No. Square. Cube. Square Root. Cube Root. No. Square. Cube. Square Root, Cube Root. 757 573049 433798093 27.5136330 9·113781 820 672400 551368000 28.6356421 9.359901 758 574564 43551 9512 27.5317998, 9·117798 821 674041 553387661 28 6530976,9-363704 759 576081 437245479 27 5499546 9.121801 | 822 675684 555412248 28-6705424 9-367505 760 577600 438976000 27·5680975 9·125805 823 677329 557441767 28-6879766 9.371302, 761,579121 440711081 27.5862284 9·129806 824 678976 559476224 28·7054002,9-375096 762 580644 442450728 27·6043475 9-133803 825 680625 561 51 5625 28-7228132 9-378887 763 582169 444194947 27·6224546 9-137797 826 682276 563559976 28-7402157 9.382675 764 583696 445943744 27·6405499 9-141788 827 683929 565609283 28.7576077 9.386460| 765 585225 447697125 27 ·6586334 9·145774 828 685584 567663552 28 7749891 9.390241 766 586756 449455096 27 6767050 9-149757 829 687241 569722789 28-79236019-394020 767 588289 451217663 27·6947648 9.153737 830 688900 571787000 28-8097206 9.397796 768 589824 452984832 27 7128129 9.157713 831 690561 573856191 28-8270706 9-401 569 769 591361 454756609 27 7308492 9.161686 832 692224 575930368 28-8444102 9.405338 770 592900 456533000 27·7488739 9.165656 833 693889 578009537 28.8617394 9.409105 771 594441 458314011 27·7668868 9.169622 834 695556 580093704 28-8790582 9-412869 772 595984 460099648 277848880 9.173585 835 697225 582182875 28 8963666 9.416630 773 597529 461 889917 27 8028775 9.177544 836 698896 584277056 28.91366469-420387 774 599076 463684824 27·8208555 9-181 500 837 700569 586376253 28-9309523.9.424141 775 600625 465484375 27·8388218 9-185452 838 702244 588480472 28-9482297 9-427893 776 602176 467288576 27·8567766 9 189401 839 703921 590589719 28 9654967 9-431642 777 603729 469097433 27.8747197 9-193347 840 705600 592704000 28-9827535 9-435388 778 605284 470910952 27·8926514 9·197289 841 707281 594823321 29-0 9-439130 779 606841 472729139 27 9105715 9.201228 842 708964 596947688 29 0172363 9-442870 780 608400 474552000 27.9284801 9-205164 843 710649 599077107 29-0344623 9-446607 781 609961 476379541 27.9463772 9.209096 844 712336 601211584 29 0516781 9-450341 782 611524 478211768 27-9642629 9-213025 845 714025 603351125 29 0688837 9-454071 783 613089 480048687 27-9821372 9-216950 846 715717 605495736 29-0860791 9-457799 784 614656 481890304 28.0 9-220872 847 717409 607645423 29 1032644 9.461 524 785 616225 483736025 28 0178515 9-224791 848 719104 6098001 92 29·1204396 9-465247 786 617796 485587656 28-0356915 9-228706 849 720801 611960049 29·1376046 9-468966 787 619369 487443403 28-0535203 9-232618 850 722500 614125000 29 1547595 9-472682 788 620944 489303872 28 0713377 9-237527 851 724201 616295051 29 17190439-476395 789 622521 491169069 28 0891 438 9-240433 852 725904 61 8470208 29-1890390 9-480106 790 624100 493039000 28·1069386 9-244335 853 727609 620650477 29-2061637 9-483813 791 625681 494913671 28.1247222 9.248234 854 729316 622835864 29-2232784 9-487518 792 627264 496793088 28 1424946 9-252130 855 731025 625026375 29-2403830 9.491219 793 628849 498677257 28 1602557 9.256022 856 732736 627222016 29-2574777 9-494918 794 630436 500566184 28 1780056 9-259911 857 734449 629422793 29 2745623 9-498614 795 632025 502459875 28 1957444 9-263797 858 736164 631628712 29-29163709-502307 796 633616 504358336 28-2134720 9.267679 859 737881 633839779 29 308701 8,9-505998 797 635209 506261573 28-2311884 9.271559 860 739600 636056000 29 3257566 9.509685 798 636804 508169592 28-2488938 9.275435 861 741 321 638277381 29 342801 5.9.513369| 799,638401 510082399 28-2665881 9.279308 862 743044 640503928 29 3598365 9.517051 800 640000 51 2000000 28-2842712 9.283177 863 744769 642735647 29 3768616 9.520730 801 641601 513922401 28 301 9434 9.287044 864 746496 644972544 29 3938769 9-524406 802 643204 51 5849608 28-31 96045 9-290907 865 748225 647214625 29 4108823 9-528079 803 644809.517781627 28-3372546 9.294767 866 749956 649461896 29-4278779 9-581749 804 646416 51 9718464 