Table of Chords; Radius

=

1.0000 (continued).

M.

65°
5° 66° 67° 68° 69° 70° | 71° 72° 73° M.

C123456

0' 1.0746 1.0893 1.1039 1.1184 1.1328 1.1472 1.1614
1.0748 1.0895 1.1041 1.1186 1.1331 1.1474
1.0751 1.0898 1.1044 1.1189 1.1333 | 1.1476
1.0753 1.0900 1.1046 1.1191 | 1.1335 | 1.1479
1.0756 1.0903 1.1048 1.1194 1.1338 1.1481
1.0758 1.0905 1.1051 1.1196 1.1340 1.1483
1.0761 1.0907 1.1053 1.1198 1.1342 1.1486
1.0763 1.0910 1.1056
1.1345 1.1488

1.1756 1.1896

1.1616

1.1758 1.1899

1.1619

1.1760 1.1901

1.1621

1.1763 1.1903

1.1624

1.1765 1.1906

1.1626

1.1767 1.1908

1.1628

1.1770 1.1910

1.1201

1.1631

1.1772 1.1913

61234567889

Table of Chords;

M. 74° 75° 76°

8

10

Radius = 1.0000 (continued).

178° 79° 80° 81° 82° M.

0' 1.2036 1.2175 1.2313 1.2450 1.2586 1.2722 1.2856 1.2039 1.2178 1.2316 1.2453 1.2589 1.2724 1.2858 1.2041 1.2180 1.2318 1.2455 1.2591 1.2726 1.2860 1.2043 1.2182 1.2320 1.2457 1.2593 1.2728 1.2862 1.2046 1.2184 1.2322 1.2459 1.2595 1.2731 1.2865 5 1.2048 1.2187 1.2325 1.2462 1.2598 1.2733 1.2867 1.2050 1.2189 1.2327 1.2464 1.2600 1.2735 1.2869 1.2053 1.2191 1.2329 1.2466 1.2602 1.2737 1.2871 1.2055 1.2194 1.2332 1.2468 1.2604 1.2740 1.2874 9 1.2057 1.2196 1.2334 1.2471 1.2607 1.2742 1.2876 1.2060 1.2198 1:2336 1.2473 1.2609 1.2744 1.2878 11 1.2062 1.2201 1.2338 1.2475 1.2611 1.2746 1.2880 1.2064 1.2203 1.2341 1.2478 1.2614 1.2748 1.2882 13 1.2066 1.2205 1.2343 1.2480 1.2616 1.2751 1.2885 1.2069 1.2208 1.2345 1.2482 1.2618 1.2753 1.2887 15 1.2071 1.2210 1.2348 1.2484 1.2620 1.2755 1.2889 1.2073 1.2212 1.2350 1.2487 1.2623 1.2757 1.2891 1.2076 1.2214 1.2352 1.2489 1.2625 1.2760 1.2894 18 1.2078 1.2217 1.2354 1.2491 1.2627 1.2762 1.2896 1.2080 1.2219 1.2357 1.2493 1.2629 1.2764 1.2898 20 1.2083 1.2221 | 1.2359 1.2496 1.2632 1.2766 1.2900 1.2085 1.2224 1.2361 1.2498 1.2634 1.2769 1.2903 22 1.2087 1.2226 1.2364 1.2500 1.2636 1.2771 1.2905 1.2090 1.2228 1.2366 1.2503 1.2638 1.2773 1.2907 24 1.2092 1.2231 1.2368 1.2505 1.2641 1.2775 1.2909 1.2094 1.2233 1.2370 1.2507 1.2643 1.2778 1.2911 26 1.2097 1.2235 1.2373 1.2509 1.2645 1.2780 1.2914 27 1.2099 1.2237 1.2375 1.2512 1.2648 1.2782 1.2916 28 1.2101 1.2240 1.2377 1.2514 1.2650 1.2784 1.2918 29 1.2104 1.2242 | 1.2380 1.2516 1.2652 1.2787 1.2920 1.2106 1.2244 1.2382 1.2518 1.2654 1.2789 1.2922 1.2108 1.2247 1.2384 1.2521 1.2656 1.2791 1.2925 1.2111 1.2249 1.2386 1.2523 1.2659 1.2793 1.2927 33 1.2113 1.2251 1.2389 1.2525 1.2661 1.2795 1.2929 1.2115 1.2254 1.2391 1.2528 1.2663 1.2798 1.2931 35 1.2117 1.2256 1.2393 1.2530 1.2665 1.2800 1.2934 36 1.2120 1.2258 1.2396 1.2532 1.2668 1.2802 1.2936 37 1.2122 1.2260 1.2398 1.2534 1.2670 1.2804 1.2938 1.2124 1.2263 1.2400 1.2537 1.2672 1.2807 1.2940 39 1.2127 1.2265 1.2402 1.2539 1.2674 1.2809 1.2942 40 1.2129 1.2267 1.2405 1.2541 1.2677 1.2811 1.2945 1.2131 1.2270 1.2407 1.2543 1.2679 1.2813 1.2947 42 1.2134 1.2272 1.2409 1.2546 1.2681 1.2816 1.2949 1.2136 1.2274 1.2412 1.2548 1.2683 1.2818 1.2951

