CD r- o MECHANICS' TABLES, CONTAINING AREAS AND CIRCUMFERENCES OF CIRCLES, AND SIDES OF EQUAL SQUARES ; CIRCUMFERENCES OF ANGLED HOOPS, ANGLED OUTSIDE AND INSIDE; CUTTING OF BOILER PLATES, COVERING OF SOLIDS, &c., AND WEIGHTS OF VARIOUS METALS, &c., &c., &c., &c. MISCELLANEOUS NOTES, COMmiSING DIMENSIONS OF MATERIALS, ALLOYS, PAINTS, LACKERS, &C. BY CHARLES H. HASWELL, MARINE ENGINEER, NEW YORK: HARPER & BROTHERS, PUBLISHERS, FRANKLIN SQUARE. 1856. v*V Entered, according to Act of Congress, in the year one thousand eight hundred and fifty-six, by HARPER f 14 4 5 f 16 if 5 81 17 llf 6 3f . 19 9| 4 G| 14 4f 5 | 16 2f 5 8| 18 0-1 6 3| 19 101 4 7 14 4f 5 2 16 2f 5 9 18 Of 6 4 19 10 4 74 4 <"i 14 5| 14 54 5 24. 5 2i 16 4 16 34 5 94 18 li 5 91 18 14 6 41 1 19 11 19 11 4 7f 14 of 5 2| 16 3| 5 9f 18 1| 6 4| 19 ll; 4 7i 14 6i 5 21 16 41 5 91 18 21 6 44 20 4 7| 14 6| 5 2| 16 4| 5 9f 18 2f 6 4f 20 4 7f 14 7} 5 2f 16 54 5 9f 18 3 6 4f 20 1 4 7* 14 71 16 5| 5 9| 18 3| 6 4| 20 1 4 8 14 7| 5 3 16 5| 5 10 18 3| 6 5 20 1 4 84, 14 81 5 31 16 61 5 101 18 41 6 5^ 20 21 4 81 14 8| 5 3i 16 6-| 5 101 18 4f 6 ^T" 20 24 4 8f 14 9 5 3f 16 7 5 lOf 18 5 6 "5f 20 3 4 81 14 9| 5 34 16 7f 5 101 18 5f 6 54 20 3| 4 sf 14 9| 5 3| 16 7| 5 10| 18 5| 6 5| 20 3| 4 8f 14 101 5 3| 16 81 5 lOf 18 6i 6 5f 20 44 4 8| 14 lOf 16 8f 5 10| 18 6| 6 5| , 20 4| 4 9 14 11 5 4 16 9 . 5 11 18 7 6 6 20 5 4 9 14 Hf 5 4J- 16 9f 5 111 18 7f 6 r. i 20 5| 4 91 14 llf 5 4J- 16 94 5 Hi 18 74 6 6i ; 20 5! 4 9| 15 0| 5 4 16 10| 5 llf 18 8| 6 6f : 20 64 4 91 15 Of 5 4J- 16 lOf 5 114 18 84 6 61 20 6J 4 9| 15 1 5 4] 16 11 5 llf ! 18 9 6 6| 20 7 4 9^- 15 If 15 If t) 4-* 5 4 16 llf 16 llf 5 llf 5 ll| 18 9f 18 9f 6 6f 6 6| 20 7| 20 7 4 10 4 104, 15 21 15 2| 5 5 5 54 17 04 17 Of 6 6 0| 18 101 18 10| 6 6 20 8 20 8 4 101 15 2j 5 5 17 1 6 01 18 lOf 6 i 20 8- 4 10f 15 3f 5 5 17 If 6 Of 18 Hi 6 1 20 9 4 10} 15 3f 5 5 17 li 6 04 18 llf 6 4 20 9^ 4 10-1 15 41 5 5 17 2- 6 0| 19 04 6 1 20 10- 4 104 15 44 5 5 17 2 6 Of 19 04 6 f 20 10- 4 10| 15 4| 5 b\ 17 2- 6 0| 19 Of 6 7| 20 10; 4 11 15 51 5 6 17 3- 6 1 19 li 6 8 20 11- 4 111 15 5f 15 64 I a 17 3 17 4 6 14 6 if 19 If 19 2 6 84, 6 S-- 20 11- 21 4 llf 15 64 5 6l 17 4 6 If i 19 24 6 8; 21 0] 4 H 15 6| 5 G| 17 4 6 14 ' 19 2f 6 S\- 21 Of 4 111 15 7i 5 6f 17 5 6 1| 19 31 6 8^ 21 11 4 114 15 ll 5 6f 17 5 6 14 19 3f 6 21 If 4 ll| 15 8" 5 G| 17 6 6 l| 19 4 G 8^ 21 2 FEET, INCHES, AND EIGHTHS. 19 21 3| 7 9 8 1\ 8 8 9 0| 9 Of Circum. 26 8f 26 8f 26 91 26 9i 26 10 26 10| 26 lOf 26 111 26 1U 26 11| 27 Oi 27 0-| 27 21 27 2f 27 3 27 3i 27 3| 27 4 27 4-| 27 5 27 5| 27 5f 27 6 27 el 27 7 27 7| 27 7f 27 8-J- 27 8} 27 9 27 9$ 27 9f 27 101 27 101 27 10| 27 HI 27 llf 28 01 28 Ol 28 0* 28 11 28 If 28 2 28 2t 28 2| 28 31 28 3| 28 4 28 4 28 4f 28 51 28 of 28 6 20 CIRCUMFERENCES OF CIRCLES IN Circum. Diam. Circum. Diam. Circum. Diam. Circum. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. 1 FT. IN. 28 6| 9 8 30 4| 10 3 32 2 10 10 34 Of r 28 6f 9 81 30 44 10 34 32 2f 10 104, 34 Of - 28 74 9 81 30 51 10 31 32 3} 10 101 34 14 28 71 9 8# 30 54 10 3| 32 34 10 lOf 34 11 ', 28 8 9 81 30 6 10 31 32 3| 10 104 34 l| - 28 83 9 8-| 30 6 10 8| 32 4| 10 10| 34 2| 28 84 ; 28 9| 9 84 9 8| 30 64 30 7| 10 34 10 8} 32 4f 32 5} 10 lOf 10 10| 34 24 34 3| 28 91 9 9 30 7| 10 4 32 54 10 11 34 34 - 28 9| - 28 101 9 94, 9 91 30 7| 30 81 10 44 10 41 32 52 32 61 10 114, 10 Hi 34 3| 34 4| 28 104 9 9| 30 8f 10 4$ 32 6| 10 llf 34 4f 28 111 9 91 30 9J 10 44 32 7 10 Hi 34 5 28 ll| 28 111 - 29 01 9 9| 9 9f 9 9| 30 94 30 9| 30 10| 10 4| 10 44 10 4| 32 74 32 74 32 8| 10 ll| 10 114 10 Hi- 34 51 34 5| 34 61 29 Of 9 10 30 lOf- 10 5 32 8f ll 34 6f - 29 1 9 10J 30 11 10 51 32 9 11 04 34 7 29 11 9 101 30 11| 10 51 32 9| 11 Of 34 7| 29 ll 9 103 30 111 10 5f 32 9i 11 0| 34 7f , 29 21 9 101 31 01 10 54 32 101 11 04 34 8i 29 2f 9 10| 31 Of 10 5| 32 lOf 11 Of 34 8| - 29 3 9 lOf 31 1 10 5f 32 11 11 Of 34 9 - 29 3f 9 10| 31 If 10 6| 3211f 11 Of 34 9f 29 3f 9 11 31 If 10 6 32 llf 11 1 34 94 r 29 41 9 Hi 31 21 10 61 33 01 11 ll 34 10| . 29 4f 9 Hi 31 24 10 61 33 Of 11 ll 34 104, - 29 5 9 11$ 31 3 10 6| 33 1 11 ia 34 11 > 29 5| 29 5f 9 1H 9 11| 31 3^ 31 34 10 64 10 6lt 33 If 33 If 11 14 11 1| 34 llf 34 llf 29 4 9 114 31 4 10 6f 33 2| 11 If 35 04 29 61 9 11| 31 44 10 6| 33 24, 11 l| 35 0| 29 7 10 31 d 10 7 33 21 11 2 35 29 7$ 10 Oi 31 53 10 71 33 3f 11 2i 35 li 29 74 10 01 31 5f 10 71 33 3f 11 21 35 If 29 81 10 0$ 31 6i 10 7| 33 4 11 2| 35 2| 29 81 10 01 31 61 10 74 33 4 11 21 35 24 29 8| 10 ol- 31 6| 10 7| 33 4| 11 2i 35 2| 29 91 29 9-f io Of 10 Of 31 7i 31 7| 10 7f 10 7| 33 51 33 5| 11 24 11 2| 35 31 35 3 29 104 10 1 31 8i 10 8 33 61 11 3 35 4 29 101 10 li 31 84 10 81 33 64 11 3J 35 41 29 10l 10 j- 31 81 10 81 33 6| 11 31 35 4| 29 111 10 2 31 9* 10 8| 33 71 11 3f 35 51 29 llf 10 4 31 9| 10 84, 33 7f 11 34 35 5| 30 10 I 31 10 10 8|- 33 8 11 3-| 35 6 30 01 10 f 31 10f 10 8J 33 8 H 3f 35 6f 30 Of 10 | 31 10$ 10 8| 33 8$ 11 3| 35 6f 30 li 10 2 31 111 10 9 33 91 11 4 35 7i 30 If 10 21, 31 11-! 10 91, 33 9f 11 44, 35 7f 30 2 10 21 32 10 91 33 10 11 41 35 8 30 2J 10 2f 32 05 10 9 33 10| 11 4| 35 8$ 30 24 ! 30 3J- 30 3f 10 21 10 2| 10 24 32 Of 32 14 32 ll 10 94 10 9| 10 9f 33 lOf 33 ll| 33 111 11 44 11 4-| 11 44 35 8f 35 91 35 94 30 4 10 2| 32 2 10 9| 34 " 11 4| 35 10 FEET, INCHES, AND EIGHTHS. 21 Diam. Circum. Diam. Circum. Diam. Circum. Diam. Circum. FT IN. FT. IN FT. IN. FT. IN. FT. IN. FT. IN. FT. IN 11 5 35 lOf 12 37 8f 12 7 39 6| 13 2 41 41 11 5J 35 lOf 12 01 37 8f 12 74 39 6f 13 21 41 4J 35 111 12 0| 37 91 12 7i 39 7| 13 2i 41 5, 11 5f 35 111 12 Of O"7 Gi 12 7f 39 7* 13 2f 41 5i 11 51 35 11| 12 Oi 37 a| 12 74 39 7| 13 24 41 5^ 11 5| 36 Oi 12 0| 37 101 12 7| 39 81 13 2| 41 6 36 Of 36 ij 12 Of 12 Of 37 lOf 37 111 12 7f 12 7| 39 8| 39 9| 13 2f 13 2| 41 6| 41 7 11 6 36 14, 12 1 37 1H 12 8 39 91 13 3 41 7| 11 61 36 1 12 1-| 37 11| 12 81 39 9| 13 31 41 1\ 11 61 36 21 12 l| 38 Oi 12 81 39 101 13 31 41 8J 11 6| 36 2f 12 If 38 Of 12 8f 39 10| 13 3| 41 8| 11 64 36 3 12 li 38 1 12 81 39 11 13 34 41 9 11 e| 36 31 12 If 38 If 12 8| 39 llf 13 3| 41 9| 11 6f 36 3| 12 If 38 l- 12 8f 39 11| 13 3f 41 9i 11 4 36 41 12 l| 38 2i 12 8-| 40 Oi 13 3|- 41 10J 11 7 36 4f 12 2 38 24 12 9 40 Of 13 4 41 10] 11 74, 36 5 12 21 38 3 12 91 40 1 13 44, 41 11 11 71 36 5f 12 21 38 3f 12 9i 40 If 13 4i 41 11| 11 7f 36 5 12 2f 38 3f 12 9f 40 If 13 4f 41 11^ 11 71 36 6i 12 24 38 41 12 94 40 2| 13 41 42 OJ 11 7| 36 6J 12 2| 38 4f 12 9| 40 2f 13 4| 42 Oi 11 7f 36 7 12 2f 38 5 12 9f 40 3 13 4f 42 1 11 7} 36 7f 12 2| 38 5f 12 9| 40 3f 13 4| 42 1| 11 8 36 7f 12 3 38 5f 12 10 40 3f 13 5 42 1| 11 81 36 84, 12 31 38 61 12 101 40 44 13 51 42 2 11 81 36 8J 12 31 38 61 12 101 40 4| 13 51 42 2J 11 8| 36 9 38 6|- 12 lOf 40 4| 13 5f 42 21 11 81 36 9f 12 3| 38 7f 12 101 40 5f 13 54 42 3J 11 8| 36 9f 12 3f 38 7f 12 lOf 40 5f 13 5| 42 3? 11 8- 36 101 12 3f 38 81 12 10-f 40 64 13 5f 42 4J 11 8| 36 101 12 3| 38 81 12 10| 40 61 13 6j 42 4l 11 9 36 10 12 4 38 8| 12 11 40 6f 13 6 42 4^ 11 91 36 111 12 41 38 9i 12 114 40 71 13 61 42 5J 11 91 36 llf 12 41 38 9f 12 111 40 7| 13 61 42 5 11 9g 37 0| 12 4f 38 101 12 llf 40 81 13 6| 42 6 11 91 37 Oi 12 41 38 104 12 111 40 81 13 64 42 6| 11 9| 37 0| 12 4| 38 10J 12 11| 40 8| 13 6| 42 6^ 11 9f 37 li 12 4f 38 llj 12 llf 40 9.J 13 6f 42 7J 11 9| 37 If 12 4| 38 llf 12 ll| 40 Of 13 6|- 42 7| 11 10 37 2 12 5 39 13 40 10 13 7 42 8 11 301 37 21 12 51 39 Of 13 01 40 lOf 13 71 42 8| 11 101 37 2| 12 51 39 01 13 Oi 40 10! 13 7i 42 8^ 11 lOf 37 31 12 5| 39 I? 13 Of 40 Hi 13 71 11 101 37 3f 12 54 39 If 13 Oi 40 llf 13 71 42 9J 11 10| 37 4 12 6J 39 2 13 0-| 41 13 7| 42 10 11 lOf 37 4f 12 5f 39 2f 13 Of 41 Of 13 7f 42 10| 11 10| 37 4f 12 5| 39 2f 13 0| 41 Of 13 7| 42 10| 11 11 37 5} 12 6 39 31 13 41 14 13 8 42 114 11 111 37 54 12 61 39 8| 13 1 41 14 13 8i 42 11J 11 Hi 37 6 12 61 39 4 13 i 41 2 13 8i 43 11 llf 37 6f 12 61 39 4f | 13 i 41 2f 13 8f 43 0^ 11 114 37 6f 12 6* 39 4f 13 I 41 2f 13 84 43 0^ 11 ll| 0-7 rjF 12 6l 39 51 13 I 41 31 13 8| 43 lj 11 Hf 37 71 12 6f 39 54 13 If 41 34 13 8f 43 li 11 llf 37 7| 12 6| 39 5| 13 l| 41 3| 13 8| 43 1, 22 Diam. C Circum. [RCUMFERENCES Diam. | Circum. OF CIRCLES I Diam. i Circum. M Diam. Circum. 13 9 13 9J 43 21 43 2f 14 4 14 4| 45 Oi 45 Of 14 11 14 111 46 101 46 10| 15 6 15 61 48 8| 48 8| 13 9i 43 3| 14 4i 45 li 14 11; 46 111 15 6 i 48 9 13 9| 43 31 14 4| 45 l| 14 llf 46 Hi 15 6 48 9| 13 91 43 3| 14 41 45 l| 14 11J. 46 ll| 15 6 ', 48 9J 13 9| 43 4 14 4 45 2i 14 llf 47 Oi 15 6 i 48 10 13 9f 43 4 14 4f 45 2f 14 llf 47 0| 15 G [ 48 10] 13 9| 43 5 14 4| 45 3 14 ll| 47 1 15 6 I 48 11 13 10 43 51 14 5 45 3f 15 47 11 15 7 48 11| 13 10J 43 5| 14 5| 45 3| 15 Oi 47 l| 15 t 48 11^ 13 101 43 61 14 5 45 41 15 Oi 47 2| 15 [ 49 OJ 13 10| 43 el 14 5f 45 4| 15 Of 47 2| 15 I 49 0] 13 101 i 43 T 14 51 45 5 15 Oi 47 3 15 ', 49 1 13 10| 43 7f 14 5| 45 5f 15 0| 47 3| 15 ^ 49 Ijj 13 lOf 13 10| 43 7f 43 8i 14 5f 14 5| 45 5f 45 61 15 Of 15 0| 47 3f 47 4 15 15 7 1 49 l\ 49 2{ 13 11 43 8| 14 6 45 6| 15 1 47 4f 15 8 49 21 13 111 43 9 14 61 45 7 15 11 47 5 15 8 t 49 3 13 11J 13 11 43 9f 43 9f 14 61 45 7f 14 6f ! 