28 3548938 9.298623 867 751689 651714363 29-4448637 9.535417 805 648025 5216601 25 28-3725219 9-302477 868 753424 653972032 29 461 8397 9-539081 806 649636.523606616 28-3901 391 9-306327 869 755161 656234909 29-4788059 9-542743 807 651249 525557943 28-4077454 9.310175 870 756900 658503000 29-4957624 9.546402 808 652864 527514112 28 4253408 9.314019 871 758641 660776311 29-5127091 9.550058 809 654481 529475129 28-4429253 9.317859 872 760384 663054848 29-5296461 9.553712 810 656100 531441000 28 4604989 9.321697 873 762129 665338617 29-5465734 9.557363 811 657721 533411731 28.4780617 9.325532 874 763876 667627624 29.5634910 9.561010 812 659344 535387328 28-4956137 9-329363 875 765625 669921875 29.5808989 9-564655 813.660969 537367797 28-5131549 9-333191 876 767376 672221376 29-5972972 9.568297 814 662596 5393531 44 28-5306852 9.337016 877 769129 6745261 33 29 61 41858 9.571987 815 664225 541313375 28.5482048 9:340838 878 770884676836152 29-6310648 9:575574 816 665856 543338496 28-5657137 9.344657 879 772641 6791 51 439 29-6479325 9.579208 817,667489 545338513 28-5832119 9.348473 880 774400'681472000 29-6647939 9-582839 818 669124 547343422 28 6006993 9.352285 881 776161,688797841 29-681 6442 9-586468 819 670761 549353259 28.6181760 9-356095882,777924,686128968 29-6984848 9.590098| No. Square. Cube. Square Root. Cube Root. No. Square. Cube. Square Root. Cube Root. 9.888767 9.892174 883 779689 688465387 29-71531 59 9-593716 942 887364 835896888 30 6920185 9.802803 884 781 456 690807104 29-7321375 9-597337 943 889249 838561807 30·7083051| 9·806271 885 783225 6931 54125 29-7489496 9-600954 944, 891136 841232384 30 7245830 9.809736 886 784996 695506456 29-7657521 9.604569 945 893025 843908625 30 7408523 9-813198 887 786769 697864103 29-7825452 9.608181 946 894916 846590536 30 7571130 9.816659 888 788544 700227072 29-7993289 9-611791 947 896809 849278123 30-7733651 9.820117 889 790321 702595369 29·8161030 9.61 5397 948 898704 851971392 30 7896086 9.823572 890 792100 704969000 29-8328678 9.61 9001 949 900601 854670349 30.8058436 9.827025 891 793881 707347971 29.8496231 9.622603 950 902500 857375000 30 8220700 9.830475 892 795664 709732288 29.8663690 9.626991 951 904401 860085351 30 8382879 9-833923 893 797449 712121957 29-8831056 9.629.97 952, 906304 862801 408 30 8544972 9.837369, 894 799236 71451 6984 29-8998328 9.633390 953 908209 865523177 30 8706981 9-840812) 895 801025,716917375 29 9165506 9.636981 954 910116 868250664 30.8868904 9.844253 896 802816 7193231 36 29.9332591 9640569 955 912025 870983875 30.9030743 9.847692 897 804609 721734273 29.9499583 9-644154 956 913936 873722816 30 9192497 9.851128 898 806404 724150792 29-9666481 9-647736 957 915849 876467493 30-9354166 9.854561, 899 808201 726572699 29 9833287 9 651316 958 917764 879217912 30-9515751 9.857992 900 810000 729000000 30.0 9.654893 959 919684 881974079 30.9677251 9.861421 901 811801 731 432701 30-0166620 9'658468 960 921600 884736000 30·9838668 9.864848 902 813604733870808 30 03331 48 9 662040 961 923521 887503681 31 0 9.868272 903 815409 73631 4327 300499584 9 665609 962 925444 890277128 31 0161248 9.871694| 904 817216 738763264 30 0665928 9 669176 963 927369 893056347 31 0322413 9.875113 905 819025 741217625 30-0832179 9.672740 964 929296 895841344 310483494 9.878530 906 820836 743677416 SO 0998339 9.676301 965 931225 898632125 31 0644491 9881945 907 822649 7461 42643 30 1164407 9-679860 966 933156 901428696 31·0805405 9.885357 '908 824464 748613312 30-1330383, 9·683416| 967 935089 904231063 31 0966236 909 826281 751089429 30 1496269 9-686970 968 937024 907039232 31·1126984 910 828100 753571000 30-1662063 9.690521 969 938961 909853209 311287648 9.895580 911 829921 756058031 30 1827765 9 694069 970 940900 912673000 31·1448230 9.898983 912 831744 758550528 30·1993377 9-697615 971 942841 915498611 31 1608729 9.902383 913 833569 761048497 30-2158899 9-701158 972 944784 918330048 31-1769145 9.905781 914 835296 763551944 30-2324329 9.704698 