EXAMINATION PAPER-No. II, Page 460. I. 506,055,084. 2. FOR SECOND-CLASS. Sum 1282 tons I cwt. o qr. 19 lbs.; product 20512 tons 18 cwt. 2 qrs. 24 lbs. 3. Product 33201610691092. 4. Quotient 471036768. 5. Quantity remaining on board 122 tons 4 cwt. o qr. 17 lbs. 6. 28.75 X 10'5 × 8′25 = 2490'46875; dividing by 42 = 59°296875 tons = 59 tons 5 cwt. 3 qrs. 21 lbs. 7. 9 X 24 228 knots per day; then 228: 1507 :: 20: 132 tons 3 cwt. 3 qrs. 12 lbs. 8. Effective pressure 40'75 lbs. 9. Pressure to blow off 5.748 lbs. 10. Circumference of wheel 89'5356; feet in knots 59280; number of revolutions 662*1. II. 133 X 6080 ÷ 25 12. 3234 56 number of revolutions. 24 : (24 — 10}) 131 :: 240 : 135 lbs. 13. Height of valve to be raised 2.25 in. 14. Capacity of pump 7854 X 7°32 X 15 = 627-80949 cubic inches; this X X 13 X 60 = 3264609348 cubic inches, quantity delivered in an hour; this divided by 1728=(12 X 12 X 12) gives 188.924 cubic feet. 15. 642 X 7854 X 22°371739′06432 × 6 × 66 ÷ 33000 = 860 87 horse-power. 16. 4'69 X 4500 = 95220 lbs. I. FOR FIRST-CLASS. Side of square 31°1496; remainder 141984. 2. Wages to be paid £179 148. 6d. 3. 317677 lbs., the required weight. 4. - 12 + 10.5 22.5 X (12) 10.5) 1'5 = 33°75 diff. of squares of diameters; then 7854 X 33'75 X 20 = 530'145 lbs. 5. 9365 895 lbs.; number of stays 92.6 or 93 stays. 6. Total heating surface 112790'958 square inches, or 783 27 square feet. 7. 1175 X 106 X 60 ÷ 6080 = 12.29 knots, advance of screw per hour; then 100: (100-175) 82°5: 12.29: 10:14 knots.* = 9. METHOD I.-4 times sum of evens = 98.078 X 4 = 392.312; twice sum of odds = 70′5 X 2 = 141; sum of first, last, evens, and odds 593 312 3 = 197'771; to this add 45 X 4 = 180 before expansion; and the sum 377'771, divided by 12, the number of parts into which the cylinder is divided, gives 31481 lbs., mean pressure. = 31479 lbs. METHOD II.-Ratio 3; its hyperbolic log. + 1 = 2.09861 X or 15 METHOD III.-Ratio 3; its tabular multiplier 69954, multiplied by the effective pressure 45 gives 31478 lbs., mean pressure. METHOD IV.-Ratio '33333; ordinates '05; 1; 1; 1; 08333; '06667; '05555; '04762; *04167; 03704; 01667; sum ·69855 X 45 = 31°435 lbs. 10. Top 179 lbs.; bottom 19:53 lbs.; mean 18.71 lbs. EXAMINATION PAPER-No. III, Page 461. 1. Forty-six thousand seven hundred and twelve million three hundred and eighty-nine thousand four hundred and sixty-seven. 2. 64-5=59; 59 X 3'1416 ÷ 6 = 185'3544 ÷ 6 = 30·8924, or 31 bolts. 3. No. of rivets in circular seam (36 × 6) — 6 × (7 + 1) = 1680 rivets. No. of rivets in vertical seam 14 X 6 - 12 X 7 = 504 rivets. Total number 2184 rivets. 4. = 801001 6001795000. 1od 10h 15000 min. 795000 15000 53 rev. 5. 16 X 4800 7. 33 X 224073920 lbs. ; 73920 (1480 X 24) =2.081 lbs. *The pitch of a screw, or the circumference of a paddle-wheel, multiplied by the revolutions, and two figures cut off for decimals, give the speed in knots, nearly. It is too much in the exact proportion of 304 to 300. 8. 382 7854 (= 1134°1176) × 61 2= = 69181*1736 × 66 = 4565957°4576 × 60 × 7 × = 479425533*04801728 = 277445 331 lbs. 9. 63752 (= 4064 0625) X 7854 (= 3191′9146875) × 6 = (19151-488125) × 58 X 2=== = 2221572-6225 1166 X 33000 = 384780002221572·6225 = 17:32 lbs. = 10. 120" X 96" X 5 = 57600, 1728 × 35 = 60480, .*. 