45 7f 15 li ! 47 54 15 if 47 5f 15 8 15 8 i 49 3- 49 3^ 13 11J 43 101 14 61 i 45 81 15 l| 47 6} 15 8 49 4 13 111 43 101 14 6| 45 8i 15 1| 47 61 15 8 49 4 13 llf 43 11 14 6f 45 9 15 If 47 6 15 8 I r 49 4j 13 111 43 llf 14 6| 45 9-f 15 l| 47 7f 15 8 f 49 5; 14 43 llf 14 7 45 9f 15 2 47 7f 15 9 49 5 14 01 44 Of 14 7 45 10* 15 21 47 81 15 9 49 6 14 of 44 Oi 14 71 45 101 15 SI 47 81 15 9 49 61 14 Of 44 Of 14 7f 45 10-f 15 2| 47 8| 15 9 49 e; 14 01 44 li 14 71 45 HI 15 21 47 91 15 9 49 7- 14 0| 44 If 14 74 45 ll| 15 2| 47 9| 15 9 49 7- 14 Of 44 2i 14 7f 46 Oi 15 2f 47 10| 15 9- 49 8 14 0| 44 2| 14 7| 46 OJ 15 2| 47 lOf 15 9 49 8f 14 1 44 2 14 8 46 Of 15 3 47 10| 15 10 49 8f 14 1 44 3i 14 8 46 li 15 31 47 ll| 15 10- r 49 91 14 l| 44 3f 14 81 46 If 15 31 47 llf 1510^ I 49 9f 14 l| 44 4 14 8i 46 2 15 3| 48 15 10- i 49 10| 14 li 44 41 14 81 46 2 15 3| 48 03 15 10 49 101 14> if 44 4-| 14 8|- 46 21 15 3| 48 0| 15 10- : 49 lOf- 14 If 44 5| U 8f 46 31 15 3f 48 U 15 10j 49 111 14 l| 44 5| 14 8| 46 3| 15 3| 48 1| 15 10- f 49 llf 14 2 44 6 14 9 46 4 15 4 48 2 15 11 50 14 2k 44 6f 14 91 46 4| 15 41 48 2f 15 11J r 50 01 14 2? 44 6| 14 91 46 4| 15 4i 48 2f 15 11 50 0| 14 2| 44 7| 14 9| 46 51 15 4| 48 31 15 111 50 l| 14 21 44 7|- 14 91 46 5| 15 41 48 31 15 Hi ; 50 l| 14 2| 44 8 14 9| 46 6 15 4| 48 4 15 11^ 50 2 14 2f 14 2-J 44 8| 44 8f 14 9f 14 9| 46 6f 46 6f 15 4f 15 4| 48 4f 48 4f 15 11^ 15 ll] - 50 2f 50 2| 14 3 44 9 14 10 46 71 15 5 48 5^ 16 50 3 14 3i 44 91 14 101 46 71 15 51 48 51 16 OJ 50 3 14 31 44 9| 14 101 46 7| 15 51 48 51 16 50 3 14 3| 44 10| 14 lOf ! 46 8f 15 5| 48 6f 16 0| 50 4- 14 31 44 lOf 14 lOf 46 8f 15 51 48 6f 16 Oi 50 4 14 3| 44 HI 14 lOf ; 46 9| 15 5| 48 71 16 Oi 50 & 14 3f 14 3| 44 1H 44 llf 14 lOf i 46 91 14 10| 46 9| 15 5f 15 5| 48 71 16 (H 48 7| i 16 0\ 50 5i- 50 5- FEET, INCHES, AND EIGHTHS. 23 Diam. Circum. Diam. Circum. Diam. Circum. Diam. Circum. T. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN 6 1 50 6J 16 8 52 41 17 3 54 21 17 10 56 Oi 6 11 50 64 16 8i 52 4f 17 3i 54 2| 17 101 56 0| 6 l| 50 7 16 s 52 5 17 31 54 3 17 101 56 1 6 If 50 7| 16 8f 52 5^ 17 3| 54 3 17 lOf 56 1| 6 1 50 71 16 8t 52 5 17 3^ 54 3| 17 10| 56 1| 6 If 50 8i 16 8f 52 61 17 3| 54 41 17 10$ 56 2 6 If 6 if 50 8f 50 9 16 8f 16 8| 52 6f 52 7 17 3f 17 3| 54 44 54 5 17 lOf 17 10| 56 21 56 3 6 2 50 9f 16 9 52 7| 17 4 54 5f 17 11 56 3| 6 21 50 9f 16 9i 52 7f 17 41 54 5f 17 111 56 3^ 6 2| 6 2f 50 101 50 10| 16 Si 16 9$ 52 8i 52 8f 17 4 17 4f 54 61 54 6f 17 Hi 17 llf 56 4j 56 4J 6 21 50 11 16 91 52 9 17 4^ 54 7 17 111 56 5 6 2| 50 11| 16 9| 52 9f 17 4f 54 7f 17 llf 56 5| 6 2f 50 llf 16 9f 52 9 17 4f 54 7f 17 llf 56 5i 6 2l 51 0| 16 9| 52 101 17 4| 54 8| 17 ll| 56 6^ 6 3 51 Oi 16 10 52 10J 17 5 54 8| 18 56 6 6 31 51 1 16 10^ 52 11 17 5i 54 8| 18 01 56 6^ 6 3i 51 If 16 101 52 llf 17 51 54 9f 18 Oi 56 7 6 3f 51 If 16 10-f 52 llf 17 5f 54 9f 18 Of 56 7 6 31 51 2| 16 101 53 Oj 17 5- 54 101 18 Oi 56 8 6 3f 51 21 16 10| 53 0^ 17 5f 54 10 18 Of 56 81 6 3f 51 2f 16 lOf 53 0| 17 5f 54 10^ 18 Of 56 8^ 6 3| 51 31 16 lOj 53 11 17 5| 54 Hi 18 Of 56 9^ 6 4 51 3| 16 11 53 If 17 6 54 llf 18 1 56 9| 6 4J 51 41 16 Hi 53 2 17 6 55 0| 18 1 56 10 6 4| 51 41 16 111 53 2^ 17 61 r5 o| 18 1 56 10| 6 4| 51 4| 16 111 53 2| 17 6| ;')> Ol 18 1 56 10^ 6 4 51 5J 16 11 53 31 17 6k 55 11 18 1 56 11J 6 4| 51 5-| 16 11$ 53 3| 17 6| :>5 if 18 1 56 ll| 6 4f 51 6 16 llf 53 4 17 6f 55 2 18 1 57 6 4| 51 6J 16 ll| 53 4^ 17 6| 55 2f 18 1 57 0| 6 5 51 6| 17 53 47- 17 7 55 2| 18 2 57 04 6 5 51 7| 17 0-J- 53 of 17 "^ 55 3i 18 21 57 1J 6 51 51 7f 17 01 53 5f 17 "1 55 3f 18 21 57 If 6 5| 51 8 17 Of 53 6 17 "| 55 4 1^ 2f 57 2 6 5^ 51 8| 17 OJ- 53 6f 17 "i 55 4f 18 2 57 2f 6 5f 51 8f 17 0| 53 6f 17 7| 55 4f 18 2| 57 2| 6 of 51 9i 17 Of 53 71 17 "f 55 51 18 2f 57 3| 6 5| 51 91 17 0| 53 7-| 17 1 55 5| 18 2| 57 3| 6 6 51 10 17 1 53 8 17 8 55 6 18 3 57 4 6 6i 51 lOf 17 H 53 . 8f 17 8i 55 6f 18 31 57 4f 6 6i B a 51 lOf 51 111 17 l| 17 If 53 8f 53 9 17 81 17 8| 55 64 55. 7| 18 31 18 3| 57 4 57 5 s G| 51 111 17 if 53 9| 17 8* 55 7i 18 3i 57 & 5 6f 52 17 If 53 10 17 8| 55 !\ 18 3f 57 & 8 6f 5 6| 52 Of 52 Of 17 If 17 l| 53 lOf 53 lOf 17 8f 17 8| 55 8f 55 8f 18 3f 18 3| 57 6 57 & 5 7 52 H 17 2 53 Hi 17 9 55 91 18 4 57 7 6 7* 6 1 52 H 52 ll 17 2i 17 21 53 11 53 11 17 9| 17 9| 55 91 55 9| 18 41 18 41 57 7- 57 1\ 5 I 52 21 17 2| 54 Oi 17 9f 55 101 18 4| 57 8- s i 52 2-| 17 2| 54 Of 17 9| 55 lOf 18 4^ 57 8- 6 f S f 5 1 52 31 52 3| 52 3| 17 2f 17 2f j 17 2f l 54 li 54 1^ 54 If 17 9-| 17 9| 17 9| 55 11* 55 111 55 ll| 18 4| 18 4f 18 4| 57 9 57 9i 57 9| 24 CIRCUMFERENCES OF CIRCLES. Diam. Circum. Circum. 18 8 19 2^ 19 2 "s 3 59 81 59 8f 59 9 59 9f W 9f 59 101 59 10* 59 11 59 llf 59 llf CO 0| 60 01 19 41 19 7J 61 51 61 5| 19 9 61 9 61 9f 61 9f 61 10J 61 101 61 11 61 llf 61 llf 62 0| 62 01 62 0| 62 l| 62 l| 62 2J 62 2 62 2 62 31 62 3f 62 4 62 4f 62 4 62 51 62 5f 62 6 62 6f 62 6f 62 ?J 62 7| 62 8 62 85 62 8f 62 9^ 62 91 62 91 62 10| 62 lOf 62 HI 62 111 62 11 1 63 01 63 0| AREAS AND CIRCUMFERENCES OF CIRCLES. 25 APPLICATION OF THE PRECEDING TABLE (P. 5-9). EXAMPLE 1. What is the area of a circle 10 feet 6 inches in di- ameter ? At page 5, in column 8, and opposite to 10J, is 86.590, which is the result required. EXAMPLE 2. What is the circumference of a circle 10^ inches in diameter ? At page 5, in -column 9, and opposite to 10, is 32.99, which is the result required. When it is required to reduce the decimal remainders in this table to de- nominations of yards, feet, inches, etc, Multiply the decimal by the number of parts in the denomination required, and cut off as many places for a remainder, to the right hand, as there are places in the given decimal. '.+ -. ' EXAMPLE. What is the value of .590 foot ? .590 12 inches in a foot. > . 7.080 7 inches and .080 of an inch. APPLICATION OP THE PRECEDING TABLE (P. 16-24). In addition to the general use of this table in giving the circum- ferences of circles from one inch to twenty feet in diameter, in the ordinary designations of feet, inches, and eighths, it is of especial utility in its adaptation to the requirements of boiler-makers and blacksmiths in the determination of the length of materials required for hoops, tyers, etc., etc. Rote. In the formation of metallic hoops, tyers, etc., a contraction of their in- ner surface takes place, the exact allowance for which is the thickness of the metal, which, therefore, must be added to the diameter for which the circumfer- ence is required. EXAMPLE. What is the length of a bar required to form a hoop of 6 feet 9^ inches in diameter, the thickness of the metal being \ an inch? 6 feet 9 inches, added to \ an inch, gives 6 feet 9| inches for the diameter, the circumference for which (page 19) is 21 feet 4$ inch- es, which is the result required. Note. When, in the formation of hands, etc., the bar of metal is to be bent upon, its edge, the breadth of the bar must be added to the diameter, instead of the thickness of it. B 26 CIRCUMFERENCES OF CIRCLES. When a flanged or ribbed bar is used, as with rail-car tyers, tanks, etc. The contraction of the inner surface of the metal and the neces- sary addition to the diameter of the wheel or hoop will depend upon the conformation of the bar, inasmuch as the weakest edges will both contract or attenuate the most, according as they are upon the inner or outer surface. When the tyer or bar has its flange, on the outside. To the inner diameter add the thickness of the metal and two thirds of the breadth of the flange. Application of the preceding table to an elliptic hoop. To half the sum of the diameters add the thickness of the metal, and proceed as directed for plain bars. In the construction of elliptic hoops of angled iron, reference must be had to the tables for angled iron : thus, when the angle is out- side, it must be added to the diameter, and when it is on the inside, it must be subtracted therefrom. NOTE. In determining the length of a bar, an allowance for the thickening of the ends must be made where welding is necessary. Mr. James Foden, of Liverpool, has found that, in an angled bar of uniform thickness, the curve that will exactly compensate for the greater contraction of its inner surface, when it is bent in a ring, is one of which four times the circum- ference of the ring is its radius. Application of the table to the construction of teethed wheels. To ascertain the circumference and diameter of a wheel, for a given num- ber of teeth and pitch. RULE. Multiply the pitch of the teeth by the number of teeth the wheel is to contain, and the product will be the circumference. EXAMPLE. The pitch of a tooth is to be 2 inches, and the num- ber of teeth 60 ; what will be the circumference and diameter of the wheel ? 