RULE, Coggeshall's sliding, is chiefly used for measuring the superficies and so lidity of timber, &c. It consists of two rulers, each a foot long, one of which slides in a groove made along the middle of the other.
On the sliding side of the rule are four Ines of numbers, three whereof are dou ble ; that is, are lines to two radiuses ; and one, a single broken line of numbers the three first, marked A, B, C, are figured 1, 2, 3, &c. to 9 ; then 1, 2, 3, &c. to 10. The single line, called the girt-line, and marked D, whose radius is equal to the two radiuses of any of the other lines, is broke for the easier measurement of tim ber, and figured 4, 5, 6, 7, 8, 9, 10, 20, 30, &c. From 4 to 5 it is divided into ten parts, and each tenth subdivided into 2, and so on, from 5 to 6, &c. On the hack side of the rule are, 1. A line of inch measure, from 1 to 12; each inch being divided and subdivided. 2. A line of foot measure, consisting of one foot, divid ed into 100 equal parts, and figured 10, 20, 30, &c. The back part of the sliding piece is divided into inches, halves, &c. and figured from 12 to 24; so that when drawn wholly out, there, may be a mea sure of two feet.
" Use of Coggeshall's Rule for measur ing plane superficies." 1. To measure a square : suppose, for instance, each of the sides 5 feet ; set 1 on the line B, to 5 on the line A r then against 5 on the line B is 25 feet, the content of the square on the fine A. 2. To measure .a long square.
Suppose the longest side 18 feet, ancitthe shortest 10; set 1 on the line B, to 10 on the line A ; then against 18 feet, on the line B, is 189 feet, the contents on the line A. 3. To measure a rhombus. Sup pose the side 12 feet, and the length of a perpendicular let fall from one of the ob tuse angles to the opposite side, 9 feet ; set 1 on the line I+, 12, the length of the side on the line A: then against 9, the length of the perpendicular on the line B, is 108 feet, the content. 4. To mea sure a triangle. Suppose the base 7 feet, and the length of the perpendicular let fall from the opposite angle to the base 4 feet ; set 1 on the line B, to 7 on the line A then against half the perpendicular, which is 2 on the line B, is 14 on the lino A, for the content of the triangle. 5. To find the content of a circle, its diameter being given. Suppose the diameter 3.5 feet ; set 11 on the girt line D, to 95 on the line C; then against 3.5 feet on D, is 9.6 on C, which is the content of the cir cle in feet 6. To find the content of an oval or ellipsis. Suppose the longest di ameter 9 feet, and the shortest 4. Find a mean proportional between the two, by setting the greater 9 on the girt line, to 9 on the line C; then against the less num ber 4 on the line is C 6, the mean propor tional sought. This done, find the con tent of a circle, whose diameter is 6 feet ; this; when found, by the last article, will be equal to the content of the ellipsis sought.
" Use of Coggeshall's Rule in measur ing timber." 1°. To measure timber the usual way. Take the length in feet, half feet, and, if required, quarters ; then measure half way back again ; then girt. the tree with a small cord or line ; double this line twice very evenly, and measure this fourth part of the girt or perimeter. in inches, halves, and quarters. The di mensions thus taken, the timber is to be measured as if square, and the fourth of the girt taken for the side of the square, thus ; set 12 on the girt line I), to the length in feet on the line C ; then against the side of the square, on the girt line D, taken in inches, you have, on the line C, the content of the tree in feet. For an instance : suppose the girt of a tree, in the middle, be 60 inches, and the length 30 feet, to find the content, set 12 on the girt-line I), and SO feet on the line C ; then against 15, one fourth of 60, on the girt.line D, is 46.8 feet, the content on the line C. If the length should be 9 inches, and the quarter of the girt 35 inches ; here, as the length is beneath foot, measure it on the line of sure , and see what decimal part of a foot i it makes, which you will find .75. Set 12,
therefore, on the girt line, to 75 on the first radius of the line C, and against 35 1 on the girt-line is 64 feet on C, for the content. 2'. To measure round timber the true way. The former method, though that generally in use, is not quite ! just. To measure timber accurately, in stead of the point 12 on the girt-line, use another, viz 10.635; at which there should be placed a centre-pin. This 10.635 is the side of a square equal to a circle, whose diameter is 12 inches. For an instance : suppose the length 15 feet, and i of the girt 42 inches, set the point i 10.635 to 15, the length ; dien against 42 on the girt-line is 233 feet for the con tent sought ; whereas by the common way, there arises only 184 feet. In effect, the common measure is only to the true measure, as 11 to 14. 3°. To measure a cube. Suppose the sides to be 6 feet each ; set 12 on the girt.line D, to 6 on C; then against 72 inches (the inches 6 feet) on the girt.line, is 216 feet on C, which is the content required. 4°. To measure unequally squared timber ; that is, where the breadth and depth are not equal. Measure the length of the piece, and the depth (at the end) in inches : then find a mean proportional between the breadth 1 and depth of the piece. This mean pro portional is the side of a square, equal to . i the end of the piece ; which found, the piece may be measured as square timber. For an instance : let the length of the piece of timber be 13 feet, the breadth 23 inches, and the depth 13 inches ; set 23 on the girt-line I), to 23 on C ; then against 13 on C is 17.35 on the girt-line D, fbr the mean proportional. Again, setting 12 on the girt-line D, to 13 feet, the length of the line C ; against 17.35 on the girt-line is 27 feet, the content. 5°. To measure taper timber. The length being measured in feet, note one-third of it ; which is found thus : set 3 on the line A, to the length on the line B ; then against 1 on A is the third part on B: then, if the solid be round, measure the diameter at each end in inches, and sub tract the less diameter from the greater ; add half the difference to the less diame ter ; the sum is the diameter in the mid dle of the piece. Then set 13.54 on the girt to the length of the line C, and against the,diameter in the middle on the girt-line is a fburth number on the line ? C. Again, set 13.54 on the girt-line to ? ,the third part of the length on the line C; then against half the difference on the girt-line is another fourth number on the line C ; these two fourth numbers, added together, give the content. For an in stance : let the length be 27 feet (one third whereof is 9) the greater diameter 22 inches, and the lesser 18 ; the slim of the two will be 40, their difference 4, and half the difference 2, which, added to the less diameter, gives 20 inches for the di ameter in the middle of the piece. Now set 13.54 on the girt-line to 27 on the line C, and against 20 on D is 58.9 feet. Again, set 13.44 of the girt-line to 9 on the line C; and against 2 on the girt-line (represented by 20) is .196 parts ; there fore, by adding 58.9 feet to .196 feet, the sum is 59.096 feet, the content.
If the timber be square, and have the same dimensions : that it, the length 27 feet, the side of the greater end 22 inch es, and that of the lesser 18 inches ; to find the content, set 12 on the girt-line to 27, the length on the line C, and against 20 inches, the side of the mean square on the girt line is 75.4 feet. Again, set 12 on the girt-line to 9 feet, one third of the length, on the line C, and against 2 inch es, half the difference of the sides of the squares of the ends on the girt-hue is .25 parts of a foot ; both together make 75.65 feet, the content of the solid.
The girt or circumference of a tree, or round piece of timber, given ; to find the side of the square within, or the number of inches of a side, when the round tim ber is squared. Set 10 on A to 9 on B, then against the girt on A are the inches for the side of a square on the line B.
RUM, a species of vinous spirit, dis tilled from sugar canes.