In a field I took two ftations P and Q, at the distance of 10 chains from each other :

From a ftation within a field of five fides I mea fured the distances to the feveral corners, beginning with that on the weft, and measuring round towards the north, viz. 1ft distance 7345 lin's, the 2d = 5980, the 3d 6495, the 4th 6015, and the 5th

7050; alfo the angles formed by thefe diftances in the fame order were 714, 55, 494, and 811, degrees. What is the area? Anf. 979ac. 2r. 35.921p.

From a place o, near the middle of a field ABCDEF, from which I could fee all the angles, I measured the distances to the feveral corners, and obferved the quantities of the angles formed at o by thofe diftances, as below.

2

Distances

Having made choice of a station within a piece of land, I measured from thence the feveral bearings and distances of the corners as below: Required the

TH

OF CASK GAUGING.

HE meaning of the word Gauging is restricted to the measuring of cafks, and other things falling under the cognizance of the officers of the

002

excife;

excife; and it has received its name from a gauge or rod used by the practitioners of the art.

The bufinefs being performed, or the calculations made, commonly by means of the inftruments, called the gauging or diagonal rod, and the fliding rule or gauging rule, it will be neceflary to treat of these inftruments, which I fhall do as below.

CHAPTER I.

The Defcription and Ufe of the Sliding Rule. This is a fquare rule, having confequently four fides or faces, three of which are furnifhed with fliding picces running in grooves. The lines upon them are moftly logarithmic ones, or diftances which are proportional to the logarithms of the numbers placed at the ends of them; which kind of lines were placed upon rules, by Mr. Edmund Gunter, for expeditioufly performing arithmetical operations; in which bufinefs he used a pair of compatles for taking the feveral logarithmic distances: but instead of the compaffes, fliding pieces were added, by Mr. Thomas Everard, as being more convenient and certain in practice.

Upon the first face are three lines, namely, two marked A, B, for multiplying and dividing; and the third, MD, for malt depth, because it ferves to gauge malt. The middle one в is upon the flider, and is a kind of double line, being marked at both the edges of the flider, for applying it to both the lines A and MD. Thefe three lincs are all of the fame radius, or distance from 1 to 10, each containing twice the length of the radius. A and B are placed and numbered exactly alike, each beginning at 1, which may be either 1, or 10, or 100, &c, or '1, or •01, or oo1, &c; but whatever it is, the middle divifion 10, will be 10 times as much,

much, and the last divifion 100 times as much. But I on the line MD is oppofite 215, or more exactly 21504 on the other lines, which number 2150.4 denotes the cubic inches in a malt bufhel, and its divifions numbered retrograde to those of A and B. Upon these two lines are alfo feveral other marks and letters: thus, on the line A are MB, for malt bushel, at the number 21504; and A for ale, at 282, the cubic inches in an ale gallon; and upon the line в is w, for wine, at 231, the cubic inches in a wine gallon ; alfo si, for fquare infcribed, at 707, the fide of a fquare infcribed in a circle whofe diameter is ; se, for fquare equal, at 886, the fide of a fquare which is equal to the fame circle; and c for circumference, at 3.1416, the circumference of the fame circle.

Upon the fecond face, or that oppofite the firft, are a flider and four lines, marked D, C, D, E, at one end, and root, fquare, root, cube, at the other; the lines c and E containing refpectively the fquares and cubes of the oppofite numbers on the lines D, D ; the radius of D being double to that of A, B, C, and triple to that of E fo that whatever the first on D denotes, the firft on c is the fquare of it, and the first on E the cube of it,; fo if D begin with 1, c and E will begin with 1; but if D begin with 10, c will begin with 100, and E with 1000; and fo on. Upon the line c are marked oc at 0796, for the area of the circle whose circumference is 1; and od at 7854 for the area of the circle whole diameter is 1. Alfo, upon the line D are wG, for wine gauge, at 17.15; and AG for ale gauge, at 18.95; and MR, for malt round, at 5232; thefe three being the gauge points for round or circular meafure, and are found by dividing the fquare roots of 231, 282, and 2150.4 by the fquare root of 7854. allo мs, for malt fquare, are marked at 46.37, the malt gauge point for fquare measure being the fquare root of 2150*4.

MS,

Upon the third face are three lines, one upon a flider inarked N; and two on the ftock, marked ss and SL, for fegment ftanding and fegment lying, which ferve for ullaging standing and lying cafks.

And upon the fourth, or oppofite face, are a fcale of inches, and three other fcales, marked spheroid or ift variety, 2d variety, 3d variety; the fcale for the 4th, or conic variety, being on the infide of the flider in the third face. The use of these lines is to find the mean diameters of casks.

Befides all thofe lines, there are two others on the infides of the two first fliders, being continued from the one flider to the other. The one of thefe is a fcale of inches, from 12 to 36; and the other is a fcale of ale gallons between the correfponding numbers 435 and 3.61; which form a table to fhew, in ale gallons, the contents of all cylinders whofe diameters are from 12 to 36 inches, their common altitude being 1 inch.

As the fliding rule is for performing, very expeditiously, any operations of multiplication, divifion, and extraction of roots, which may be required by any precept propofed in words, &c; fo the manner of making thefe operations will appear in the following problems.

To find the Product of Two Given Numbers, by the Sliding Rule.

RULE. To either of the given numbers on A fet I on B, then against the other number on в is the product on A.

EXAMPLE 1. Required the product of 12 and 25. By placing 1 on B under 12 on A, above 25 on B ftands 300 on A; which is the product required.

NOTE. When the Ion B has been fet to the one

factor