60 number of teeth. 2|- pitch. 120" 30 7j 12)157* 13 H circumference of wheel. In column 8, page 17, opposite to this, is 4 feet 2 inches, which is the diameter required. NOTE. In the construction of these tables, where the last fraction has been equal to or exceeded .5, 1 has been added. Thus, 3.14159, if set down to four places of decimals, would be 3.1416. CIRCUMFERENCES OF AKGLED HOOPS. 27 CIRCUMFERENCES OF ANGLED HOOPS, From 6 inches to 10 feet. ANGLED OUTSIDE. Fig. 1. NOTE. The breadth of the edge flange (2 }) must be added to the inner diameter (10) of the hoop or ring required. INCH. 6. 10. FT. IN, 1 &3 1 6 II 10* lOf St 1 11 1 11 2 2 2 2 1 2 1 2 2 2 2| 2 2 3J 2 3J 2 3 2 41 2 4 2 5 2 51 2 5| 2 6 2 2 2 2 2 74 2 1 28 CIRCUMFERENCES OF ANGLED HOOPS. Diam Circum. Diam. Circum. Dinm. Circum. Diam. Circum. FT. I> FT. IN. FT. IN FT. IN. FT. IN. FT. JN. FT. IN. FT. JN. 2 2 6 41 2 9 8 Of 3 4 9 91 3 11 11 5f 2 2- r 6 4| 2 9^ I 8 It 3 4 9 9f 3 111 11 6i 2 2 : 6 5 2 9, f 8 l| 3 41 9 10 3 Hi 11 e| 2 2; ! 6 51 2 9 8 if 3 4| 9 lOf 3 ll| 11 6| 2 2- 6 5| 2 9- , 8 2i 3 41 9 lOf 3 111 11 71 2 2 6 6 2 9 8 2J 3 q 9 ll| 3 11| 11 7f 2 2; 6 6| 2 9- i . 8 2} 3 4f 9 IH 3 llf 11 8 2 2- 6 6f 2 9- !; 8 3i 3 4| 9 ll| 311|- 11 8f 2 3 6 7p 2 10 8 3f 3 5 10 Oi 4 11 8f 2 3 5 . 6 7: 2 10- r 8 4 3 51 10 Oi 4 01 11 9} 2 3 6 7: 2 10, 8 4| 3 51 10 0| 4 0| 11 9| 2 3| 6 8- 2 10 L 8 4f 3 5g 10 li 4 Of 11 9f 2 3. 6 8j- 2 10^ r 8 5i 3 51 10 U 4 Of 11 10|- 2 3j 6 9 2 10 [ 8 5| 3 U 10 2 4 Of 11 10| 2 2 3j 6 9|- 6 9 2 10, 2 10- 8 of 8 61 B 5f 3 5| 10 2f 10 2f 4 o| 11 10| 11 11^ 2 4 6 10 2 11 8 6| 3 6 10 31 4 1 11 11| 2 4J 6 10$ 2 11^ 8 7 3 6| 10 31 4 11 12 2 4-. 6 lOf 2 11 8 74 3 61 10 3| 4 li 12 0| 2 4* 6 ll| 2 11 8 7f 3 6| 10 4i 4 If 12 Of 2 4J . 6 111 2 11J 8 8 3 6i 10 4| 4 li 12 U 2 4? 6 ll| 2 11 8 8f 3 6| 10 5 4 l| 12 li 2 44 7 Oi 2 11| 8 8f 3 6f 10 51 4 If 12 l| 2 4 7 Of 2 11 8 9| 3 6| 10 5| 4 4 12 2i 2 5 7 1 3 8 9i 3 10 6 4 2 12 2 2 5J 7 If 3 0^ 8 9| 3 1 10 6| 4 21 12 2| 2 5< 7 1- 3 0; , 8 101 3 i 10 6| 4 21 12 31 2 5* 7 2 3 Oj : 8 10f 3 f 10 7i 4 2f 12 3f 2 5 7 2- 3 OJ - 8 11 3 \ 10 7|- 4 2i 12 4 2 5" 7 2v 3 Oi 8 llf 3 7f 10 74 4 1 12 4f 2 5, 7 3 3 r 8 llf 3 7f 10 81 4 2f 12 4f 2 5^ - 7 3 r 3 0] ; 9 01 3 7| 10 8| 4 2$ 12 5J 2 6 7 4 3 1 9 01 3 8 10 9 4 3 12 51 2 6] 2 6; 7 4 7 4} 3 1J 3 1- 9 Of 9 if 3 8i 3 81 10 9f 10 9f 4 31 4 31 12 5| 12 61 2 6j 7 5 3 ll | 9 11 Q Q3 d og 10 10| 4 3| 12 6| 2 fr 7 5| 3 1 9 if 3 81 10 101 4 3i 12 7 2 6i 7 5f 3 li 9 21 3 8| 10 10| 4 3f 12 7f 2 6i 7 6* 3 1* - 9 2f 3 8f 10 llg 4 3f 12 7f 2 6- 7 6j 3 1- 9 3 3 8f 10 llj 4 3| 12 8 2 7 7 6| 3 2 9 3f 3 9 10 11| 4 4 12 8| 2 7- 7 3 3 2^ r 9 3 3 91 11 Oi 4 4i 12 8f 2 7; 7 7| 3 2j - 9 4 3 91 11 Of 4 4| 12 91 2 7 7 8 3 2 : 9 4| 3 9J 11 1 4 4=| 12 91 2 7 2 7 7 8g 7 3 2 3 2 | 9 4| 9 51 3 91 3 9g 11 If 11 If 4 41 4 4f 12 9|- 12 101 2 7 7 ft- 3 2- 9 5f 3 9f 11 2| 4 4f 12 10| 2 7 7 9 39 Z \ 9 6 3 9| 11 21 4 4| 12 11 2 8 7 9 3 3 9 6| 3 10 11 2| 4 5 12 llf 2 8- 7 10 3 3, 9 6| 3 10 11 3| 4 5i 12 llf 2 8^ 7 10 3 3. 9 7 3 101 11 3| 4 5| 13 0| 2 8 7 10 3 3 9 7f 3 104 11 3| 4 5| 13 Of 2 8 7 11; 3 3- 9 7f 3 10i 11 4^ 4 5i 13 Of 2 8 7 11 3 3 9 8| 3 10| 11 4f 4 5| 13 l| 2 8 2 8 8 8 0$ 3 a- 3 3 9 81 9 a| 3 10* 3 10| 11 5 11 5| 4 5f 4 6| 13 l| 13 l| CIRCUMFERENCES OF ANGLED HOOPS. 29 Dism. ! Circ II 19 19 19 19 10]^ 19 llf 19 llf 20 30 CIRCUMFERENCES OF ANGLED HOOPS. Diam. Circnm. Diam. Circum. Diam. Circum. Diam. ; Circum. FT. IN. FT. IN. FT. IN FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. 6 10 20 Of 7 5 ' 21 84 8 23 5f 8 7 25 1| 6 104 6 101 20 Of 20 14, 7 5J 7 5^ 21 9| 21 9| 8 01 23 5-| 23 61 8 7* 8 71 25 21 25 2f 6 10} 20 14 7 5] 21 10 8 of 23 G| 8 7f 25 3 6-101 20 If 7 5i 21 lOf 8 Oi 23 6| 8 71 25 3f 6 10* 20 21 7 5| 21 lOf 8 M 23 7| 8 7| 25 3f 6 lOf 20 21 7 5i 21 114 8 Of 23 7| 8 7| 25 4| 6 lOf 20 2| 7 5, _' 21 111 8 Of 23 8 8 7| 25 4| 6 11 20 31 7 6 21 111 8 1 23 8f- 8 8 25 4-| 6 Hi 20 31 7 6 22 Of 8 14, 23 8f 8 8 25 51 6 Hi 20 4 7 C 22 0| 8 li 23 9 8 81 25 5| 6 llf 20 4f 7 6- - 22 Of 8 If 23 9f 8 8| 25 6 6 114 20 4f 7 6J 22 li 8 14 23 9f 8 84 1 25 61 6 llf 20 63 7 6; ' 22 if 8 If 23 10^ 8 8f : 25 4 6 llf 20 5 7 6; . 22 2 8 If 23 10| 8 ,8f i 25 7 6 11| 20 5| 7 6^ " 22 2f 8 if 23 10 8 8| 25 7f 7 20 61 7 7 22 21 8 2 23 Hi 8 9 25 71 7 01 20 4 7 7J 22 3} 8 24 23 llf 8 9J i 25 8| 7 ot 20 7 7 7; 22 3| 8 2i 24 8 9i 25 84 7 Of 7 04 20 7f 20 7f 7 7 22 34 22 4| 8 2| 8 21 24 Of 24 Of 8 9f 8 94 25 8| 7 Of 20 8 7 22 4 8 2| 24 l| 8 9| 25 9| 7 Of 20 8f 7 22 5 8 2f 24 14 8 9f 25 10 7 0| 20 8f 7 J 1 22 51 8 2| 24 1| 8 9| 25 10| 7 1 20 91 7 8 22 5| 8 3 24 21 8 10 25 10J 7 li 20 94 7 8] \ 22 6 8 34, 24 24 8 101 25 114 7 li 20 9| 7 8 : 22 6f 8 31 24 2| 8 10 25 111 7 l| 20 101 7 8: 22 6f 8 3f 24 3i 8 10 i 25 ll| 7 14 20 10| 7 8- 22 7$ 8 3i- 24 3| 8 10 26 0| 7 If 20 11 7 8- 22 74 8 3j 24 4 8 10 ! 26 01 7 If 20 llf 7 8- 22 7| 8 & 24 4f 8 lOf i 26 0| 7 If 20 llf 7 8- ' 22 8i 8 3| 24 4f 8 10; 26 1^ 7 2 21 7 9 22 8f 8 4 24 5| 8 11 26 lj 7 2J 21 04 7 9J ; 22 9 8 44 24 54 8 11| 26 2 7 2i 7 2| 21 04 21 l| 7 9 22 9f 22 91 8 4- 8 4 24 5| 24 6i 8 Hi 8 ll| 26 2f 26 2 7 24 21 14 7 9 22 10^ 8 4-- 24 6| 8 114 26 3 7 2f 21 l| 7 9 22 10| 8 4- 24 7 8 llf i 26 3 7 21 21 2i 7 9i 22 lOf 8 4 24 71 8 111 ' 26 3 7 2| 21 2| 7 9- 22 ll| 8 4| 24 7| 8 ll| 26 4 7 3 21 3 7 10 22 114 8 5 24 8 9 26 4 7 34 21 3f 7 10 22 11 4. 8 51 24 8f 9 04, 26 4 7 3 21 3f 7 10- 23 01 8 5i 24 8f 9 ! 26 5 7 3i 21 41 7 10 23 Of 8 5f 24 9k 9 ! 26 5 7 34 21 41 7-10- 23 1 8 5J 24 94 9 26 6 7 34 21 4| 7 10 23 If 8 o| 24 9| 9 ; 26 6f 7 3 21 51 7 Ifr 23 ll 8 5f 24 10j 9 ! 26 64 7 3J 21 5| 7 10 23 2| 8 5| 24 lOf 9 OJ ! 26 I] 7 4 21 6 7 11 23 24 8 6 24 11 9 1 26 11 7 44, 21 61 7 11 \ 23 2| 8 64, 24 llf 9 14, 26 7J 7 4- 21 6| 7 11- I 23 31 8 6i 24 llf 9 1 26 81 7 4 21 7 7 11 23 3$ 8 6| 25 0| 9 li 26 8J 7 4 21 7f 7 11 23 4 8 6| 25 04 9 1^ 26 9 7 4 21 7f 7 11 23 41 8 6f 25 0| 9 1^ ! 26 9| 7 4- 7 4 21 84 21 8f 7 11 7 11 23 4 23 5 8 6| 8 6| 25 l| 9 If 9 if i 26 9| Diam. CIR Circum. CUMFER Diam. ENCES C Circum. >F ANGI Diam. .ED HOC Circum. )PS. Diam. 3 Circum. 9 2 26 lOf 26 10| 9 4i 9 4| 27 5f 27 61 9 7 28 H 28 l| 9 9i 9 9f 28 8f 28 8i 9 2| 26 111 9 4| 27 6| 9 71 28 If 9 9| 28 9^ 9 2| 26 lli 9 4 27 6| 9 7| 28 2i 9 9f 28 9i 9 2* 26 ll| 9 5 27 7i 9 1\ 28 2i- 9 10 28 9| 9 2| 27 Oi 9 51 27 74 9 7-| 28 2} 9 10^ 28 101 9 2f 27 0| 9 5i 27 8 9 7f 28 31 9 101 28 lOf 9 2| 27 1 9 5-f 27 8f 9 7| 28 3| 9 10-1 28 11 9 3 27 If 9 51 27 8-| 9 8 28 4 9 10| 28 11 9 34 27 If 9 5| 27 9 9 8i 28 4f 9 10| 28 11^ 9 31 27 2i 9 5f 27 9f 9 8i 28 4f 9 lOf 29 9 3f 27 21 9 5| 27 9f 9 8| 28 oj 9 10| 29 9 31 27 2f 9 6 27 101 9 84 28 5.1, 9 11 29 O; 9 3 27 34, 9 61 27 101 9 8-| 28 5^- 9 Hi 29 1 9 3f 9 3| 27 31 27 3| 9 61 9 6| 27 10| 27 Hi 9 8f 9 8| 28 6i 28 6-f 9 111 9 ll| 29 1 29 1^ 9 4 27 41 27 ll| 9 9 28 7 9 1H 29 2 9 4^ 27 4-f 9 6 28 9 '9| 28 7f 9 ll| 29 2 9 4-1 9 4| 27 5 27 5f 9 6f 9 6| 28 Of 28 Of 9 9f 28 7f 28 8 9 111 9 ll| 29 3 29 3{ EXAMPLE. The inner diameter of a hoop of 2 inches angled iron (fig. 1, p. 27) is to be 10 inches ; what is the length of the bar re- quired ? = 12^, and the circumference for this (page 27) is 3 feet and f ths of an inch. The preceding table is calculated upon the proportion of the diam- eter of a ring (of angled metal) to its circumference, being as 1 to 2.9312. 32 CIRCUMFERENCES OF ANGLED HOOPS. CIRCUMFERENCES OF ANGLED HOOPS, From 6 inches to 10 feet. ANGLED INSIDE. Fig. NOTE. The breadth of the inner flange must be taken from the outer diameter of the ring or hoop required. Cireunu Diam. i Cirenm. 7. 8. 9. 2 3 3 5 81 10 101 101 1 10 1 11 i lit 1 111 1 11* 1 111 1 llf ml 2 2 04 2 *> 3 2 0-5 2 Q\ 2 1 2 1 2 1, 2 1 2 1 2 1 2 1^ 2 li 5 111 6 03 6 Of 6 1-1 6 2 6 2? G 3| G 3f 6 41 6 4 6 5 6 5i 6 of 6 GI G Gf 6 7 G 7|- 6 8 6 8| G 8 G 9| G 9f G lOi- 6 lOf G 11 6 111 6 11 -J 7 Of 7 Of 7 li 7 li 7 2~ 7 2f 7 2 7 3f 7 3f 7 4| 7 4| CIRCUMFERENCES OF ANGLED HOOPS. CIRCUMFERENCES OF ANGLED HOOPS. Diarn. Circum. Diam. Circum. Diam. Circum. Diam. Cinroro, IT, IN. FT. IN. FT. IN. PT. IN. FT. IN. FT. IN. FT. IN. FT. IN, 4 6 15 5 5 1 17 4f 5 8 19 4| 6 3 21 4| 4 6 15 5f 5 1| 17 54 5 8^ 19 5| 6 31 21 oi 4 6i- 15 5f 5 l| 17 5f 5 8 19 5f 6 31 21 5f 4 6 15 6i 5 If 17 6i 5 8| 19 V s 6 3f 21 6|- 4 6 15 6| 5 11 17 6 5 8| 19 6| 6 31 21 61 4 6^ 15 7 5 if 17 7 5 8f 19 7 6 3| 21 1" 4 6; 4 6| 15 7J 15 7| 5 if 5 if 17 71 17 7| 5 4 5 8| 19 7f 19 7| 6 3f 6 3| 21 7f 21 7| 4 7 1 15 8| 5 2 17 8| 5 9 19 81 6 4 21 81 4 7 1 15 81 5 21 17 8f 5 9i 19 8f 6 4 21 8f 4 7* ! 15 91 5 21 17 &i 5 9^ 19 H 6 4i 21 91 4 7 ! 15 9| 5 2| 17 9| 5 9f 19 9| 6 4| 21 91 4 7 ! 