RULE
, The Carpenters, a folding ruler generally used by carpenters and other artificers; and is otherwise called the sliding Rule.
This instrument consists of two equal pieces of boxwood, each one foot in length, connected together by a folding joint. One side or face, of the Rule, is divided into inches, and half quarters, or eighths. On the same face also are several plane scales, divided into 12th parts by diagonal lines; which are used in planning dimensions that are taken in feet and inches. The edge of the Rule is commonly divided decimally, or into 10ths; viz, each foot into 10 equal parts, and each of these into 10 parts again, or 100dth parts of the foot: so that by means of this last scale, dimensions are taken in feet and tenths and hundreds, and multiplied together as common decimal numbers, which is the best way.
On the one part of the other face are four lines, marked A, B, C, D, the two middle ones B and C being on a slider, which runs in a groove made in the stock. The same numbers serve for both these two middle lines, the one line being above the numbers, and the other below them.
These four lines are logarithmic ones, and the three A, B, C, which are all equal to one another, are double lines, as they proceed twice over from 1 to 10. The lowest line D is a single one, proceeding from 4 to 40. It is also called the girt line, from its use in casting up the contents of trees and timber: and upon it are marked WG at 17.15, and AG at 18.95, the wine and ale gauge points, to make this instrument serve the purpose of a gauging rule.
Upon the other part of this face is a table of the value of a load, or 50 cubic feet, of timber, at all prices, from 6 pence to 28. a foot.
When 1 at the beginning of any line is accounted only 1, then the 1 in the middle is 10, and the 10 at the end 100; and when the 1 at the beginning is accounted 10, then 1 in the middle is 100, and the 10 at the end 1000; and so on. All the smaller divisions being also altered proportionally.
By means of this Rule all the usual operations of arithmetic may be easily and quickly performed, as multiplication, division, involution, evolution, finding mean proportionals, 3d and 4th proportionals, or the Rule-of-three, &c. For all which, see my Mensuration, part 5, sect. 3, 2d edition.
Rules of Philosophizing. See Philosophizing.
Rule, in Arithmetic, denotes a certain mode of operation with figures to find sums or numbers unknown, and to facilitate computations.
Each Rule in arithmetic has its particular name, according to the use for which it is intended. The first four, which serve as a foundation of the whole art, are called addition, subtraction, multiplication, and division.
From these arise numerous other Rules, which are indeed only applications of these to particular purposes and occasions; as the Rule-of-three, or Golden Rule, or Rule of Proportion; also the Rules of Fellowship, Interest, Exchanges, Position, Progressions, &c, &c. For which, see each article severally.
Rule-of-Three, or Rule of Proportion, commonly called the Golden Rule from its great use, is a Rule that teaches how to find a 4th proportional number to three others that are given.
As, if 3 degrees of the equator contain 208 miles, how many are contained in 360 degrees, or the whole circumference of the earth?
The Rule is this: State, or set the three given terms down in the form of the first three terms of a proportion, stating them proportionally, thus:
| deg. | mil. | deg. | miles. | |
| as | 3 : | 208 :: | 360 : | 24960 |
| 360 |
| 12480 |
| 624 |
| 3)74880 |
| 24960 |
This rule is often considered as of two kinds, viz. Direct, and Inverse.
Rule-of-Three Direct, is that in which more requires more, or less requires less. As in this; if 3 men mow 21 yards of grass in a certain time, how much will 6 men mow in the same time? Here more requires more, that is, 6 men, which are more than 3 men, will also perform more work, in the same time. Or if it were thus; if 6 men mow 42 yards, how much will 3 men mow in the same time? here then less requires less, or 3 men will perform proportionally less work, in the same time. In both these cases then, the Rule, or the proportion, is direct; and the stating must be thus, as 3 : 21 :: 6 : 42, or thus, as 6 : 42 :: 3 : 21.
Rule-of-Three Inverse, is when more requires less, or less requires more. As in this; if 3 men mow a certain quantity of grass in 14 hours, in how many hours will 6 men mow the like quantity? Here it is evident that 6 men, being more than 3, will perform the same work in less time, or fewer hours; hence then more requires less, and the Rule or question is inverse, and must be stated by making the number of men change places, thus, as 6 : 14 :: 3 : 7 hours, the time in which 6 men will perform the work; still multiplying the 2d and 3d terms together, and dividing by the 1st.
For various abbreviations, and other particulars re- | lating to these Rules, see any of the common books of arithmetic.
Rule-of-Five, or Compound Rule-of-Three, is where two Rules-of-three are required to be wrought, or to be combined together, to find out the number sought.
This Rule may be performed, either by working the two statings or proportions separately, making the result or 4th term of the 1st operation to be the 2d term of the last proportion; or else by reducing the two statings into one, by multiplying the two first terms together, and the two third terms together, and using the products as the 1st and 3d terms of the compound stating. As, if the question be this: If 100l. in 2 years yield 9l. interest, how much will 500l. yield in 6 years. Here, the two statings are,
| 100 | }: 9 ::{ | 500 |
| 2 | 6 |
Then, to work the two statings separately,
| as | 100 : | 9 :: | 500 : | 45l. |
| and | 2 : | 45 :: | 6 : | 135l. |
| 100 | 500 | |
| 2 | 6 | |
| 200 | : 9 :: 3000 | : 135l. the answer. |
| 2.00) 270.00 | (135l. |
See the books of arithmetic for more particulars.
Central Rule. See Central Rule.
Parallel Ruler. See Parallel Ruler.