973 946729 921167317 31·1929479 9.909177 915 837225 766060875 30-2489669 9.708236 974 948676 924010424 31 -2089731 9.912571 916 839056,768575296 30 2654919 9.711772 975 950625 926859375 31 2249900 9.915962 917 840889 771095213 30-2820079 9.715305 929714176 31 2409987 9.919351 918,842724 773620632 30-29851 48 9.718835 932574833 31 2569992 9.922738 919 844561 776151559 30 31 501 28,9 722363 935441352 31 2729915 9.926122| '920 846400 778688000 30-331 501 8 9.725888 938313739 31 -2889757 9.929504 1921 848241 781229961|30-3479818 9.729410 941192001 31 ·3049517 9-932883) 922 850084 783777448 30-3644529 9 732930 944076141 31-3209195 9.936261 923 851929 786330467 30-3809151 9-736448 946966168 313368792 9.939636 924 853776.788889024 30.3973683 9.739963 983 966289 949862087 31 ·3528308 9.943009 925 855625 791453125 30-4138127 9.743475 984 968256 952763904 31 3687743 9.940379 926 857476 794022776 30-4302481 9.746985 985 970225 955671625 313847097 9.949747 927 859329 796597983 30-4466747 9.750493 986 972196 958585256 31-4006369 9.953113 528 861184 7991 78752 30·4630924 9.753998 987 974169 961504803 31·4165561 929 863041 801765089 30-4795013 9.757500 988 976144 964430272 31 4324673 930 864900 804357000 30-4959014 9.761000 989 978121 967361669 31·4483704 931-866761 806954491 30·5122926 9.764497 990 980100 970299000 31·4642654 9·966554 932 868624 809557568 20:5286750 9.767992 991 982081 973242271 31 4801525 9.969909 933 870489 812166237 30-5450487 9-771484 992 984064 976191488 314960315 9.973262 (934 872356 814780504 30.561 41 36 9-774974 993, 986049 979146657 31 5119025 9.976612 935 874225 817400375 30.5777697 9.778461 994 988036 982107784 31 5277655 9.979959 936 876096 820025856 30.5941171 9-782946 995 990025 985074875 31.5436206 9.983304 937 877969 822656953 30·6104557 9·785428 996 992016 988047936 31 5594677 9.986648 988 879844 825293672 30-6267857 9-788908 997 991009 991026973 31 5753068 9.989990 1939 881721 827936019 30 6431069 9.792386 998 996004 994011992 31-5911380 9-993328 940 883600 830584000 30-6594194 9.795861 999 998001 997002999 31 6069613 9.996665 941 885481 833237621 30-6757233 9-799333 1000 1000000 1000000000 31·6227767 100 976 952576 980 960400 9.956477 9.959839 9.963198 2297h. A power is that number which is obtained by multiplying a number several times by itself. A square is the number multiplied by itself; a cube by multiplying it twice by itself. The square is called the second power; the cube is called the third power; when multiplied again by itself it becomes the fourth power, which is commonly called the bi-quadrate; and so on : 2297i. We shall now at once proceed to the general principles on which the measurement and estimation of work in the several artificers' departments are conducted. = 2298. DIGGING is performed by the solid yard of twenty-seven cubic feet (that is, 3 feet x 3 feet x 3 feet 27 feet). Where the ground is soft in consistence, and nothing more is necessary beyond cutting with a spade, a man may throw up a cubic yard per hour, or 10 cubic yards in a day; but if of firmer quality, hacking becomes necessary, and an additional man will be required to perform the same work; if very strong gravel, more assistance will be required. If, therefore, the wages of a labourer were 2s. 6d. per day, the price of a yard would be 3d. for cutting only, without profit to the contractor; 6d. for cutting and hacking, and 9d. if two hackers be necessary. In sandy ground, where wheeling becomes necessary, three men will remove 30 cubic yards in a day to the distance of 20 yards, two for filling and one for wheeling. But to remove the same quantity in a day to a greater distance, an additional man for every 20 yards will be required. 