15 10 5 21 17 10 5 91 19 10 6 41 21 10 4 7] 1 15 101 5 2| 17 10| 5 9| 19 101 6 4| 21 lOf 4 7^ 15 10| 5 2f 17 lOf 5 9f 19 10J 6 4f 21 10 4 7 i 15 llf 5 2| 17 ll| 5 9| 19 Hi 6 4 21 Hi 4 8 4 81 15 llf 16 Oi 5 3 5 3J 17 llf 18 0| 5 10 5 101 19 llf 20 01 6 5 6 5J 21 llf 22 01 4 8- 16 Of 5 3l 18 Of 5 101 20 0| 6 5i 22 Of 4 8 16 1 5 3] 18 1 5 10| 20 1 6 5| 22 1 4 8 16 If 5 3J 18 H 5 101 20 11 6 51 22 If 4 8 16 if 5 3f 18 If 5 10-f 20 l| 6 5| 22 \l 4 8f 16 2f 5 3i 18 2| 5 lOf 20 21 6 5f 22 21 4 8| 16 2f 5 3f 18 2f 5 10| 20 2f 6 4 22 2f 4 9 16 31 5 4 18 31 5 11 20 31 6 6 22 3i 4 9 16 3f 5 4J 18 4 5 11| 20 3i 6 6J 22 3| 4 9, 16 4 5 41 18 4 5 Hi 20 4 6 61 22 4 4 9j 16 41 5 4f 18 4| 5 llf 20 41 6 6| 22 4| 4 9i 16 4 5 41 18 4| 5 1U 20 4| 6 61 22 4| 4 9 16 5f 5 4| 18 5f 5 llf 20 5i 6 6| 22 51 4 9- 16 5f 5 4f 18 5f 5 llf 20 5f 6 6f 22 5f 4 9 16 61 5 4 18 6} 5 ll| 20 61 6 6J 22 6| 410 16 6f 5 5 18 6| 6 20 6| 6 7 22 61 4 10 16 7 '5 5 18 7 6 0| 20 7 6 7 22 7 4 10 16 7| 5 5 18 7 6 OJ 20 7 6 7 22 7f 4 10 16 7 5 5 18 7| 6 Of 20 7| 6 7 22 7f 4 10 16 8 5 5 18 81 6 01 20 8i 6 7 22 81 4 10 16 8- 5 5 18 8f 6 0| 20 8f 6 7 22 8| 4 10; 16 9 5 5 18 9 6 Of 20 91 6 7 22 9| 410| 16 9 5 5; 18 If 6 0| 20 9| 6 7 22 91 4 11 16 10 5 6 18 10 6 1 20 10 6 8 22 10 4 11 16 101 5 6J 18 101 6 1| 20 101 6 81 i 22 lOf 4 11 16 10J 5 6 18 lOl 6 li 20 10| 6 S| 1 22 10| 4 11 16 llf 5 6f 18 111 6 If 20 ll| 6 8f 22 Hi 4 11 16 llf 5 61 18 llf 6 11 20 llf 6 81 22 llf 4 11 17 0| 5 6| 19 Of 6 H 21 0| 6 8-| 23 01 4 Hi 17 Of 5 6f 19 0|- 6 If 21 Of 6 8f i 23 Ok 4 11 17 1 5 6| 19 1 6 l| 21 1 6 8| 23 1 5 17 14 5 7 19 H 6 2 21 If 6 9 23 If 5 c} 17 1' 5 7* 19 ll 6 2J 21 1| 6 9 23 if 5 W 17 2 5 7 19 2| 6 21 21 2-| 6 91 23 21 5 0| 17 2 5 7 19 2f 6 2f 21 2f 6 9f 23 2| & 0^ 17 3 5 7 19 3| 6 21 21 31 6 91 23 S$ 5 0] 17 3 5 7 19 3| 6 2| 21 3| 6 9f 23 3l 5 (M 17 4 5 7 19 4 6 2f 21 4 6 9f 23 4 5 OJ 17 4* 5 7 19 4J 6 2| 21 4g 6 9| ! 23 4| CIRCUMFERENCES OF AKGLED HOOPS. 35 Diam. Circum. Diam. Circum. Diam. Ciicum. Diam. Circum. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. FT. IN. 6 10 6 IQi 23 4 23 5i 7 5 7 5i 25 4f 25 5i 8 8 01 - 27 4f 27 5i 8 7 8 7| 29 4f 29 54 6 101 23 64 7 4 25 5| 8 0; , 27 5| 8 71 29 51 6 10| 23 6i 7 5f 25 6 8 0; ' : 27 6 8 7f 29 6 6 101 23 6| 7 5 25 6 8 0- 27 6| 8 1\ 29 61 6 10| 23 7 7 5f 25 7 8 0^ 27 6| 8 7-| 29 6| 6 lOf 23 7| 7 5f 25 7f 8 0^ 27 7| 8 7f 29 7| 6 10| 23 7f 7 5| 25 7f 8 0- 27 7f 8 7| 29 7| 6 11 23 8J 7 6 25 81 8 1 27 81 8 8 29 81 6 11| 23 8f 7 6i 25 8f 8 1J f7J 27 8| 8 8i 29 8| 6 111 23 9i 7 6J 25 9 8 1; 27 9 8 8i 29 9 6 llf 23 9-| 7 6f 25 9* 8 1 [j 27 91 8 8-| 29 9| 6 11 23 10 7 6J 25 10 8 1- a 27 9| 8 81 29 9| 6 llf 23 lOf 7 6| 25 lOf 8 1 f 27 lOf 8 8f 29 10^ 6 llf 23 10 7 6x 25 lOf 8 k 27 lOf 8 8f 29 10J 6 llf 23 lli 7 6| 25 HI 8 1( ri 27 Hi 8 8| 29 ll| 7 23 llf 7 7 25 llf 8 2 27 llf 8 9 29 11| 01 24 Oi 7 7| 26 8 2J 28 8 91 30 OJ 24 7 7| 26 01 8 2 : 28 0| 8 91 30 Oi Of 24 1 7 7<[ 26 1 8 2 28 0| 8 9f 30 Of 0* 24 If 7 7A 26 If 8 2- 28 If 8 9| 30 1| Of 24 If 7 7| 26 If 8 2 28 If 8 9| 30 If Of 24 21 7 7- 26 2i 8 2| 28 2i 8 9f 30 2| 7 Of 24 2f 7 7| 26 2f 8 2^ r 28 2f 8 9| 30 2| 7 24 3 8 26 3 8 3 28 3 8 10 30 3 7 i 7 1 24 31 24 4" H 8i 26 31 26 4 8 3J 8 3- ' 28 31 28 3J 8 10| 8 10| 30 3i 30 3^ 7 I 24 4f 8f 26 4f 8 3\ [ 28 4f 8 lOf 30 4 7 I 24 4| 8i 26 4f 8 3 28 4f 8 101 30 4^ 7 1 24 5i 7 8f 26 5| 8 3j ,. . 28 5i 8 lOf 30 5, 7 f ,24 5| 7 8f 26 5| 8 3^ 28 5f 8 lOf 30 5 7 ! 24 61 7 8f 26 6 8 3] 28 6 8 10| 30 6 7 2 24 6| 7 9 26 6 8 4 28 6| 8 11 30 61 7 2i 24 7 7 91 26 6| 8 4^ 28 6| 8 \\\ 30 fr 7 21 24 7f 7 9i 26 7f 8 4 28 7f 8 HI 30 7 7 2| 24 7f 7 9| 26 7f 8 4:- : 28 7f 8 llf 30 7 7 2* 24 8i 7 91 26 8i 8 -4 28 81 8 IH 30 8 7 2f 24 8| 7 9| 26 8| 8 4 28 8f 8 llf 30 8 7 2f 24 9i 7 9f 26 9 8 d ' 28 9 8 llf 30 9 7 2| 24 9 7 9| 26 9J 8 4: 28 91 '8 ll| 30 9| 7 3 24 10 7 10 26 9 8 5 28 9| 9 30 9 7 3i 24 lOf 7 10i 26 lOf 8 5\ 28 lOf 9 30 10 7 3i 7 3f 24 10| 24 ll| 7 101 7 lOf 26 lOf 26 HI 8 5, 8 5 28 lOf 28 Hi 9 of 9 Of 30 10 30 H 7 3i 24 llf 7 101 26 111 8 5 28 llf 9 Of 30 11 7 3| 25 01 7 10| 27 8 5 29 9 Of 31 7 3| 25 0| 7 lOf 27 01 8 5; 29 0^ 9 Of 31 Oi 7 3f 25 1 7 10| 27 0| 8 b\ 29 Of 9 0| 31 Of 7 4 25 If 7 11 27 If 8 6 29 U 9 1 31 U 7 41 7 41 25 If 25 2i 7 HI 7 111 27 If 27 21 8 <; 8 6^ 29 If 29 2| 9 11 9 li 31 If 31 2| 7 4| 25 2f 7 111 27 2f 8 6 29 2f 9 If 31 2f 7 4 25 3 7 1H 27 3 8 6 29 3 9 H 31 3 7 4f 25 3 7 ll| 27 3f 8 6 29 3J 9 If 31 3i 7 4f 25 4 7 llf 27 3| 8 6; 29 3| 9 If 31 3| 7 4$ 25 4| 7 ll| 27 4| 8 6 29 4f 9 1| 31 4j 86 CIRCUMFERENCES OF ANGLED HOOPS. Circum. Diam. 9 6| FT. IN 9 7 9 7* 9 '9 S> 9 32 9| 33 6" EXAMPLE. The outer diameter of a hoop of 2^ inch angled iron (tig. 2, p. 32) is to be 12^ inches ; what is the required length of the hoop? 12^ 2^ = 10, and the circumference for this (page 32) is 2 feet 10 inches. The preceding table is calculated upon the proportion of the diam- eter of a ring (of angled metal) to its circumference, being as 1 to 3.4248. CUTTING OF BOILER PLATES, ETC. 37 CUTTING OF BOILER PLATES, MATERIALS FOR ROOF- ING, AND THE COVERING OF SOLIDS. Under this head it is thought necessary to illustrate only such of the cases as occur in general practice. 1. To ascertain the covering for a cone, A B C,fig. 1. d From B as a centre, with the radius B C, describe the arc of a circle C d ; make C d equal in length to the circumference of the base of the cone (which can be found by a reference to the table of the circumferences of a circle) and join B d ; then the figure determined by B d C will be that of the required surface of the cone. 2. To ascertain the surface of an envelope for a frustum of a cone, . 2. Produce A C, B D, until they meet at E ; then from E as a cen- tre, with the radii E A and E C, describe the arcs B f and D g, and set off D g equal to the cir- cumference of the base of the cone, and join E g ; then the fig- ure B D f g, will be that of the required surface of the frustum. 38 CUTTING OP BOILER PLATES, COVERING 3. To ascertain the surface of an envelope for a given cylinder, /* O. Let A B C D be the given cylinder, having one of its ends at an angle to its sides, as A B. Upon the base C D draw a semicircle, which divide into a num- ber of equal parts (the more there are the more correct will be the result required), as 1, 2, 3, 4, 5, and 6 ; from the points draw the lines 1 1, 2 2, 3 3, &c,, parallel to the plane of the cylinder; then set off, as in Jig. 4, the line E F G, equal in length to the circumfer- " I ' iS ^ ^ i - I i i 1 1 E 3 2 G ence of the base of the cylinder, or twice the semicircle C o D; upon E F G mark off on each side of F the same number of equal distances as in the semicircle C o D, and draw lines, as F h, 1 1,22, 3 3, &c., perpendicular to E F G ; make F h equal in length to A C, and E i, G k, each equal to D B, and also each of the perpendicu- lars equal to the lines bearing the same figures, as 1 1, 2 2, 3 3, &c. ; then a line traced through these points will form a side of , the en- velope, the whole of which is contained in the figure E i k G. NOTE. This problem is a very useful one to boiler-makers and coppersmiths who are in the habit of making pipes to join each other at any given angle the shape of the plate of metal for making which will be readily found by the fore- going rule. TO DOMES, AND VARIOUS FIGURES. 39 COVERING OF CIRCULAR ROOFS, ETC. Circular roofs may be covered upon two different principles : First Method. Assume the vertical section or axis to be divided into a number of small equal parts, and the roof or figure cut by planes through the points of division parallel to the base, and then consider the portions of the figure as so many frustums of cones ; the surface of each frustum can then be determined as by rule 2, p. 37. Second Method. Divide the circumference of the base into a num- ber of small equal parts, and assume sections to be made perpendic- ularly through these points of division ; then estimate the surface of each of these divisions on the surface of the figure. 4. To cover a dome by the first method. Let F A H, fi D TO DOMES, AND VARIOUS FIGURES. 47 in. . in. in. : : 18 : slant of edge of cone, or radius of circle of 4i the outer edge of the template. 72~ _9 "324 inches. The diameter of the semicircular ends be- ing 9 inches, the circumference of each part will be 9x3.1416-^-2 = 28.2744-^2 = 14.13 inches for the larger end, and for the versed sine proceed as before shown. 324 being the radius of the arc, and 14.13-f-2=7.06 half the chord of the arc ; therefore, 324 7.06 324 7.06 c 2 , 49.8436=c i 3 , and 104976 - 49.8436 = 104926.2, the square root of which is 323.9, which, when subtract- ed from 324, gives ,l=f i, the versed sine of arc c fd of outer edge of template,^. 