SLIDING. RULE. 



you will find on the line marked FC, 4.1 inches to be added 

 to 24 inches : the reft, carried on as before, gives the con- 

 tent of the caflc 87.93 ale-gallons. 



14. A ca(k partly empty, lying with its axis parallel 

 to the horizon ; to find the quantity of liquor in it. Find 

 its whole content as above, which fuppofe 97.455 gallons ; 

 and fuppofe the inches left dry, S, and the bung-diametcr 

 32 : then, as the bung-diameter on C is to lOO on the line 

 of fegments L, fo are the dry inches on C to a fourth 

 number on the hne of fegments : and as 100 upon B is to 

 the cafe's whole content on A, fo is that fourth number 

 to the liquor wanting to fill up the cafli, which, fubtrafted 

 from the whole content of the cadi, gives the liquor re- 

 maining therein ; e. gr. fet 32, the bung-dtameter on C, to 

 100 on the fegment-line L; then againit 8, the dry inches 

 on C, ftands 17.6 on the fegment-liae : fet, therefore, 100 

 on B to the caflc's whole content on A ; and againll 17.6 

 on B, you have l (^.^ gallons on A : fubtracling, therefore, 

 the faid gallons from 97.45, the veffel's whole content, the 

 liquor in the caflc will be 80.95 gallons. 



15. A caflc ftanding upright, or with its axis perpen- 

 dicular to the horizon, to find the liquor therein. Sup- 

 pofe the length of the caflc 40 inches, and 10 of them dry ; 

 fet 40 inches on the line C, to 100 on the fegment-line S ; 

 and againft 10, the dry inches on the line C, ftands 24.2 

 on S, the fegment-line. Set then looon B to 97.455, the 

 caflc's whole content on A ; and againft 24.2 on B, you will 

 have 2^.5 gallons, which is what is wanting to fill up the 

 caflc : "this, therefore, fubtrafted from the whole content 

 97-455' g""^^ 73-955 gallons, for the quantity of hquor 

 remaining in the caflc. 



16. To find the content of any right-angled parallele- 

 piped (f. gr. a ciftcrn, uting-fat, or the like) in malt 

 buftiels. Suppofe the length of tlie bafe 80 inches, the 

 breadth 50, and depth 9 inches ; fet the breadth 50 on B, 

 to the depth 9 on C ; then againll the length 80 en A, 

 ftand 16.8 buftiels on B, the number required. 



SLiDiXG-/?u/f, Coggejliall's, is principally ufed in meafur- 

 ing of the fuperficies and (olidity of timber, &c. 



It confifts of two rulers, each a foot long, which are 

 framed or put together various ways ; fometimes they are 

 made to Aide by one another, like glaziers' rules : fometimes 

 a groove is made in the fide of 3 common two-foot joint- 

 rule, aud a thin fliding-piece put in, and Caggefhall's lines 

 added on that fide : but the moft ufual and commodious 

 way is, to have one of the rulers Aide in a groove made 

 along the middle of the other, as it is reprefented in Plate 

 VII. Surveying, Jig. 5. 



On the Aiding fide of the rule are four lines of numbers, 

 three of which are double, that is, are lines to two radiufes, 

 and one, a fingle broken line of numbers : the three firft, 

 marked A, B, C, are figured i, 2, 3, &c. to 9; then 

 1, 2, 3, &c. to 10. Their conftruftion, ufe, &c. are the 

 fame as thofe on Everard's Aiding rule. The fingle line, 

 called the girt-line, and noted D, whofe radius is equal to 

 the two radiufes of any of the other lines, is broken, for the 

 eafier meafuring of timber, and figured 4, 5, 6, 7, 8, 9, 10, 

 20, 30, Sec. from 4 to 5. It is divided into 10 parts, 

 and each tenth fubdivided into two, and fo on from 5 to 

 10, &c. 



On the backfide of the rule are, 1. A line of inch- 

 Bfieafure, from i to 12; each inch being divided and fub- 

 divided. 



2. A line of foot-meafure ; confifting of one foot, di- 

 vided into 100 equal parts, and figured 10, 26, 30, &c. 