2299. The method of ascertaining the quantity of excavation will, of course, be obvious; the quantity is the length multiplied into the depth and width. In the cases of trenches merely dug for the reception of walls, which, of course, are sloped to prevent the earth falling in on the excavators, a mean width is to be taken. Thus, suppose an excavation 24 feet long, 4 feet wide at top, and 2 feet at the bottom (average width therefore 3 feet), 24x3x5 and 5 feet deep, we have for the quantity of yard 13.33 cube yards. 27 2300. BRICKWORK. In measuring and estimating the value of brick work, the following points must be remembered. A rod of brickwork is a mass 16 feet square; hence the quantity of superficial feet which it contains is 272 feet (165 x 16.5), but the of the foot is too trifling to make it worth while to embarrass calculations with it, and consequently 272 feet is universally taken as the superficial standard content of a rod. Its standard thickness is one brick and a half (or 13 inches). Hence it follows, that a cubic rod of brickwork would be 272 feet x 13 inches-306 feet cube. The allowance for the number of bricks is taken on an average at 4500. Much, however, depends on the closeness of the joints and the nature of the work. In walling, a reduced foot is generally taken as requiring 17 bricks; a foot superficial in Flemish bond, laid in malm facing, about 8 bricks; and a foot superficial of gauged arches, 10 bricks. In paving, a yard requires 82 paving bricks, or 48 stock bricks, or 144 Dutch clinkers laid on edge, or 36 bricks laid flat. 2301 In tiling, which is measured by the square of 100 superficial feet, a square will require 800 at a 6-inch gauge, 700 at a 7-inch gauge, and 600 at an 8-inch gauge. The gauge necessarily regulates the distance of the laths, and, at the same time, must be dependent on the slope of the roof, which, if flat, should not be less than 6 inches, as for instance, above the kerb in a kerb roof; and not more than 8 inches in any case. A square of plain tiling requires about on an average a bundle of laths, two bushels of lime, and five of sand, and at least a peck of oak pins. The laths are sold in bundles of 3, 4, and 5-feet lengths. A bundle of the 3-feet contains eight score, the 4-feet six score, and the 5-feet five score to the bundle. The nails used are fourpenny; they are purchased by the long hundred, that is, of six score, and, in day work, are charged by the bricklayer 5-score to the hundred. The name of nails, as fourpenny. fivepenny, &c., means fourpence, fivepence, &c. per hundred. The number of nails required for a bundle of 5-feet and 6-feet laths, are 500 and 600 respectively. 2302. A square of pantiling requires 180 tiles laid at a 10-inch gauge, and a bundle of 12 laths 10 feet long. 2303. In lime measure, what is called a hundred is 100 pecks, or 25 striked bushels (old measure). 2304. In sand measure, 18 heaped bushels, or 21 striked bushels, equal to 1 yard cube, is a single load, and about 24 cubic feet 1 ton. 2305. In mortar 27 cubic feet make 1 load, which on common occasions contains half a hundred of lime with a proportional quantity of sand. Eleven hundred and thirty-four cubic inches make a hod of mortar; that is, a mass 9 inches wide, 9 inches high, and 14 inches long. Two hods of mortar are nearly equal to half a bushel. The following measures and weights it may be also useful to remember : 23 cubic feet of sand = 1 ton; hence 1 cubic foot weighs 95.3 lbs. 17 cubic feet of clay 1 ton; hence 1 cubic foot weighs about 130 lbs. 18 cubic feet of common earth = 1 ton; hence 1 cubic foot weighs nearly 124 lbs. 306 cubic feet of brickwork to full 95 lbs. = 13 tons; hence 1 cubic foot is equal 2306. In the measurement of brickwork, from the surface being 272 feet and the standard thickness 14 brick, it will be immediately seen that nothing more is requisite than, having ascertained the thickness of each part of the work, to reduce it to the standard thickness above stated, and this will be found sufficiently easy in almost all cases. Where, however, this cannot be done, we can always ascertain with sufficient accuracy the cubic contents in fect of any mass of brickwork; and dividing by 306 we have the number of rods. 2307. We here present an illustration in a wall of the most common occurrence (fig. 808.), which we will suppose 20 feet long without reference to any wall which might return from it, and thus diminish its length in measuring therewith a returning wall. The following is the method of entering and calculating the dimensions. 