15. The diameter of the small side of the semicircular ends will be (9 ix2) 8 inches, consequently, the circumference of 8x3.1416 = 26.70 2 : 2 inches. each will be = 13.35 NOTE. In these examples it will be perceived that the length of the chord is measured upon the plate from the length of the curve of the arc ; this is not strictly correct, as the chord is shorter than the arc ; this difference, however, is so little in or- dinary cases, that is, the example, p. 45, being but .16 of an inch, that it was considered an unnecessary element to bring into the calculation for ordinary practice, inasmuch as it involves a complexity at variance with the purpose of these rules. In cases, however, requiring exactness of dimension, the manner of proceeding is as follows : To find the chord of the arc. Multiply the versed sine by 2, and subtract the product from the diameter; then subtract the square of the remainder from the square of the diameter, and the square root of the remainder will give the chord required. WEIGHT OF SQUARE ROLLED IRON. WROUGHT IRON. WROUGHT IRON expands 14 ^ o00 of its length for one degree of heat; will bear on a square inch, without permanent alteration, 17,800 Ibs., and an extension in length of j^Vo 5 its cohesive force is diminished 3^7 by an increase of 1 degree of heat. Compared with cast iron, its strength is 1.12 times, its extensibility 0.86 times, and its stiffness 1.3 times. WEIGHT OF SQUARE ROLLED IRON, From -f^th of an inch to 12 inches square. ONE FOOT IN LENGTH. Size in I Weight in inches. | pounds. Size in inches. Weight in pounds. Size in inches. Weight in pounds. Size in inches. Weight in pounds. jjy .0132 2.1 19.063 5. 106.931 8.f 266.193 .0528 24 21.122 5 't 111.737 9. 273.744 s. .1188 2.| 23.287 5.1 116.647 9.i 281.401 i .2112 2.1 25.558 6. 121.164 9.| 289.163 JL .3300 2. 1 27.934 6.4 126.786 9.1 297.031 $ .4753 3. 30.416 6.- 132.014 9.1 305.004 i s5> .6469 3.4 33.003 6. 137.347 9.1 313.084 i .8449 3-i 35.697 6. 142.786 9.f 321.269 1.069 3. 1 38.495 6. 148.331 9.1 329.559 1.320 1.597 3.i 3.| 41.400 44.410 8.1 e.j 153.981 159.737 10. 10.1 337.955 346.457 , 1.901 3 -f 47.525 / . 165.598 10.1 355.064 is 2.231 3.| 50.746 74 171.565 10. | 363.777 1 2.587 4. 54.073 7-1 177.638 10.1 372.597 L| 2.970 4.J 57.505 7-1 183.816 10.|- 381.520 1. 3.380 41 61.043 7.1 190.100 10. f 390.550 1.1 4.277 4.| 64.687 7.1 196.489 10. 1 399.685 1.1 5.281 4.1 68.436 7-f 202.984 11. 408.926 l.| 6.389 4.1 72.291 7.| 209.585 11. i 418.272 1.1 ll 7.604 8.924 t:t 76.251 80.317 8. 8.1 216.291 223.103 11.1 11.1 427.725 437.282 l.f 10.350 5. 84.489 8.1 230.021 11.1 446.946 1. 11.881 54 88.766 8. f 237.044 11. 1 456.715 2. 13.518 5 i 93.149 8.1 244.173 11.1 466.589 2 1 15 262 5.1 97.637 8.| 251.407 11. 1 476.570 y 17.109 4 102.232 8.f 258.747 12. 486.656 WEIGHT OF WROUGHT IRON SHAFTING. 49 WEIGHT OF ROUND ROLLED IRON AND SHAFTING, From ^th of an inch to 30 inches diameter. ONE FOOT IN LENGTH. Diameter iu inches. Weight in pounds. Diameter in inches. Weight in pounds. Dianwter in inches. Weight is pounds. TS .0104 4.J 50.803 9.f 245.889 .0415 44 53.748 9.f 252.317 Tff .0933 4.f 56.775 9.J 258.828 i .1659 4.f 59.886 10. 265.422 i5 .2592 4,| 63.079 104 272.190 f .3733 5. 66.355 10.1 278.859 JHJ .5080 5.i 69.715 10. 285.702 1 .6636 5.'| 73.157 10. ^ 292.628 ae .8398 5.| 76.682 10. | 299.636 1.037 5.1 80.290 10. f 306.729 li 1.255 *** 83.981 10. 1 313.904 I 1.493 1.752 5 'f 87.755 91.612 11. 11.1 321.162 328.502 | 2.032 6. 95.552 11.1 335.926 ^f 2.333 6.| 99.575 11. 1 343.432 1. 2.654 64 103.681 n.l 351.022 14 3.359 6.f 107.869 11. | 358.694 1.1 4.147 64 112.140 ii.l 366.449 l.| 5.028 6.| 116.505 n.| 374.288 1.1 1-1 5.922 7.009 6 "t 120.943 125.463 12. 12.1 382.208 390.212 1-f 8.129 7. 130.057 12.1 398.300 l.f 9.331 74 134.753 12. | 406.470 2. 10.617 7.1 139.522 12.1 414.722 2 4 11.985 7-f 144.375 12. | 423.059 2 -l 13.437 14.971 7 't 149.300 154.318 12. | 12. | 431.477 439.979 1:1 16.589 18.259 20.073 p 159.419 164.603 169.870 13. 134 13. | 448.564 457.232 465.982 24 21.939 84 175.220 13 2. 474.816 3. 23.888 8.1 180.653 134 483.732 34 25.920 8.1 186.169 13.| 492.732 3. 28.035 8.| 191.767 13. f 501.814 3.^- 30.233 8.f 197.449 13. | 510.980 3'. S.l 3.| 32.514 34.878 37.325 39.855 8.| 9. 94 203.214 209.061 214.992 221.005 14. 144 14.1 14. | 520.228 529.559 538.973 548.470 4. 42.468. 9.1 227.102 14.1 558.050 1! 45.163 47.942 9. jf 233.281 239.544 14. f 14. | 567.713 577.459 50 WEIGHT OF WROUGHT IRON SHAFTING. Diameter in inches. Weight in pounds. Diameter in inches. Weight in pounds. Diameter in inches. Weight in pounds. 144 587.288 20. 1061.689 25.1 1692.232 15. 597.200 20.1 1088.397 25.} 1725.908 6171273 20.} 1115.437 25. f 1759.915 15 .*} 637.677 20. 1 1142.809 26. 1794.254 15. | 658.413 21. 1170.512 26.1 1828.925 16. 679.481 21.1 1198.547 26.} 1863.927 16 i 700.881 21.} 1226.915 26. f 1899.262 16.'* 7221612 21. f 1255.613 27. 1934.928 16. | 744.675 22. 1284.644 27.1 1970.926 17. 767.070 22.1 1313.006 27.} 2007.256 789.797 22.} 1343.700 27. | 2043.917 17 'I 8121855 22. f 1373.726 28. 2080.910 17. f 836.246 23. 1404.083 28.1 2118.235 18. 859.968 23.1 1434.773 28.1 2155.892 18.1 884.022 23.} 1465.794 28. f 2193.880 18.} 908.408 23. f 1487.147 29. 2232.207 18. 1 933.125 24. 1528.832 29.1 2270.853 19. 958.174 24.1 1560.849 29.1 2309.837 19.1 983.555 24.} 1593.197 29. | 2359.152 1009 1268 24. 1 1625.877 30. 2388.800 gj 1035.313 25. 1658.889 WEIGHT OF FLAT ROLLED IRON. 51 WEIGHT OF FLAT ROLLED LEON, From i X J Inch to 5| X 6 Inches, AND ONE FOOT IN LENGTH. Breadth in inches. Thickness in inches. Weight in pounds. Breadth in inches. Thickness in inches. Weight in pounds. Breadth n inches. Thickness in inches. Weight in pounds. 4 0.211 1-1 0.580 1-1 M 8.132 0.482 1.161 1,1 8.871 0.634 1.742 !! 9.610 i \ 0.264 0.528 ;: 2.325 2.904 M '' 0.792 1.584 0.792 . 3.484 , ; 2.376 1.056 rt 4.065 3.168 1 '] *1 .i 1 0.316 0.633 0.950 1.265 1.584 14 1:1 4.646 5.227 5.808 0.633 1.266 1.900 T-(T-llH 1 3.960 4.752 5.544 6.336 7.129 7.'921 1 4 0.369 1 2.535 1 8.713 ^i. 0.738 f 3.168 l^ 9.505 8 1.108 t 8. 3.802 J t 10.297 "1 1.477 i 4.435 i! 11.089 :| 1.846 2.217 1. 14 5.069 5.703 2. 0.845 1.689 i. 0.422 1.1 6.337 2.534 0.845 1-1 6.970 3 379 1.267 1.1 0.686 4.224 1.690 1.372 5.069 2.112 J 2.059 m 5.914 2.534 2.746 6.758 2.956 t . 3.432 7.604 14 .. 0.475 .. 4.119 8.448 .. 0.950 ,! 4.805 9.294 . 1.425 1. 5.492 10.138 .- 1.901 14 6.178 LI 10.983 .. 2.375 1.1 6.864 l.f 11.828 2.850 1.1 7.551 l.| 12.673 ,. 3.326 1 i 8.237 24 898 i. 3.802 M 4 0.739 8 '. 1.795 i.j, 0.528 i 1.479 2.693 1.056 .. 2.218 ,. 3.591 .. 1.584 .. 2.957 ij 4.488 .. 2.112 .. 3.696 ,. 5.386 .. 2.640 ,. 4.435 . 6.283 . 3.168 5.178 1. 7.181 .. 3.696 i! . 5.914 14 8.079 i. 4.224 14 6.653 l.| 8.977 l.i 4.752 14 7.393 1-1 9.874 52 WEIGHT OP FLAT ROLLED IRON. Breadth in inches. Thickness in inches. Weight in pounds. Breadth in inches. Thickness in inches. Weight in pounds. Breadth in inches. Thickness in inches. Weight in pounds. 24 1.1 10.772 24 2. 16.896 24 l.f 13.360 1'f 11.670 2.- 17.952 1-1 14.574 l.f 12.567 2.^ 19.008 1-1 15.789 l.| 13.465 2. 20.064 l.f 17.003 2. 14.362 " 2. f 1.109 1-1 18.218 24 .950 ** a 2.218 2. 19.432 1.900 3.327 2 4 20. 47 2.851 4.436 2-i 21.861 3.802 5.545 2.4 23.076 4.752 6.654 2. 1 24.290 5.703 '" . - 7.763 2-1 25.505 6.653 1! 8.872 2-f 26.719 . 7.604 14 9.981 3. _1 1.267 i 8.554 i.l 11.090 ! 2.535 "1 9.505 i.| 12.199 1 3.802 8 10.455 i.l 13.308 _JL 5.069 1 11.406 i.l 14.417 1 6.337 f 12.356 i.f 15.526 f 7.604 l.f 13.307 lit 16.635 I 8.871 l.| 14.257 2. 17.744 1. 10.138 2. 15.208 2-1 18.853 },} 11.406 24 16.158 2.: 19.962 1 I 12.673 2. 1.003 2. 21.071 l-I 13.940 *"8 2.006 2. 22.180 1.1 15.208 3.009 2.f 1.162 I.I 16.475 4.013 * 2.323 L -i 17.742 5.016 3.485 14 19.010 ;, 6.019 4.647 2. 20.277 - 7.022 ;i[ 5.808 2 4 22.811 1.' 8.025 I 6.970 2.| 25.346 i'4 9.028 4 8.132 2.f 27.881 14 10.032 1. 9.294 3.i .1 1.373 t 1.1 11.035 i.J 10.455 .i 2.746 14 12.038 i.j 11.617 .1 4.119 l.f 13.042 l. 12.779 .1 5.492 i.l 14.045 l. 13.940 .1 6.865 l.| 15.048 l.; 15.102 '-~M 8.237 2. 16.051 lJ 16.264 .1 9.610 2.J 17.054 iJ 17.425 1. 10.983 2.^ 18.057 2. 18.587 1-i 12.356 24 1.056 2.112 2 4 2-1 19.749 20.910 1. 1. ,13.730 15.102 3.168 2.1 22.072 I.I 16.475 4.224 2.1 23.234 l.f 17.848 "; ~ 5.280 2-1 24.395 l.f 19.221 *1 6.336 24 1.215 14 20.594 t l 7.392 8 2.429 2. 21.967 l'. 8 8.448 'A 3.644 2. 24.712 9.504 m . 4.858 2.| 27.458 10.560 f . 6.072 2.f 30.204 J 11.616 ,j 7.287 3. 32.950 12.672 ,. 8.502 34 4 1.479 f . 13.728 1. 9.716 t i 2.957 .. 14.784 14 10.931 1 4.436 ,. 15.840 1-1 12.145 4 5.914 WEIGHT OP FLAT ROLLED IKON. Breadth Thickness Weight in in inches, in inches, pounds. Breadth in inches. Thickness in inches. Weight in pounds. Breadth in inches. Thickness in inches. Weight in pounds. 34 f 7.393 4-4 4 1.795 5. 1. 16.897 f 8.871 ,i 3.591 1.1 21.122 1 10.350 4 7.181 I.i 25.346 1. 11.828 i 10.772 1.1 29.570 13.307 1. 14.364 2. 33.795 14.785 i.* 17.953 2.1 38.019 - 16.264 i.I 21.544 2.1 42.243 17.742 i.I 25.135 2.1 46.468 19.221 2. 28.725 8. 50.692 20.699 2.1 32.316 3.1 54.916 22.178 2.1 35.907 3.1 59.140 2. 23.656 2 \ 39.497 3-1 63.365 2.1 26.613 3. 43.088 4. 