5760060480 cwt. o qr. 5 lbs. = *9524 tons = 19 II. 21 tons X 2240 = 47040 lbs.; 66 × 6 = 396,..4 • 47040 ÷ 396 = 11879 basketfuls. 12. Length of shaft 19 ft. 3 in. — 6 in. = 18 ft. 9 in. or 225 in. 8°5a × *7854 = 56·74515 X 225 = 12767·65875. Flanges=18a × ·7854 × 6=1526·8176; 12767·65875+1526-8176 - 14294°47635, . ́. 14294°47635 ÷ 3'6 = 3971.6879 lbs., or 1 ton 15 cwt. I qr, 22·699 lbs. EXAMINATION PAPER-No. IV, Page 462. Iold. per lb. 11. 4d 15b 45m. 12. 5625; 1*125a × 7854 = '9940218750; 5625÷99402 = 5658.8, &c., lbs. 10. 17 158. 3d. Tuesday 11h 45m P.M. = Cubic inches discharged each stroke 102 X 7854 X 14 × = 755′9475; 755'9475 X (95 X 2) X 60 8617801 500 cubic inches discharged in an hour ÷ 1728 4987-15364 cubic feet discharged in an hour. 350 tons X 35 · 12250 cubic feet contained in tank, 888 - 2h 456 2h 27m 216. 15 ft. 7 in. 3. £7 78. 4. 3'41797, &c., gals. per day. 5. Dia. of shaft 18 in. + 1 in. = 19 in., . . 18 in. + 193 in. = 375 in.; 19} in. — 18 in. = 15 in.; 37'5 X 15 X 7854 X 54 X 3 = 715.69575 lbs. 6. 3'35416 X 19'5 = 65°406120, &c., sq. ft. 4398 24; 35 X 50 X 2 = 3500; 4398·24 + 3500 = 7898·24 ÷ 6. 6.1667 X 20'25 X 34 = 4245'77295; 8 X 7854 X 10 X (68 X 2) X 90 (= 615250944) 1728 gives 35'6048; .. 4245°772953546048 gives 119m 2472, or 1h 591m. 7. 603 X7854 X 32 X 18 X 51 1728 4806-6458; being less than 5000 is not strong enough. 19635; 641 19'635 = 32·646, .". 84 : 74 :: 32·646: 28·76 lbs. 9. 690° - 560°, 130°÷2240 = *05909 X 10 = '59 + 10'00 = 10. Mean width 6 feet.; 20:25 X 9 X 6 ÷ 45 = 10:59 tons. 24°3 tons, or 24 tons 6 cwt. II. 750 X 24 X 23°256 X 10 = 41860802240 – 1868.785 tons of coal. 12. 45: 41: 23 lbs.: 19:09 lbs. = ÷ 36 = 527 lbs. 3. 195" X 153" X 3125 (= 1") X 4126 3846 8503125 lbs., .. £64 28. 3'4d. = 124°. 7854 X 1800 =) 2208 9375 = 34'13 bolts. 8. 1149'6 102 ÷ 42 = 24*7. 10. 23.8 per cent. 121104; 80 26 lbs. 12. 162 X 18 X 7854 = 3619′1252 capacity of air-pump; 35a X 7854 × 36 = 34636·14 capacity of cylinders. If air-pump had been single-acting it would not have met the requirements of the Board of Trade, but being double-acting it is of greater capacity in the proportion of 4329°5175: (3619°1252 × 2), or as 1 : 167. I. 226. EXAMINATION PAPER-No. VIII, Page 465. 218 166; 120 11 = 170; 3′′9 or 78 stroke. 6. 5'52 X 7854 = 23°75835; 3°25* X *7854 X 2 = 16'591575; 1: 69. 8'25 = 3′975 ÷ (9'7 — 8·25) 1°45 == 2*74. 1600 ÷ 198 = 8·08; 9'7 X 24 = 232·8; 1600 ÷ 232.8 = 6·87. 2nd consumption 69 3872 = 3333 121 = 2*75. EXAMINATION PAPER-No. IX, Page 466. Nine hundred millions nine hundred and ninety-nine thousand and nine. 5. 22′ 4′′ X 13′ 11′′ × 16′ = 22°333 × 13′916 (≈ 310-786028) × 16' = 4972 57644845 (= 110'501699) ÷ 12 = 9'208, &c., tons. (NOTE.-45 cubic feet is allowed for 1 ton). 6. Leverage of weight = 4" 375 +4375 = 48125, .*. P – 250 × 4'8125 802-083; with friction 802.083 + of 802.083 = 882-291 lbs. = 15 7. A's share, £54 108.; B's share, £44 198.; and C's share, £20 118. = 9. Whole depth of face of valve 57; whole width of face of valve = 23′; depth of whole depth of valve - 2 faces 10"; height of walls above the face depth thickness of back and face of valve = 34"; total length of 4 walls 63"; cubic = valve port = = 10. 48' 3". II. = = 270 25; sides 30; back 150; 4 walls 177 1875 = total 627.4375 cubic = C, K = 15 × 9'6 = 144′0; C K, = 12 X 10'1 = 121°2; K, — K = 10'1 — 9⋅6 = 0'5, . .. 