 The backfide of the fliding-piece is divided into inches, 



halves, &c. and figured from 1 2 to 24 ; fo that when did 

 out, there may be a meafure of two feet. 



Sliding-/? u/i?, in mcafm-ing plain Juperficia, ufe of Cogge- 

 fljaWs. I. To mcafu'e a fquare. Suppofe, f.^r. the fides 

 be each five feet : fet i on the line B, to 5 on the line A ; 

 then againit 5 on the line B is 25 feet, the content of the 

 fquare on the line A. 



2. To meafure a long fquare. Suppofe the longeft fide 

 18 feet, and the fhortelt 10 : fet i on the line B, to 10 on 

 the line A : then againft 18 feet on the line B is 180 feet, 

 the content on the line A. 



3. To meafure a rhombus. Suppofe the fide 1 2 feet, 

 and the length of a perpendicular let fall from one of the 

 obtufe angles to the oppofite fide, 9 feet : fet i on the 

 line B, to 12, the length of the fide, on the line A ; 

 then againft 9, the length of the perpendicular on the line 

 B, is 108 feet, the content. 



4. To meafure a triangle. Suppofe the bafe 7 feet, and 

 the length of the perpendicular let fall from the oppofite 

 angle to the bafe 4 feet : fet i on the line B, to 7 on the 

 line A : then againft half the perpendicular, which is 2 

 on the line B, is 14 on tlie line A, tor the content of the 

 triangle. 



5. To find the content of a circle, its diameter being 

 given. Suppofe the diameter 3.5 feet: fet 11 on the 

 girt-line D, to 95 on the line C ; then againft 3.5 feet 

 on D, is 9.6 on C, which is the content of the circle in 

 feet. 



6. To find the content of an oval or ellipfis. Suppofe 

 the longeft diameter 9 feet, and the Aiorteft 4. Find a 

 mean proportional between the two, by fetting tiie greater 

 9 on the girt-line, to 9 on the line C ; then, againft the lefs 

 number 4, on the line C, is 6, the mean proportional fought. 

 This done, find the content of a circle, whofe diameter is 

 6 feet ; this, when found by the laft article, will be equal 

 to the content of the ellipfis fought. 



Sliding-ZJu/it, in meafuring limber, ufe of Coggejhall's. 

 I. To meafure timber the utual way. Take the length 

 in feet, half feet, and, if required, quarters ; then niealure 

 half-way back again ; there girt the tree with a fmall cord 

 or line ; double thie line twice, very evenly ; and meafure 

 this fourth part of the girt or perimeter, in inches, halves, 

 and quarters. The dimenfions thus taken, the timber is to 

 be meafured as if fquare, and the fourth of the girt taken 

 for the tide of the fquare, thus ; fet 12 on the girt-line 

 D, to the length in feet on the line C ; then againft the 

 fide of the fquare, on the girt-line D, taken in inches, 

 you have, on the hne C, the content of the tree in feet. 



For an inftance : fuppofe the girt of a tree, in the middle, 

 be 60 inches, and the length 30 feet, to find the content : 

 fet 12 on the girt-Une D, to 30 feet on the line C ; then 

 againft 15, one-fourth of 60, on the girt-fine D, is 46.8 

 feet, the content on the line C. If the length fliould be 

 9 inches, and the quarter of the girt ^^ inches, here, as 

 the length is lefs than a foot, meafure it on the lir.e of foot- 

 meafure, and fee what decimal part of a foot it makes, 

 which you will find .75 : fet 12, therefore, on the girt-line, 

 to 75 on the firft radius of the line C, and againft 35 oa 

 the girt-line is 6.4 feet on C, for the content. 



2. To meafure round timber the true way. The former 

 method, though that generally in ufe, is not quite juft. 

 To meafure timber accurately, inllead of the point 12 on 

 the girt-line, ufe another, 1)12. 10.635 ; at which tiiere 

 Aiould be placed a centre-pin. This 10.635 '^ '^^ '''^^ °^ 

 a fquare equal to a circle, whofe diameter is 12 inches. 

 For an inftance: fuppofe the length 15 feet, and 5th of 

 the girt 43 inches : fet the point 10.635 •■'' '5> '''^ length ; 



then 