67.589 2.1 29.570 46.679 4-i 71.813 2.1 32.527 50.269 44 76.038 3. 35.485 53.860 4.i 80.262 3.1 38.441 4.. 57.450 5.1 4.436 3.f 4 1.584 44 l 3.802 8.871 .1 3.168 1 7.604 13.307 -ir 4.752 .1 11.406 1. 17.742 4 6.336 1. 15.208 li 22.178 !" 7.921 1.1 19.010 1.1 26.613 . 9.505 1-1 22.812 1.1 31.049 z 11.089 1.1 26.614 2. 35.484 i 12.673 2. 30.415 2.1 39.920 14 14.257 2.1 34.217 2.1 44.355 1.1 15.841 2-i 38.019 2.T 48.791 i.f 17.425 2.f 41.820 3. 53.226 i.I 19.009 3. 45.623 3.1 57.662 i.f 20.594 3-i 49.425 3.1. 62.097 i.j 22.178 3.$ 53.226 3.f 66.533 i. 23.762 B.I 57.028 4. 70.968 2. 25.346 4. 60.830 4.1 75.404 2.1 28.514 4.1 64.632 79.839 24 31.682 4.f ^ 4.013 4 f 84.275 Sfei 34.851 *T 8.026 5.'* 88.710 3. 38.019 I 12.039 54 4.647 3.i 41.187 J 16.052 9.294 34 44.355 i-i 20.066 13.940 4. .i 1.690 14 24.079 ' 1. 18.587 .1 3.380 i.i 28.092 I.i 23.234 .1 6.759 2. 32.105 1.1 27.881 1 10.138 2.1 36.118 1.} 32.527 1. 13.518 2.1 40.131 2. 37.174 1.1 16.897 2.1 44.144 2.1 41.821 p 20.277 23.656 3. 48.157 52.170 2.| 46.468 51.114 2. 27.036 3.1 56.184 3'.* 55.761 2.1 30.415 3.1 60.197 3.1 60.408 24 33.795 4. 64.210 3.} 65.055 2.f 37.174 4.1 68.223 69.701 3. 40.554 4.f 72.235 4]* 74.348 3.i 43.933 5. % 4.224 4.1 78.995 3.| 47.313 "j 8 449 4.|- 83.642 3.f 50.692 I 12.673! 4-1 88.288 54 WEIGHT OF FLAT ROLLED IRON. Breadth in inches. Thickness in inches. Weight in pounds. Breadth in inches. Thickness Weight in in inches. pounds. Breadth in inches. Thickness in inches. Weight in pounds. 54 5. 92.935 5.f l.f 34.006 5.| 3.f 72.870 5.J 97.582 2. ,38.864 4. 77.728 5.f 4.858 2.J ! 43.722 4 -i 82.585 *f 9.716 2.1 48.580 4.1 87.443 *1 14.574 2.1 I 53.437 4*1 92.301 ll 19.432 3. 58.296 5. 97.159 n 24.290 29.148 3.i 63.154 3.| ! 68.012 a 102.017 106.876 J 6. 116.592 APPLICATION OF THE PRECEDING TABLES. The dimensions of a bolt or bar of iron being given, find its weight in the appropriate column, which is for the length of one foot ; multiply this weight by the number of feet and parts thereof in the bolt or bar, and the product is the weight. EXAMPLE 1. What is the weight of a BAR OF SQUARE IRON !$ inches square and 6^ feet in length? Opposite to 1 inches in size, in table at page 48, is 7.604 Ibs., which is the weight of such a bar for a length of one foot. Hence 7.604 Ibs., multiplied by 6 feet, 4562T 3802 is equal to 49.426 pounds. If the lesser denomination of ounces is required, the result is obtained as follows : Multiply the remainder by 16, pointing off the decimals as in multiplication of decimals, and the figures remaining on the left of the point indicate the number of ounces. Thus, .426 of a Ib. = .426 16 6.816 ounces. The weight, then, is 49 Ibs. 6 ounces and -fthfc- If the weight for less than afoot in length was required, the readiest operation is this : EXAMPLE 2. What is the weight of a bar or bolt 6 inches square and 9f inches long ? On page 48, column 5th, opposite to 6, is 132.040, which is the weight for a foot in length. WEIGHT OF HOUND ROLLED IRON. 55 6jrXl2 inches ^132.040 " is~T = G6.020 3. " is i of 6= 33.010 .* " is | of 3= 5.5016 v .i " isiofj= 2.7508 94 =107.2824, or 107 pounds and -ffififc. EXAMPLE 3. What is the weight of a BOLT OR ROD or IRON 2 inches in diameter and 9 f feet in length ? Opposite to 2 inches in column 1st, page 49, is 10.617, which is the weight of such a rod for the length of one foot. Hence 10.617 Ibs. 9f feet 95.553 5.308 2.654 103.515 pounds. EXAMPLE 4. What is the weight of a BAR OF FLAT IRON of an inch in thickness by 5 inches in breadth, and 7 feet 6^ inches in length? Opposite to 5, and to in thickness, in column 9th, page 53, is 13.307 Ibs., which is the weight of such a bar for a length of one foot. Hence 13.307 7 feet 93.149 pounds. Then, to determine the weight for 6 inches, proceed as shown above, in example 2, or in the following manner : Divide the weight for one foot by 12 (12 inches), and the result is the weight for one inch in length. Thus ^=1-109. Then 1.109 multiplied by 6 6.654 554 is equal to 7.208 pounds, which, added to the 93.149 before obtained, is equal to 100.357 pounds. 56 CAST AND WROUGHT IRON AND LEAD. CAST IRON. To ascertain the weight of a cast iron BOLT or BAR, find the weight of a wrought iron bolt or bar of the same dimensions in the preced- ing tables, and from the weight deduct the -j^-th part ; Or, as 486.65 : 450.55 : : the weight in the table : to the weight re- quired. EXAMPLE. What is the weight of a piece of cast iron 4 X 3f X 12 inches ? In table, page 53, the weight of a piece of wrought iron of these dimensions is 50.692 Ibs. Then 486.65 : 450.55:: 50.692 : 46.93 Ibs. To find the weight of a piece of CAST or WROUGHT IRON of any size or shape. Find the number of cubic inches in the piece, multiply them by the weight of a cubic inch, and the product will be the weight in pounds, EXAMPLE 1. What is the weight of a block of WROUGHT IRON 10 inches square by 15 inches in length ? 10x10x15 = 1500 cubic inches. .2816 weight of a cubic inch of wrought iron. 442.4000 pounds. EXAMPLE 2. "What is the weight of a CAST IRON ball 15 inches in diameter? By table, page 62, a cast iron ball 15 inches in diameter = 176.7149 cubic inches. .2607 weight of a cubic inch of cast iron. 460.6957 pounds. LEAD. To ascertain the weight of Lead. RULE. Find the number of cubic inches in the piece, multiply them by .41015, and the product will be the weight in pounds. EXAMPLE. What is the weight of a leaden pipe 12 feet long, 3| inches in diameter, and 1 inch thick ? Area of (34 + 1 + 1)= 25.967 " " 3| = 11.044 Difference, 14.923, or area of ring. 144 =12 feet. 2148.912 X. 41015^881.376 pounds. WEIGHT OF COPPER BOLTS AND COPPER. 57 WEIGHT OF COPPER BOLTS OR RODS, From i to 4 inches in diameter. ONE FOOT IN LENGTH. Diameter. Pounds. Diameter. Pounds. Diameter. Pounds. 1 .1892 I.f 3.8312 2-1 17.0750 A .2956 *'A 4.2688 24 18.9161 I .4256 l.J 4.7298 24 20.8562 >& .5794 i-A 5.2140 2-1 22.8913 .7567 5.7298 24 25.0188 .JL .9578 i-A 6.2547 3. 27.2435 4 1.1824 14 6.8109 34 29.5594 B 1.4307 i-A 7.3898 M 31.9722 4 1.7027 i.f 7.9931 3.| 34.4815 H 1.9982 i.f 9.2702 3.J 37.0808 2.3176 i-l 10.6420 34 39.7774 ii 2.6605 2. 12.1082 34 42.5680 1. 3.0270 2-1 13.6677 3-1 45.4550 ii 3.4170 2-i 15.3251 4. 48.4330 To find the weight of a bolt or rod of a greater or less length than one foot, proceed as by the rules given in pages 54 and 55, to find the weights of wrought iron bolts or bars. COPPER. To ascertain the weight of copper. RULE. Find the number of cubic inches in the piece, multiply by .32118, and the product will be the weight in pounds. EXAMPLE. What is the weight of a copper plate i an inch thick by 16 inches square ? 16X16=256 .5 for \ an inch. 128.0 X. 32118=41.111 pounds. BRAZIER'S SHEETS are 30 x 60 inches, and from 12 to 100 Ibs. per square foot. SHEATHING COPPER is 14 X 48 inches, and from 14 to 34 oz. per square foot. C2 58 WEIGHT OF A SQUARE FOOT OF CAST IKON, ETC. WEIGHT OF A SQUAEE FOOT OF CAST AND WROUGHT IRON, COPPER, AND LEAD, From to 2 inches thick. Thickness. Cast Iron. Wrought Iron. Hard rolled. Copper. Hard rolled. Lead. Pounds. Pounds. Pounds. Pounds. T5 2.346 2.517 2.890 3.691 4 4.693 5.035 5.781 7.382 A 7.039 7.552 8.672 11.074 .1 9.386 10.070 11.562 14.765 .5^ 11.733 12.588 14.453 18.456 4 14.079 15.106 17". 344 22.148 A 16.426 17.623 20.234 25.839 4 18.773 20.141 23.125 29.530 A 21.119 22.659 26.016 33.222 4 23.466 25.176 28.906 36.913 *H 25.812 27.694 31.797 40.604 I 28.159 30.211 34.688 44.296 .ft 30.505 32.729 37.578 47.987 4 32.852 35.247 40.469 51.678 H 35.199 37.764 43.359 55.370 i. 37.545 40.282 46.250 59.061 14 42.238 45.317 52.031 66.444 i.j 46.931 50.352 57.813 73.826 14 51.625 55.387 63.594 81.210 14 56.317 60.422 69.375 88.592 14 61.011 65.458 75.156 95.975 i.| 65.704 70.493 80.938 103.358 14 70.397 75.528 86.719 110.740 2. 75.090 80.563 92.500 118.128 WEIGHT OF RIVETED COPPER PIPES AND BRASS. 59 WEIGHT OF RIVETED COPPER PIPES, From 5 to 31 inches in diameter, and from fyhs to &ths thick. ONE FOOT IN LENGTH. Diameter in inches. Thickness in 16ths. Weight in pounds. Diameter in inches. Thickness in 16ths. Weight in pounds. 5. 3 12.497 15. 5 59.588 5. 4 16.880 16. 4 50.752 k| 3 13.628 16. 5 63.470 5.| 4 18.395 17. 4 53.856 6. 3 14.765 17. 5 67.344 6. 4 19.908 18. 4 57.037 .| 3 15.897 18. 5 71.258 64 4 21.415 19. 4 60.142 7. 3 17.034 19. 5 75.233 7. 4 22.932 20. 5 78.208 74 4 24.447 21. 5 82.984 8. 4 25.961 22. 5 86.771 84 4 27.471 23. 5 90.571 9. 4 28.985 24. 5 94.308 94 4 30.598 25. 5 98.122 10. 4 32.208 26. 5 101.897 11. 4 35.200 27. 5 105.700 12. 4 38.456 28. 5 109.446 13. 4 41.456 29. 5 113.221 14. 4 44.640 30. 5 116.997 15. 4 47.646 31. 