of the rope when extended in a right-line, being equal to the circumference of its centre, when formed into a circle, in taking the girt of the tree. Ans. The true girt is 41.858364 inches, and the solidity 21.293157 feet; hence appears the propriety of girting trees with a small string, or with measuring-tape. 25. A leaden pipe 12 feet in length, weighs 100 lb. avoirdupois; required the thickness of the lead, the diameter of the bore being 2 inches. Ans. .2408 of an inch. 26. Required the thickness of the shell of a hollów sphere of copper, weighing 3 lb. avoirdupois, so that being put into common water, it may be just immersed by its own weight. Ans. .1042 of an inch: 27. The bore of a syringe which holds one pint, wine measure, is 1 inch in diameter; what is the length of the piston ? Ans. 16.33986 inches. 28. If a balloon contains 1000 yards of silk, of a yard wide; what is its diameter, admitting it to be a perfect sphere? Ans. 15.45095 yards. 29. A hollow sphere of ebony, whose diameter is 18 inches, is found to sink just 6 inches in sea-water; required the thickness of the shell. Ans. .647333 of an inch. 30. One ev❜ning I chanc'd with a tinker to sit, Now, to save him from ruin, I pray find him out Note. This ingenious question was, 1 believe, first proposed in the Ladies' Diary, for the year 1711. PART V. ARTIFICERS' WORK. The Artificers whose works are here to be treated of, are Bricklayers, Masons, Carpenters and Joiners, Slaters and Tilers, Plasterers, Painters, Glaziers, Plumbers, and Pavers. THE Contents of the works of all artificers, whether superficial or solid, must be found by the Rules given in the foregoing Problems, for the respective figures. This ought to be particularly attended to in taking the dimensions. The following Rule, which should be got by heart, is better adapted for Cross Multiplication, than any other I have seen; and as 12 fourths make 1 third, 12 thirds 1 second, 12 seconds 1 inch, and 12 inches 1 foot; these numbers, when not too large, may be more expeditiously turned into the higher denominations by the Pence Table, than by dividing them by 12. RULE. Feet multiplied into feet give feet. Feet multiplied into inches give inches. Feet multiplied into seconds give seconds. Inches multiplied into inches give seconds. Inches multiplied into seconds give thirds. Seconds multiplied into seconds give fourths. The measures chiefly used by Artificers, are contained in the following Table: Note. As the number 2724 is rather troublesome to divide by, it is customary, in practice, to divide by 272, omitting the ; but if this be not thought correct enough, convert the into decimals; or reduce the divisor to the impro 1089 4 per fraction --, and multiply the content in feet, by 4, and divide the product by 1089; and the quotient will be the number of rods sought. Divide the remainder, if any, by 4, and the quotient will be feet. The rod of 2724 square feet, is the square of 16 feet; but in some places the customary rod is the square of 18 feet; viz. 324 square feet. BRICKLAYERS' WORK. Bricklayers generally compute their work by the rod of 2724 square feet, and at the rate of a brick and a half thick; consequently if a wall be more or less in thickness, than this standard, it must be reduced to it, in the following manner: Multiply the superficial content of the wall, in feet, by the number of half bricks which it is in thickness; and of the product will be 13 the content sought. In some places, however, brick-work is measured by the rood of 63 square feet; that is, 21 feet in length, and 3 feet high; and then no regard is paid to the thickness of the wall, in measuring; as the price of the workmanship is regulated according to the thickness. Note 1. In taking the dimensions of a building, measure half round the outside and half round the inside; and the sum of these two will be the true compass of the building. Or, 4 times the thickness of the wall taken from the whole compass, on the outside, or added to the whole compass within, will give the true compass; which multiply by the height, and the product will be the superficial content of the walls; and if the breadth of the building be multiplied by the height of one gable-end, you will obtain the content of both the gable-ends. In some places it is customary to take the whole compass, on the outside, in order to make an allowance to the workmen, for the trouble of turning the corners; but this should not be done for both workmanship and materials' except specified iu the agreement; but for workmanship only. If the workmen be allowed so much per yard, lineal measure, for the corners, which is the custom in some places, the true compass of the building ought then to be taken for both workmanship and materials. 2 When the height of a building is unequal, measure a piece round the bottom, so as to make the upper part all of one height; and in doing this, holes must be dug in the ground, to enable you to take your dimensions to the foundation. Several altitudes of the bottom part must be taken; and their sum divided by their number, may be considered as a mean altitude. 3. In most buildings of two or more stories, the walls decrease in thickness, towards the top; and this diminution generally consists of half a brick, in each story. The thickness is set off on the inside, and commonly in a place where the floor will be laid; a contrivance by which the set-off is concealed. The stories that are of different thicknesses must be measured separately; except, by agreement, one price be allowed for the whole, which is not often the case. When the walls of a building are of different thicknesses, the upper rooms are broader than the lower ones; hence a set-off may be discovered, although the walls be plastered and the floors laid. 4. Doors and windows must always be deducted for materials, if there be no stipulation to the contrary; but for workmanship, these deductions are seldom made, except the doors and windows be very numerous, as in work-shops, &c.; or larger than the usual size, as in shop-fronts, &c. In these cases the Surveyor must exercise a discretionary judgment; for the windows of buildings vary so much in size and number, that no special Rule can be given. 5. If a chimney stand by itself, without any party-wall being joined to it, take the girt, in the middle, for the length, and the height of the story for the breadth; but if the chimney-back be a parts-wall, and the wall be measured by itself, you must girt the chimney round, to the wall, on each side, for the length; and take the breadth the same as before. When a chimncy is wrought upright from the mantle tree to the ceiling, the thickness of the whole, is generally considered the same as that of the jambs, and no deduction is ever made for the vacancy between the floor and the mantle-tree, because of the gathering of the breast and wings, to make room for the hearth in the next story. Chimney-Shafts above the roof, are measured by girting them, in the middle, for the length, and taking the height for the breadth. Their thickness is generally accounted half a brick more than it is in reality, in consideration of the plastering and scaffolding. 6. In some places double measure, for workmanship, is allowed for chimneys, in consequence of their being more troublesome to be made than the other parts of the building; and in others they are done at so much per yard, lineal measure, or at so much per piece. It is also customary, in most places, for bricklayers, to charge so much extra for every arch they turn; and this charge is regulated by the size of the arch. They also make a difference in the price between an inside and an outside arch, charging less for the former than the latter. EXAMPLES. 1. The length of a wall is 86 feet 9 inches, its height 12 feet 6 inches, and its thickness 3 bricks; how many standard rods of brick-work does it contain? By Decimals. 272)2168.750(7 rods, 264 ft. 9 in. the answer. 272)2168 9 0(7 rods, 264 ft. 9 in. the answer. 1904 264 remainder. |