 Gunter's fcale, or Gunter's line, is a fcale exprelTing the 

 logarithms of common numbers, taken in their natural 

 order. 



For the conftruftion of thif fcale, and alfo of thofe of 

 logarithmic fines, logarithmic tangents, and logarithmic 

 verlt'd fines, fee Gunter's Line, and Gun'Teu's Scale. 



We (hall here obfcrvc, that all thefe fcales (hould have 

 one common termination to one end of each fcale, i. e. the 

 10 on the numbers, the 90 on the fines, the o on the verfed 

 fines, and the 45 on the tangents, fliould be oppofite to 



each other : the other end of each of the fcales ef finei, 

 verfed fines, and tangents, will run out beyond the beginning 

 (marked i) of the numbers; nearly oppofite to which will 

 be the divifions reprefenting 35 minutes on the fines and 

 tangents, and 168^ degrees on the verfed fines. 



The double fcales are conftruftcd in the following manner. 

 The line of lines is only a fcale of equal parts, whofe 

 length is adapted to that of the legs of the feftor : thus, 

 in the fix-inch feftor, the length is about 5|- inches. 

 The length of this fcale is divided into primary divifions; 

 each of thefe into ten equal fecondary parts ; and each 

 fecondary divifion into four equal parts. The accuracy of 

 the divifion may be determined by taking between the com- 

 paffes any number of equal parts from this line, and apply- 

 ing that diitance to all the parts of the line ; and if the 

 fame number of divifions be contained between the points 

 of the compatTes in every application, the fcale may be re- 

 ceived as perfeft. The line of fines is conltruftcd by making 

 the whole length of this fcale equal to that of the line of m 

 lines ; and from this line, taking off leverally the parts (1 

 exprefTed by the numbers in the tables of the natural fines, 

 correfponding to the degrees, or to the degrees and minutes, 

 intended to be laid upon the fcale : and then by laying down 

 thefe feveral dillances on the fcale, beginning from the centre. 

 In fcales of this length, it is cuftomary to lay down divifions, 

 exprefling every 15 minutes, from o degree to 60 degrees ; 

 between 60 and 80 degrees, every half degree is exprefled ; 

 then every degree to 85 ; and the next is 90 degrees. 

 The length of the fcale of tangents is equal to that of the 

 line of lines, and the feveral divifions upon it (to 45 degrees) 

 are laid down from the tables and line of lines, in the fame 

 manner as the former ; obferving to ufe the natural tangents 

 in the tables. The fcale of upper tangents is laid down, by 

 taking 5 of fuch of the natural tabular tangents above 45 

 degrees, as are intended to be put upon the fcale. The 

 beginning of this fcale, at 45 degrees, though the pofition 

 of it on the feftor refpefts the centre of the inftrument, is 

 dillant from the centre 5 of the length or radius of the lower 

 tangents. 



The diftance of the beginning of the fcale of fecants from 

 the centre, and the manner of laying it down, are the fame 

 as thofe of the upper tangents : except that in this the 

 tabular fecants are to be ufed. 



For the fcale of chords ; its length is to be made equal 

 to that of the fines ; aad the divifions, which are twice the 

 length of the fines of half the degrees and minutes counted 

 from the centre, cxprefs every 15 minutes from o degrees 

 to 60 degrees, to be laid down as in the fcale of fines. 



The fcale of polygons ufually comprehends the fides of the 

 polygons from fix to twelve fides mclufive. The divifions 

 are laid down by taking the lengths of the chords of the 

 angles at the centre of each polygon, and laying them down 

 from the centre of the initrument. When the polygons of 

 four and five fides are alfo introduced, this line is conllrufted 

 from a fcale of chords, where the length of 90 degrees is 

 equal to that of 60 degrees of the double fcale of chords 

 on the feftor. Inftead of fome of the double fcales above 

 defcribed, there are found other fcales on the old feftors, 

 and alfo on fome of the French ones, fuch as fcales of fuper- 

 ficies, of folids, of infcribed bodies, of metals, &c. ; but 

 thefe are left out to make room for others of more general 

 ufe. See Caliber. 



In defcribing the ufe of the feftor, the terms lateral 

 dyiance, and tranfuerfe diftance, often occur. By the for- 

 mer is meant the diitance taken with the compaftes on one 

 of the fcales only, beginning at the centre of the feftor ; 

 and by the latter, the dillance taken between any two cor- 

 refponding 