5 120.772 The above weights include the laps on the sheets for riveting and calking. The weights of the rivets are not added ; the number per lineal foot of pipe depends upon their diameter, and their size upon the thickness of the metal of the pipe. BRASS. To ascertain the iceight of brass castings. RULE. Find the number of cubic inches in the piece, multiply them by .3112, and the product will be the weight in pounds. 60 WEIGHT OF CAST IRON PIPES. WEIGHT OF CAST IKON PIPES, OF DIFFERENT THICKNESS, From 1 inch to 36 inches bore. ONE FOOT IN LENGTH. Bore. Th'kness. Weight. Bore. Th'kness. Weight. Bore. Th'kness. Weight, inches. 1. inches. .1 pounds. 3.06 inches. inches. pounds. 25.70 inches. 9. inches. 1. pounds. 97.98 i 5.05 "* "I 32.91 94 48.98 1^1 3.67 .f 40.43 _i 62.02 4 1 6. 5. i 26.94 t s. 75.32 14 6.89 K 34.34 8 88.98 i 9.80 . 42.28 1. 102.90 1 o 7.80 54 4 29.40 10. 4 51.46 * 4 "f 11.04 f 37.44 t 65.08 2 .s. 45.94 s. 78.99 2. '1 8.74 12.23 6. 4 31.82 40.56 1* 93.24 108.84 2.J f 9.65 "I 49.60 104 1 53.88 4 13.48 *I 58.96 1" 68.14 24 :! 10.57 14.66 19.05 64 :j 34.32 43.68 53.30 i! 82.68 97.44 112.68 2.f f 11.54 *f 63.18 11. i 56.34 ;| 15.91 20.59 7. i 36.66 46.80 j 71.19 86.40 3. i 12.28 *i 56.96 8 101.83 _i 17.15 *t 67.60 1. 117.60 i" 22.15 i! 78.39 11.3- . 58.82 i 27.56 74 39.22 1 74.28 3.J j 18.40 23.72 '1 49.92 60.48 90.06 106.14 .f 29.64 I 71.76 l'. 122.62 34 t 19.66 25.27 i! 83.28 41 64 12. i 61.26 77.36 ri 31.20 . *f 52 .'68 i 93.70 3.f 20.90 * 64.27 8 110.48 f 26.83 *i 76.12 1- 127.42 m S. 33.07 j_ 88.20 124 4 63.70 4. 1 22.05 28.28 84 f 44.11 56.16 j 80.40 97.40 4 ' : l 34.94 23.35 : .l 68. 80.50 l. 114.72 132.35 I 29.85 1. 93.28 13. .i 66.14 \ 36.73 9. . 46.50 1 83.46 44 : 24.49 31.40 38.58 I 58.92 71.70 84.70 i! 101.08 118.97 187.28 WEIGHT OF CAST IRON PIPES. 61 Bore. Th'kness. Weight. Bore. | Th'kness. Weight. Bore. Th'kness. Weight. inches. 134 inches. pounds. 68.64 86.55 inches. 174 inches. pounds. 88.23 111.06 inches. 27. inches. 1 pounds. 204.04 239.08 m s. 104.76 f 134.16 1. 274.56 | 123.30 8 157.59 28. ^ 211.32 l'. 142.16 1. 181.33 1 247.62 14. i 71.07 18. A 114.10 1. 284.28 i 89.61 .4 137.84 29. s 218.70 SL 108.46 \ 161.90 '? 256.20 t 127.60 1. 186.24 i! 294.02 i. 147.03 19. I 120.24 30. 226.20 144 4 73.72 .3. 145.20 "i 264.79 1 92.66 8 170.47 1 303.86 f 112.10 1. 195.92 l"i 343.20 i! 8 131.86 151.92 20. i 126.33 152.53 31. :| 233.40 273.40 15. 4 75.96 .1 179.02 8 313.68 I 95.72 i. 205.80 14 354.24 i; 115.78 136.15 156.82 21. i 132.50 159.84 187.60 32. ,? 240.76 281.94 323.49 154 1 78.40 i*. 215.52 1.1 365.29 i i! 98.78 119.48 140.40 161.82 22. i. 138.60 167.24 196.46 225.38 33. 8 l.' 8 1.1 248.10 290.50 333.24 376.26 16. J 80.87 101.82 123.14 144.76 166.60 23. i.* 8 144.77 174.62 204.78 235.28 34. 8 255.45 298.88 342.88 387.13 J- 24. * 150.85 } B 431.76 164 I 83.30 104.82 126.79 140 no i! 181.92 213.28 245.08 35. ;i 262.70 307.62 352.86 i! X6b7, \}i 171.60 25. i 156.97 189.28 1:| 398.10 443.96 17. i. 85.73 107.96 130.48 153.30 176.58 26. i! i. 221.94 254.86 196.62 230.56 264.66 36. 1:1 270.18 316.36 362.86 409.34 456.46 62 WEIGHT, ETC., OF CAST IKON AND LEAD BALLS. WEIGHT AND CAPACITY OF CAST IKON AND LEAD BALLS, From 1 to 20 inches in diameter. Diameter in inches. Capacity in cubic inches. CAST IRON. Weight in pounds. LEAD. Weight in pounds. 1. .5236 .1365 .2147 1.1 1.0227 .2666 .4195 1-1 1.7672 .4607 .7248 1.1 2.8062 .7316 1.1510 2. 4.1888 1.0920 1.7180 2.1 5.9641 1.5548 2.4462 2.1 8.1812 2.1328 3.3555 * 2.1 10.8892 2.8388 4.4662 3. 14.1372 3.6856 5.7984 3.1 17.9742 4.6859 7.3721 3.1 22.4493 5.8525 9.2076 3.f 27.6117 7.1984 11.3249 4. 33.5104 8.7362 13.7443 4.1 40.1945 10.4787 16.4858 4. 47.7130 12.4388 19.5695 4.1 56.1152 14.6292 23.0156 6. 65.4500 17.0628 26.8443 5.1 75.7675 19.7523 31.0756 5.f 87.1139 22.7106 35.7298 6.1 99.5413 25.9504 40.8269 6. 113.0976 29.4845 46.3870 6.1 127.7020 33.2919 52.3770 6.} 143.7937 37.4870 58.9768 6.| 161.0315 41.9809 66.0471 7. 179.5948 46.8204 73.6608 7.1 199.5325 52.0188 81.8382 7.1 220.8937 57.5870 90.5995 7.1 243.7276 63.5397 99.9649 8. 268.0832 69.8893 109.9543 8.1 294.0096 76.6483 120.5880 8.1 321.5558 83.8296 131.8861 8.1 350.7711 91.4460 143.8688 9. 381.7044 99.5103 156.5560 9. 448.9215 117.0338 184.1251 10. 523.6000 136.5025 214.7545 11. 696.9116 181.6849 285.8383 12. 904.7808 235.8764 371.0959 13. 1150.349 299.8960 471.8158 14. 1436.7584 374.5629 589.2865 15. 1767.1500 460.6960 724.7966 16. 2144.6657 559.1143 879.6346 17. 2572.4468 670.6368 1055.0891 18. 3053.6352 796.0827 1252.4486 19. 3591.3724 936.2708 1473.0014 20. 4188.8000 1092.0202 1718.0363 NOTE. If the weight in Wrought Iron or Copper is required, mul- tiply the capacity of the ball by .2816 for the former, and .32118 for the latter. WEIGHT OP LEAD PIPE. 63 WEIGHT OF LEAD PIPE PER YARD, From f to 5 inches diameter. WATER PIPES FOR HYDRANTS, PUMPS, ETC. Diameter of bore in inches. Thickness in l-100ths of an inch. Weight per foot in pounds. Diameter of bore in Thickness in 1-lOOths of an inch. Weight per foot in pounds. t 6 .424 14 14 3.5 8 .625 17 4.25 12 1. 19 5. 16 1.25 23 6.5 19 1.5 27 8. i 7 .545 l.f 13 4. 9 .75 17 5. 11 1. 21 6.5 13 1.25 27 8.5 16 1.75 2. 15 4.75 19 2. 18 6. * 8 .727 22 7. 9 1. 27 9. 13 16 1.5 2. 24 & of an in. 8. 11. 20- 2.5 f 14. 22 3. < 17. 1 8 .969 3. 3 (( 9. 10 1.25 *F " 12. 12 1.75 !> it 16. 16 2.25 ^ " 20*. 20 3 23 3.'5 34 3T " 12.5 15. 1. 10 1.5 JL << 18.5 11 2 ^ " 22. 14 17 21 24 2.'5 3.25 4. 4.75 4. ! I 12. 16. 21. 25. i.i 10 12 14 2. 2.5 3. 44 8 f r ' 14. 18. 16 3.75 5. t " 20. 19 4.75 1 " 31. 25 6. WASTE PIPE. H inch diam. 2 Ibs. per foot. 2 " 3 Ibs. 3 " 3 and 5 Ibs. foot. per 4 in. diam. 5, 6, and 8 Ibs. per ft. 4|fV . ." 6 and 8 Ibs. " 5 " 8, 10, and 12 Ibs. per foot. 64 WEIGHT, ETC., OF METALS BY THE WIRE GUAGE. WEIGHT OF A SQUARE FOOT OF WROUGHT IRON, AS PER BIRMINGHAM WIRE GUAGE, No. of Guage. Lbs. No. of Guage. Lbs. No. of Guage. Lbs. No. of Guage. Lbs. 1 2 3 4 5 6 7 12.55 11.25 10.45 9.55 8.66 8.34 7.5 8 9 10 11 12 13 14 6.64 6.29 5.5 4.73 4.3 3.64 3.23 15 16 17 18 19 20 2.97 2.62 2.19 1.92 1.7 1.41 21 22 23 24 25 26. 1.32 1.15 .99 .95 .84 .78 VALUES OF THE BIRMINGHAM GUAGES, For Iron Wire and for Sheet Iron and Steel. No. Inches. No. Inches. No. ! Inches. No. Inches. .340 10 .134 19 .042 28 .014 1 .300 11 .120 20 .035 29 .013 2 .284 12 .109 21 .032 30 .012 3 .259 13 .095 22 .028 31 .010 4 .238 14 .083 23 .025 32 .009 5 .220 15 .072 24 .022 33 .008 6 .203 16 .065 25 .020 34 .007 7 .180 17 .058 26 .018 35 .005 8 .165 18 .049 27 .016 36 .004 S 9 .148 For Sheet Brass, Silver, Gold, frc. 1 .004 10 .024 19 .064 28 .120 2 .005 11 .029 20 .067 29 .124 3 .008 12 .034 21 .072 30 .126 4 .010 13 .036 22 .074 31 .133 5 .012 14 .041 23 .077 32 .143 6 .013 15 .047 24 .082 33 .145 7 .015 16 .051 25 .095 34 .148 8 .016 17 .057 26 .103 35 .158 9 .019 18 .061 27 .113 36 .167 MISCELLANEOUS. G5 LAP-WELDED IRON BOILER TUBES (Prosser's Patent). TABLE of the Diameter, Thiclcness, and Weight of Iron Boiler Tubes. External Diameter. Wire Guage. Weight. per foot. Diameter. Thickness of Wire Guage. Average Weight. Price per foot. Inches. No. Ibs. per ft. Cents. Inches. No. Ibs. per ft. * c. If 16 1 20 2| 12 i 21- 48 11 15 ij 29 3 " 3^7 51 If 13 if 31 8* 12 4 85 2 " 2 34 4 11 5 1 10 2 " 2 " 5 10 6| 1 50 2f M 2| 39 6 " 9 2 20 9 12| 2-i 9 o 43 7 8 12 3 00 2ft 14 21 46 8 7 16 4 00 SCREWS. TABLE showing the Number of Threads to an Inch in V thread Screws. Diam. in inches, -^ No. of threads,' 20 18 Diam. in inches, If If No. of threads, 6 5 Diam. in inches, 3| 4 No. of threads, 3 3 16 14 12 11 10 9 8 7 1| If 2 2i 2J 2f 3 5 44 44 4 4 34 34 4 44 4| 5 5 54 2 2$ 2| 2f 2f 2$ 1* If 76 3i 34- 3i 3^ 5| 6 The depth of the threads should be half their pitch. The diameter of a screw, to work in the teeth of a wheel, should be such that the angle of the threads does not exceed 10. TIN. Description. Size of sheet. Mean thickness. Mean weight of one sheet. No on wire guage. Thickness of sheet. Single ... Double X inches. 10x14 10 xH 31 27 inches. .0125 (or 80 to 1 inch) .0181 (or 55 to 1 inch) Ibs. 0.5 0.75 There are usually 225 sheets in a box. 66 MISCELLANEOUS. ALLOYS OF COPPER AND TIN. GUN METAL. Tin to be added to 1 pound of Copper. Soft gun metal Mathematical instruments Wheels Guns, large. small oz. .25 .5 .75 .50 Machinery bearings 2 to 2.50 Musical bells 3 Gongs, cymbals, &c 3.50 House bells, small 4 " " large 4.50 Church bells 5 Speculum metal 7 to 8 Temper metal for adding small quantities of copper, 32 oz. COPPER AND ZINC. Tin to be added to I pound. Copper castings 1.125 to 1.50 oz Gilding metal 1 " 1.50 Tombac (red brass) 2 Ked sheet brass. Pinchbeck and Bath metal 3 to 4 Bristol brass 6 Ordinary brass 8 Muntz's metal for ship fastenings, sheathing, &c.. 10.66 Soft spelter solder 16 COPPEE, ZINC, TIN, AND LEAD. Tin. Zinc. Copper. Brass. Extremely tenacious 1.5 oz. .5 oz. 16 oz. Wheels 1.5" 16" 2 oz. For turning 2 " 1.5 " Bearings, Nuts, &c 2.5 " 1.5 " MISCELLANEOUS. 