of three and five inches diameter, and weight of each sort to be the same; required the number there will be of each.

1st. Half of 11200 is 560 pounds.

2. Cube of 3 inches, or cube of a foot?'. Then, as 1 (cube of 1 foot): 243 (the weight of a 1 foot ball) 3,79, weight of a 3 inch

iron shot.

N. B. In this proportion 64 divides 243 on account of the fraction.

Now 5 inches of a foot, its cube. Therefore, as 1 243:25: 17,67, weight of an iron 5 inch shot.

1:

Dividing 5600 by 3,79 gives 1504, the number required of the 3 inch shot.

Dividing 5600 by 17,57 gives 313, the required number of the 5 inch shot.

A table of specific gravities and weights of bodies is added, or not, at the pleasure of the purchaser. It is not essential to the general uses of the callipers, although many curious and useful problems relative to the weights and dimensions of bodies may -be obtained from it in the most accurate manner.*

The quantity of lines placed upon the callipers may be increased or arranged at pleasure. The following 19 were the greatest number that I ever knew of being placed upon them.

1. The measures of convex diameters in inches. 2. The measures of concave diameters in inches. 3. The weights of iron shot from given diameters. 4. The weight of iron shot proper to given gun bores. 5. The degrees of a semi-circle. 6. The proportion of Troy and Avoirdupois weight. 7. The proportion of English and French feet and pounds. 8. Factors useful in circular and spherical figures. 9. Tables of the specific gravity and weights

* See Mr. Adams's Lectures, five vols. 8vo. a new and improved edition of which is now in the press, and under my correction and augmentation.

of bodies. 10. Tables of the quantity of powder necessary for proof and service of brass and iron guns. 11. Rules for computing the number of shot or shells in a finished pile. 12. Rules concerning the fall of heavy bodies. 13. Rules for the raising of water. 14. The rules for shooting with cannon. 15. A line of inches. 16. Logarithmic scales of numbers, sines, versed sines, and tangents. 17. A sectoral line of equal parts, or the line of lines. 18. A sectoral line of plans or superficies. 19. A sectoral line of solids.

or mortars.

Gunner's Quadrant.-Fig. 8, plate 33, is a representation of a quadrant used for elevating a cannon, or mortar, in the most expeditious manner. The bar A, is placed in at the mouth; the index B, brought to the arc till the bubble of the spirit level settles in the middle. The angle is then read off to minutes upon the arc by the nonius at C.

Gunner's Perpendicular.-Fig. 9, plate 33, is a representation of a small level and perpendicular. It is used to find the centre line of a piece in the operation of pointing it to an object, or to mark the point for a breech hole, &c. The spirit level A, determines the position on the gun, and the spring index point B, serves to mark the necessary points upon the surface to obtain the line by.

Shot Gauges.-Are a set of brass rings, all connected to one centre, with holes suitable to the dia✩ meters, or pounders of iron shot, from four to 42 pounders; being all respectively marked, and are too evident in their uses to need either a discription or figure here.

OF

THE SLIDING RULE,

COMMONLY CALLED

THE CARPENTER'S RULE,

AND

THE MENSURATION OF TIMBER,

BOTH CUT AND STANDING,

THE mensuration of timber may be considered as an indispensable part of knowledge, with the art of surveying, and I judge, that including it in this Appendix, will be considered useful to many of our uninformed readers, who may not have consulted any of the established works on mensuration. Coggleshall's or the Carpenter's Sliding Rule, is the original, simple, and now most commonly used instrument for taking dimensions and casting up, or instrumentally finding the contents of timber. It is generally made of box wood, one foot in length when folded tegether, by means of a middle joint, and two feet when extended. In the following description I suppose the reader to have the rule placed before him, under his inspection. On one side of the rule next to the edge, is divided inches and eights to take dimensions by, and within on the same side are several plotting scales divided by diagonal lines into 12th parts: they consist generally of the inch, 4, 4, and 4 inch, divided into the above 12ths for the conveniently planning of dimensions, that are previously taken in feet and inches.

The outer edge of the rule is usually divided into the centesimals of a foot, or the decimal of a foot into 10 parts, so as to give any dimensions taken in feet, 10ths and 100dths of a foot; this will be found the readiest method by persons acquainted with decimal arithmetic.

On the other side of the rule are four logarithmic lines of numbers marked at one end by the letters A. B. C. D: the two middle ones B and C being on the slider which is slid in a groove made for the purpose, and the other two on the rule. The figures or numbers on the slide being placed between the two lines serve of course for both. The three lines A, B, C, are called double lines, because the figures from 1 to 10 are contained twice in the length of the slide, and the other lowest line D, a single line procceding from 4 to 40, and is called the Girt Line, from its utility in computing the contents of trees and timber.

The use of the double lines A and B is for working proportions, and finding the areas of plane figures, and the use of the girt line D, and the other double line C, is for measuring solids. On the girt line are marks at 17.15, lettered W G, (wine gallons) and at 18.95 A G (ale gallons) which are wine and ale gauge points to this instrument, to answer the principal purpose of a gauging rule.

On the same side of the rule is placed a table of the amount of timber per load of fifty cubic feet at the price of 6d. per foot, to 24 pence. At 6d. per foot, it will appear to be 11. 5s.; at 9d., 11. 17s. 6d. &c. Other scales and tables are sometimes substituted for these, as a table of board measures, one of timber, measure, a line shewing for what length of any breadth will make a foot square, also a line shewing what length for any thickness will make a solid foot; the former line serving to complete the table of board measure, and the latter the table of timber

measure.

The method of notation on the rule is very simple, the figures in order, are numbered from the left hand towards the right. When 1 at the beginning is accounted 1, then 1 in the middle will be 10 and the one at the end 100; and when 1 at the beginning is accounted 10, then one in the middle is 100, and the 10 at the end 1000, and so on. And all the smaller divisions and spaces are of course altered in your mind proportionally.

When the learner has made himself familiar with the notation, he will be surprized to find with what dispatch and accuracy he will be able to work the following problems, and much less liable to errors, than by computing with the pen. By a foot slide a solution to about the 200dth part of the whole may be relied on.

PROBLEM 1. To multiply two numbers together, as 16 and 19. Set 1 on B to the multiplier 16 on A, then against the multiplicand 19 on B will be the required product 304 on A. 2. To find the product of 35 and 19. Set 1 on B to the multiplicand 35 on A, then because 19 on B runs beyond the end of the line, seek it on the other radius, or other preceding part of the line, which in value will be 1.9 or th part, so that against 1.9 on B will be found 66,5 on A. This, therefore, multiplied again by 10, which is done by taking away only the decimal point, gives the product 665. In like manner the product of 270 by 54 will be found

to be 14580.

PROBLEM 2.

quo

To divide one number by another as 480 by 12. Set the divisor 12 on A, to 1 on B, then against the dividend 480 on A, will be the tient 40 on B. 2. To divide 7680 by 24. Let the divisor 24 on A be set to 1 on B, then because 7680 is not contained on A, the tenth 7680 on A must be sought for, and against it on B will be found the quotient 32, which increased ten times for the above reason will give 320 the required quo