Note. If any of the dividends is less than the divisor, reduce it to the next denomination, and to the next again, till it be greater than, or equal to, the divisor.
Quest. 1. If 3 yards of cloth cost 8s. what is the price of 15 yards ? Answ. 40s. or 2/.
Work.
yds. s. yds.
3-8-15 15 3)120(40s.
Explanation. 3 yards and 8s. contain the supposition, and 8s. is like the thing sought ; therefore 8s. is the middle term, and yards on the left : then the demand arises upon 15 yards, and therefore it is on the right. Again, from the nature of the question, it is plain that 15 yards re quire more than 3 yards, i..e. the answer must be greater than the middle term ; wherefore 8s. is to be multiplied by 15 yards; the product is 120s. which, divided . A by 3 yards, quotes 40s. without a der ; so 403. or 21. is the number sought.
Quest. 2. if 41b. of sugar cost 2s. 9d. what is the value of 18/b.? Answer 12e. 4Ld.
Work.
lb. s. d. lb.
4-2 : 12 • 33 d.
18 264 33 4)594(148 d.
2 4 4)8(2 farthings.
Explanation. The supposition is in 41b. and 2s. 911. this last term being like the thing sought, which is connected with 1815. wherefore the terms are stated ac cording to the rule: then the middle term being mixed, it is to be reduced to pence; and then argue thus ; if 41b. cost 33d., 1815 must cost more ; therefbre multiply 33d. by 181b. and divide their product by 4; the quotient is 148d. and 2 remains, which is to be reduced to farthings, and the product, divided by the former quo tient, gives 2; so the answer is 148d. 2 farthings, or 12s. 41d. because 148d. is, by reduction, 12s. 4d.
Quest. 3. What time will 7 men be boarded for 251. when 3 men paid 25/. for 6 months ? Answ. 2 months, 16 days, rec koning 28 days to 1 month.
Work. men. months. men. 3-6-7 3 7)18(2 14 item. 4 28 7)112(16 days.
" Explanation. The 251. is a superflu ous number ; then the supposition is in the 3 men and 6 months, and the de mand regards the 7 men : the terms be ing all simple, you are to argue thus ; if 3 men are boarded 6 months for 251. (or any sum), 7 men will be boarded for the same a shorter time : therefore multiply 6 months by 3, and divide the product 18 by 7, whereby the answer is found to be 2 months and 16 days.
Note. The first two questions are what is called the rule of three direct, that is, where the third term, being greater or less than the first, requires that the An swer also be greater or lesser than the second term. The last, of the rule of three indirect, or reverse; where the third term, being greater or lesser than the first, requires the fourth contrarily lesser or greater than the second. But we have com prehended both in one general rule. And from this observation may be learned what questions are of either kind.
Hu Lc, or Butes., an instrument of wood or metal, with several lines deline ated on it, of great use in practical men suration. When a ruler has the lines of
chords, tangents, sines, &c. it is called a plane scale.
The carpenter's joint rule is an instru ment usually of box, &c. twenty-four inches long, and one and a half broad ; each inch being subdivided into eight parts. On the same side with these di visions is usually added Gunter's line of numbers, On the other side are the lines of timber and board measure; the first be ginning at 82, and continued to 36, near the other end ; the latter is numbered, from 7 to 36, 4 inches from the other end. We shall point out some of the uses of this rule.
The application of the inches, in mea suring lengths, breadths, &c. is obvious. That of the Gunter's line, see under the article GUNTER'S LINE.
The use of the other side is that with which we are now concerned. 1. The breadth of any surface, as board, glass, &c. being given, to find how much in length makes a square foot. Find the number of inches the surface is broad, in the line of board measure, and right against it is the number of inches requir ed.. Thus, if the surface were eight inch es broad, eighteen inches will be found to make a superficial foot. Or more rea dily thus : apply the rule to the breadth of the board, or glass, that end, marked 36, being equal with the edge, the other edge of the surface will show the inches, and quarters of inches, which go to a square foot. 2. Use of the table at the end of the board-measure. If a surface be one inch broad, how many inches long will make a superficial foot ? look In the upper row of figures for one inch, and under it in the second row is twelve inches, the answer to the question, 3i Use of the line of timber-measure. This resembles the former ; for having learned how much the piece is square, look for that number on the line of the timber measure ; the space thence to the end of the rule is the length, which, at that breadth, makes a foot of timber. Thus, if the piece be nine inches the length necessary to make a solid foot of timber is 211 inches. If the timber be small, and under nine inches square, seek the square in the upper rank of the table, and immediately under it is the feet and inches that make a solid foot. If the piece be not exactly square, but broader at one end than the other, le method is to add the two together, and take half the sum for the side of the square. For round timber the method is to girt it round with a string, and to allow the fourth part for the side of the square ; but this method is erroneous, for hereby you lose nearly one fifth of the true solidity ; though this is the method at present practised in buy ing and selling timber.