67 SOLDERS. For Lead, melt 1 part of Block Tin, and when in a state of fusion, add 2 parts of Lead. Resin should be used with this solder. For Tin, Pewter 4 parts, Tin 1, and Bismuth 1 ; melt them to- gether. Resin is also used with this solder. For Iron, tough Brass, with a small quantity of Borax. CEMENTS. Glue. Powdered chalk added to common glue strengthens it. A glue which will resist the action of water is made by boiling 1 pound of glue in 2 quarts of skimmed milk. Soft Cement. For steam-boilers, steam-pipes, &c. Red or white lead in oil, 4 parts ; iron borings, 2 to 3 parts. Hard Cement. Iron borings and salt water, and a small quantity of sal ammoniac with fresh water. Cement, Ashes, 2 parts} mixed ^ oil ^ regist ^ weather Sand, 1 ) equal to marble. HYDRAULIC CEMENT. A barrel contains 300 Ibs., equal to four struck bushels. BROWN MORTAR. One third Thomaston lime, Two thirds sand, and a small quantity of hair. Lime and sand, and cement and sand, lessen about in bulk when made into mortar. DIGGING. 23 cubic feet of sand, or 18 cubic feet of earth, or 17 cubic feet of clay, make a ton. 18 cubic feet of gravel or earth before digging, make 27 cubic feet when dug. 68 MISCELLANEOUS. GAS PIPES. TABLE of the Diameter and Length of Gas Pipes to transmit given . Quantities of Gas to branch Pipes and Burners. Dr. URE. No. of cubic feet of gas per hour. Length of pipe in feet. Diameter of pipe in inches. 50 100 0.40 250 200 1. 500 600 1.97 700 1000 2.65 1000 1000 3.16 1500 1000 3.87 2000 1000 4.47 2000 2000, 5.32 2000 4000 6.33 2000 6000 7. 6000 1000 7.75 6000 2000 9.21 8000 1000 8.95 8000 2000 16.65 These dimensions are applicable to the mains which conduct the gas to the places where it is to be used. If they send oft' branches for burners, the diameter may be reduced, or the length may be greater. For example, if a pipe of 5.32 inches, which transmits 2000 cubic feet through a length of 2000 feet, gives off, in this space, 1000 cubic feet of gas, then the same diameter can continue to transmit the gas through a length of 2450 feet. CISTERNS. CAPACITY OF CISTERNS IN U. S. GALLONS, For each 10 inches in depth. 2* 3 5 5i 6 6* 7 1\ 19.5 8 feet di 8* 1, 9 10 11 12 13 14 15 20 - ameter 313.33 353.72 396.56 461.40 489.20 592.40 705. 827.4 959.6 1101.6 1958.4 5>,or> 9 30 6 44 06 5997 78 33 99.14 122.40 148 10 17625 206 85 239.88 .. 275.40 MISCELLANEOUS. 69 WEIGHTS OF VARIOUS SUBSTANCES. Cubic foot in pounds. Cubic inch in pounds. 1378.94 .798 Gold 1204.41 .697 850.18 .492 Lead. 708.75 .41015 Silver 654.91 .379 Copper .... 555 .32118 Brass 537.75 .3112 Steel 489 8 .2834 "Wrought Iron 486.65 .2816 Tin 456 .263 Cast Iron 450.55 .2607 Zinc 428 54 .248 Granite 164.16 .095 Clay... 135. .0756 Stron 01 soil 127. .0735 Brick 125. .0723 Common soil 124. .0717 Coal (anthracite) 9504 .055 " (bituminous) 81.22 .047 Loose earth or sand Live Oak 95. 70. .0549 .040 Hickory 51.84 .030 White Oak 45.2 .026 44.93 .026 Salt Water (sea) 64.3 .03721 Fresh Water 62 5 .03616 Yellow Pine 33.81 .019 White Pine 29.56 .0171 Tallow 59. .03414 Cork 15. .00868 Air .07529 Steam .03689 WEIGHT OF COMPOSITION SHEATHING NAILS. Number. | L ^ ta Number in a pound. Number. | **$* Number in a pound. 1 I 290 8 1| 168 2 1 260 9 *J 110 3 1 212 10 If 101 4 4 201 11 If 74 5 H 199 12 2 64 6 i 190 13 i| 59 7 . a 184 70 MISCELLANEOUS. SLATING. Sizes of Slates. Doubles 14 by 6 inches. Ladies' 15 *' 8 Countess 22 ' 11 Duchess 26 ' 15 Imperial and Patent 32 ' 26 and Queens 39 ' 27 HEMPEN CORDS. Hempen Cords, when twisted, will support the following weights to the square inch of their section. U>s. i to 1 inch diameter 8.746 1 to 3 inches diameter .... 6.800 Lba. 3 to 5 inches diameter .... 5.345 5 to 7 inches diameter .... 4.860 STRENGTH AND STIFFNESS OF METALS, Cast Iron being 1. Strength. Stiffness. Wrought Iron 1.12 1.3 Brass 435 .49 Zinc 365 .76 Tin 182 .25 Lead 046 .0385 PAINTS AND LACKERS. White Paint. Inside work. White-lead, ground in oil 80. Boiled oil 14.5 Raw oil Spirits turpentine 8. Outside work. 80 9 9 4 New wood work requires about 1 Ib. to the square yard for 3 coats. Lead Color. White-lead, ground in oil. 75 Lampblack 1 Boiled linseed oil 23 Litharge 5 Japan varnish 5 Spirits turpentine 2.5 The turpentine and varnish are added as the paint is required for use or transportation. Gray or Stone Color. White-lead, in oil 78. Boiled oil . 9.5 Raw oil 9.5 Spirits turpentine 3. Turkey umber 5 Lampblack 25 1 square yard of new brick work requires, for 2 coats, 1.1 Ib. ; for 3 coats, 1.5 Ib. Cream Color. 1st coat. 3d coat. White-lead, in oil 66.6 70. French yellow 3.3 3.3 Japan varnish 1.3 1.3 Raw oil 28. 24.5 Spirits turpentine 2.25' 2.25 1 square yard of new brick work requires, for 1st coat, 0.75 ; for 2d coat, 0.3 Ib. Black Paint (for Iron). Lampblack 28 Litharge 1 Japan varnish 1 The varnish and turpentine are added last. Liquid Olive Color. Linseed oil, boiled 73 Spirits turpentine 1 Olive paste 61.5 Boiled oil... .. 29.5 Spirits turpentine 5.5 Paint for Tarpaulins (Olive). Dryings 3.5 Japan varnish 2. Liquid olive color 1 00 Spirits turpentine 6 Beeswax 6 1 square yard requires 2 Ibs. for 3 coats. Dissolve the beeswax in the turpentine, and mix the paint warm. LACKER % /br Iron Ordnance. Black-lead, pulverized 12 Litharge 5 Linseed oil.... .. 66 Red-lead 11 Lampblack 5 Boil it gently for about 20 minutes, stirring it constantly during that time. 72 Lacker for Small Arms, or for Water Proof Paper. Beeswax ..................... 18. I Spirits turpentine ........... 80 Boiled linseed oil ......... 3.5 I Heat the ingredients in a copper or earthen vessel over a gentle fire, in a water bath, until they are well mixed. Lacker for Bright Iron Work. Linseed oil, boiled ........ 80.5 I Litharge ..................... 5.5 White-lead, ground in oil 11.25 | Pulverized resin ........... 2.75 Add the litharge to the oil ; let it simmer over a slow fire for 3 hours ; strain it, and add the resin and white-lead ; keep it gently warmed, and stir it until the resin is dissolved. STAINING WOOD AND IVORY. Yellow. Dilute nitric acid will produce it on wood. Red. An infusion of Brazil-wood in stale urine, in the propor- tion of a Ib. to a gallon for wood, to be laid on when boiling hot, and should be laid over with alum water before it dries. Or, a solution of dragon's blood in spirits of wine may be used. Black. Strong solution of nitric acid, for wood or ivory. Mahogany. Brazil, Madder, and Logwood, dissolved in water and put on hot. Blue. Ivory may be stained thus : Soak it in a solution of verdi- gris in nitric acid, which will turn it green ; then dip it into a solu- tion of pearlash boiling hot. Purple. Soak ivory in a solution of sal ammoniac in four times its weight of nitrous acid. THE END. MARINE GLUE. In response to J. H. P.'s request in regard to marine glue, (in the issue of 22d inst.), I must refer him for a more accu- rate formula for preparing it to Tomlinson's Encyclopaedia, of the Arts and Sciences, article on glue and shellac. I have not the book at hand, and it is years since I have seen it, but I have made marine glue by its formula. The ether used must be perfectly free from alcohol, as that fluid acts as a pre- cipitant upon India rubber. Heat, however, must be applied in hastening a solution , the best means for so doing being the sand bath. [In my arti- cle on glues, yon made me say " take the scales " of certain fish ; I wrote, " take the skins. "] F. L. J. , of Ark. A CEMENT OF GKEAT ADHESIVE QUALITY, particularly said to be serviceable in attaching the brass mountings on glass lamps, as it is unaffected by petroleum, may be prepared by boiling three parts of rosin with one part of caustic soda, and five parts of water, thus making a kind of soap, which is mixed with one-half its weight of plaster of Paris. Zinc- white, white lead, or precipitated chalk may be used instead of the plaster, but when they are used the cement will be Q. D. O. Glue will unite leather, and becomes very strong if mixed with white-lead paint ; such a mixture was sold some time ago iu the streets of New- York as a new and wonderful cement for uniting leather straps and belting without rivets. As a proof of its strength, a heavily-loaded two-horse wagon was drawn by leather traces made of pieces of leather, all stuck together by this compound. A. E. S., of Mo. In the oxychloride of zinc paint, the propor- tion of oxide of zinc used may be varied. It should, however, not be less than half the weight of the chloride. The object of the tartrate of potassa is to prevent too rapid drying. This may, therefore, be used in variable proportions. The amount of water and starch used depends upon the consistency required. Experience can be the only sure guide in these particulars. By a few preliminary experiments with small quantities you will probably be able to succeed. V YB 078 j^ UNIVERSITY OF CAUFORNIA LIBRARY