INSTRUCTIONS

FOR THE

ENGINEERS' & MECHANICS'

IMPROVED

SLIDE RULE,

With a description of the several lines upon it, and plain
directions how to find any number thereon;
together with the application of those Lines to

Division, the Rule of Three, &c. &c.; the

Superfices and Solids is likewise made perfectly easy;
it is also particularly useful in Weighing all kinds
of Metals and other bodies; to which are added
a complete

TABLE OF GAUGE POINTS,

For Weighing the different Articles contained therein;

ALSO A TABLE FOR THE WEIGHT OF CAST IRON PIPES, &C.

MANCHESTER:

ABEL HEYWOOD, 58, OLDHAM-STREET.

PRINTED BY G. BOOTH, HYDE, AND SOLD BY ALL BOOKSELLERS.

1845.

INSTRUCTIONS, &C.

DESCRIPTION OF THE RULE.

This instrument is made of good box or ivory; it has a joint in the middle, and is 24 inches long when opened out; one face of the rule is marked with inches and a drawing scale, which answers every purpose of a common two foot rule. One of the edges is marked with the decimals of a foot, and the other with inches divided into 10ths and 12ths. On the other face of the rule are the lines of numbers, and a table of gauge points for square, cylinder and globe; to which is now added a table of gauge points for pumping engines, another for regular polygons, and a third for the properties of the circle, squares, and triangle.

EXPLANATION OF THE LINES OF NUMBERS.

There are four lines marked A, B, C, D, the first three lines, A, B, C, are all exactly alike, consisting of two radiuses, and numbered from the left to the right hand with the figures 1, 2, 3, 4, 5, 6, 7, 8, 9,—1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The line D is a single radius, double the length of the other, and numbered from left to right with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; the lines B and C slide between the other two, and by this operation are all questions answered upon the rule, the same as by figures.

OF NUMERATION.

Numeratiou is the first thing to be learned upon this instrument, for when once that is perfectly understood,

every thing else will be rendered quite easy; in order that this may be made as plain as possible, let it be first observed that the numbers and divisions upon the rule are all arbitrary, and the value set upon them must be such as the nature of the case requires, which will be easily discovered as soon as any question is proposed.

The figures 1, 2, 3, 4, and so on to 10, are called primes; and the long divisions, tenths; and these again are subdivided into hundredth and thousandth part of unity.

If the 1 (next the joint) represents one tenth, then will the middle 1 be one unit or one whole number, and the other figures towards the right hand are likewise whole numbers, from the middle I to 10 at the end; but if the first 1 represents one unit, then the middle 1 will be 10, and the 10 at the far end, 100;-if the first 1 is called 10, the middle 1 will be called 100, and that at the end 1000-always increasing in ten-fold proportion, according to the value you set upon the first 1: the figures between them must be called after the same manner; so that if 1 at the beginning is one tenth, 2 will be two tenths, and the next 2 towards the right hand 2 units, but if 1 at the beginning is 1 unit, then 2 will be 2 units, and the other 2 will be 20; if the first 1 is called 10, then 2 will be 20, and the next 2 is 200; they may be best represented in the following order:-1 tenth, 2 tenths, 3 tenths, 4 tenths, 5 tenths, 6 tenths, 7 tenths, 8 tenths, 9 tenths; unity, or 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; the above is the least that the primes are in general valued at; when a higher value is set on them, they will stand thus, beginning next the joint, and say 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. By repeating them again, it would still increase their value ten times; but this at present will be unnecessary, it being designed to make this instruction as short but plain as possible, I shall therefore proceed to show a few examples for the learner's practice.

I.-Let it be required to find 17 on the top line, or line A, this being the line on which all the different gauge points in the table below the lines of numbers are to be found. Look for the first or the middle 1 [it matters not which] and call it 10, then count 7 of the long divisions towards 2; this will be 17, the number sought for; it is also 170, 1,700, 17,000.

II. Let the number 2,450 be found. Look for 2 and call it 2000, and 4 of the longest divisions towards 3 are 400, and one short division is 50, which altogether make 2,450, the answer; they likewise stand for 245, 24,5, or 2,45.

III. Let the following numbers be sought: 105, 205, 705. Those and all other such like numbers that have no figures in the place of tens, are to be found in the following manner:-Look for 1 and call it 100, then 2 of the short divisions you call 2 each, and half of another short division is 1, all of which make 105, the first number required. To find the second number you look for 2 and call it 200, and the first short division is 5; this will be the answer to the second number. Proceed in the same manner for the last number: find 7 and call it 700, and half of the first division is 5, the number sought.

The best way of pointing out any number required, is to slide the 1 upon the line B gently along until you bring it opposite the number you look for upon the line A.

From what has been said, the learner will not find it difficult to point out any number in the table of gauge points on the rule.

MULTIPLICATION.

In this rule you have three numbers given to find a fourth, always calling unity one of the three. Whether they be whole numbers, mixed numbers, or decimal fractions, the proportion is: as unity on A is to the multiplier on B, so is the multiplicand on A to the product on B.