44 1.2138 1.2277 1.2414 1.2550 1.2686 1.2820 1.2954 1.2141 1.2279 1.2416 1.2552 1.2688 1.2822 1.2956 46 1.2143 1.2281 1.2418 1.2555 1.2690 1.2825 1.2958 47 1.2145 1.2283 1.2421 1.2557 1.2692 1.2827 1.2960 48 1.2148 1.2286 1.2423 1.2559 1.2695 1.2829 1.2962 1.2150 1.2288 1.2425 1.2562 1.2697 1.2831 1.2965 1.2152 1.2290 | 1.2428 1.2564 1.2699 1.2833 1.2967

51 1.2154 1.2293 1.2430 1.2566 1.2701 1.2836 1.2969 52 1.2157 1.2295 1.2432 1.2568 1.2704 1.2838 1.2971 1.2159 1.2297 1.2434 1.2571 1.2706 1.2840 1.2973 54 1.2161 1.2299 1.2437 1.2573 1.2708 1.2842 1.2976 1.2164 1.2302 1.2439 1.2575 1.2710 1.2845 1.2978 56 1.2166 1.2304 1.2441 1.2577 1.2713 1.2847 1.2980 57 1.2168 1.2306 1.2443 1.2580 1.2715 1.2849 1.2982 1.2171 1.2309 1.2446 1.2582 1.2717 1.2851 1.2985 59 1.2173 1.2311 1.2448 1.2584 1.2719 1.2854 1.2987 60 1.2175 1.2313 1.2450 1.2586 1.2722 1.2856 1.2989

Table of Chords; Radius = 1.0000 (concluded).

Lengths and Bevels of Hip and Jack Rafters.

The lines ab and be in Fig. 89 represent the walls at the angle of a building; be is the seat of the hip-rafter, and of of a jack-rafter. Draw eh at right angles to be, and make it equal to the rise of the roof; join b and h, and hb will be the length of the hip-rafter. Through e draw di at right angles to be. Upon b, with the radius bh, describe the arc hi, cutting di in i. Join b and i, and extend gf

to meet bi in j; then gj will be the length of the jack-rafter. The

in the same manner, by exFrom ƒ draw fk at right angles Make fk equal to fl by the are

length of each jack-rafter is found tending its seat to cut the line bi. to fg, also fl at right angles to be. lk, or make gk equal to gj by the arc jk; then the angle at j will be the top bevel of the jack-rafters, and the one at k the down bevel. Backing of the hip-rafter. At any convenient place in be (Fig. 89), as o, draw mn at right angles to be. From o describe a circle, tangent to bh, cutting be in s. Join m and s and n and s; then these lines will form at s the proper angle for bevelling the top of the hip-rafter.

TRIGONOMETRY.

It is not the purpose of the author to teach the use of trigonometry, or what it is; but, for the benefit of those readers who have already acquired a knowledge of this science, the following convenient formulas, and tables of natural sines and tangents, have been inserted. To those who know how to apply these trigonometric functions, they will often be found of great convenience and utility.

These tables are taken from Searle's "Field Engineering," John Wiley & Sons, publishers, by permission.