26.8 963 272 Therefore the total is 963-4 superficial feet 11 brick thick, and =3 rods, 147 feet. 2308. Upon this principle the measuring and estimation of brickwork is conducted, and having the price and quantity of bricks in a rod, and the lime, sand, and labour, which will presently be given, we may come to a pretty accurate knowledge of its value. But there are other articles which will require our attention, to which we shall presently advert. Before proceeding, however, we may as well observe that the above result of 3 rods 147 feet might have been similarly obtained by cubing the mass of brickwork and dividing the whole mass by 306, but with much more labour. 2309. In measuring walls faced with bricks of a superior quality, the area of such facing must be measured, or allowance extra is made in the price per rod of the brickwork. 2310. All apertures and recesses from any of the faces are deducted. 2311. Gauged arches are sometimes deducted and charged separately, sometimes not; but whether deducted or not does not signify, as the extra price must be allowed in the latter case and the whole price in the former. Rubbed and gauged arches, of whatever form, are measured and charged by the superficial foot. 2312. The angles of groins, outside and inside splays, bird's mouths, bull's noses, are measured by the lineal or running foot; but cuttings are measured by the foot superficial. Chimneys are measured solid to allow for the trouble of forming and pargetting the flues. The opening at bottom, however, is to be deducted. 2313. Quarters in brick nogging are measured in, as are all sills, stone strings, and timber inserted in walls. Two inches are also allowed in the height of brickwork for bedding plates if no brickwork be over them. 2314. Ovens, coppers, &c. are measured as solid work, deducting only the ash holes; but all fire stone, Welsh lumps, tiles, &c., though measured alone, are not to be deducted out of the brickwork. Pointing, colouring, &c. to fronts, is measured by the foot superficial. Plantile creesing by the foot lineal. To estimate the value of a rod of brickwork, the method is as under: 4500 stocks, at per thousand 14 hundred of lime=974 striked bushels containing 27 feet cube to the 40 40 d. 0 000 2315. In measuring and estimating all sorts of artificers' works, the method usually adopted for saving labour in making out the account is to arrange in separate columns each sort of work, and then to add them up and carry the total to the bill. In brickwork, where walls are of different thicknesses, these with their deductions are arranged in separate columns, and then all are reduced to the standard thickness. 2316. The common measure for tiling is a square of 10 feet, containing therefore 100 feet superficial. Claims are made for the eaves to the extent of 6 inches; but in pantiling this ought not to be allowed, as a claim not founded in justice, though custom is pleaded for it. 2317. The following table shows the number of bricks necessary for constructing any number of superficial feet of walling from 1 to 90,000, and from half a brick to 2 bricks thick; and thence, by addition only, to any thickness or number required, at the rate of 4500 bricks to a reduced rod. Thus, if it be required to find the number of bricks wanted to build a piece of work containing 756 feet super. of walling 14 brick thick, we find by inspection for 700 feet 11580 bricks; for 50 feet, 827 bricks; and for 6 feet, 99 bricks; in all, 11580 + 827 +99 = 12506. TABLE SHOWINg the requisite QUANTITY OF BRICKS FOR A GIVEN SUPERFICIES OF WALLING. |