1440 1212 = 22.8, and 22·8÷0'5 = 45'6. 12. Days on voyage at 1st rate, 10.851; days on voyage at 2nd rate, 10'313. Tons burnt per day at 1st rate, 130212; tons burnt per day at 2nd rate, 154'695. Difference of consumption, 154'695 13021224483; difference of days, 10.851 10.313 0.538 .. 244830538 = 45'5, &c. Answers as before. BBBB EXAMINATION PAPER-No. X, Page 466. 1. £530 os. 61d. 2. 1563. 3. 642 7854 = 3216′9984; 102 X 785478°54; 4096 sq. in. to 1 sq. in. of pipe. 4. £19 38. 4d. 5. 12 tons. 6. 30215 teeth; 1 pull = 3 teeth X 12 = 36; 15 X 12 = 180; 36: 180 :: 1:5TM. 7.9÷2=4; 4} — 2} = 2} open; 27 × 264 area open for steam. 8. 23 X 2240 X 11 X 2 (= 109480) ÷ 140 = 782; 782 × 13%÷6=91°233 lbs. 9. 5'541375 area; 137591528 lift of valve. 10. § of 4, or of t=218; 41% +218 = 71% oz. per gallon. II. 322 +58o÷30=1024 + 3364 = 4388 ÷ 30 = 146°26, &c., N.H.P. EXAMINATION PAPER-No. XI, Page 467. 1. 89.3 tons X 2240=200032 lbs. ; 35 X 785427°489; 200032÷27°489=7276·8002 ..V27276.8002 853, diameter of piston. 2. 7 X 2240 (=15680) X *055=862'4; 3'1416 × †† (= 3·6652) × 862°4 (= 3160·86848) X 57180169'5033633000=5°4897 H.P. 3. 3'1416 × 9 (= 28′2744) ÷ 66 (= 33′′ × 2) = '4284 X *05 X 100 = 2*142. 4. IX 2240 X 18 × 6 = 362880 ÷ (51520 × 1} =) 64400 = 5°6348 ·`· Va 5·6348 = 2'37. 5. 9'53 (= 857°375) × 51520 = 44171960; 5°1 × 15 = 76°5; 44171960 ÷ 76°5 = 577411 242240 = 257'77 tons. 6. 3 X 2240 X 24 X 10'2 = 1645056 ÷ (93 =) 729 = 2256′59. 7. 2'5 ·8752·5 = 1·625 ÷ 2°5 = ·65; 875° (= ·765625) × ·7854 X 200 = 120264375 (2} × § =) 1°5625=76′973; 1·625 — 2'5 X 100 = 65'0. 8. 18:9166 × 19 (= 359°4154) × 10·333 (= 3713·8393282) × 3 = 2475°8928855 × 62×5 =154743°312000 X 5'1 = 65.7659025; 12 cwt. X 112 1344 lbs., .. 1344: 65'766 :: 60m: 2m 936, or 2m 568.16. 9. Top 12 22 lbs.; bottom 12'56 lbs.; mean 12.39 lbs. 10. I. 2. 1'437 X 2 +1875 = 3^o625 – 6875=4454; 4454 X 27= 5'356287. EXAMINATION PAPER-No. XII, Page 468. 012+2'715=2*727. 01282 0163840; 01638406·81400240. 3. £11 os. od. + £5 28. od. + £4 178. 6d. = £20 198. 6d. 540 lbs. 540 lbs. at 4d. per lb. = £9; discount at 8 per cent.= £8 158. 7.2d. from 7h 15m A.M. to 7h 15m P.M. is 12 hours; Total 44d 15th = 44d-6354. Mean conMean speed per day = 13891 ÷44·6354 5. From May 19th to July 2nd is 44 days; and from 7h 15m P.M. to 10h 30m P.M. is 3h 15m. sumption per day = 480 ÷ 44·635410757 tons. =31121 knots. 6. £120 + 170 + 85= £375 per year, .. 170 N.H.P.: 1 N.H.P. :: £375: £2*2057 = £2 48. 13680d. 7. 37 tons X 35 = 1295 cubic feet. I" of foot 08333; 129508333 = 15540 621 sq. feet. 8. 342 34 X 34 11560,.. 11560 ÷ 15 = 770'66 feet above the sea. 9. Even keel before taking in bunkers 197 ft.+ 194 ft. ÷ 2 = 19'55 feet; even keel after coaling 210 ft.+ 20.8 ft. ÷ 2 = 20'9 ft., .. 20'9 — 17°55 = 1°35 ft.; 4821 X 1.35 6508 35; 6508:35 35 185.95 tons taken in. 10. 112 + 48 = 160; 160: 112 :: 5 oz.: 3'5 oz. 11. 36 inches1 lb. 16 oz.; 5 oz. = 1lb.='3125; 7" X 4" 28 sq. inch; 3125 X 112500; 11°2500 ÷ 28 = '04017 of an inch; 04017 X 32 = 1°28544. 3'6 EXAMINATION PAPER-No. XIII, Page 469. 1. 10.5 X 18 (= 1984°5) ÷ 20 = 99°225; √2 99′225 = 9′96 knots. 2. 603 X 18 (= 64800) ÷ 19°6 = 3306·122; √2 3306°122 = 57°5 rev.; 602: 57'52 :: II 10'I knots. 3. 12000 X 15-6=30000; 2240 X 60 ÷ 30000 = 4°48 inches. 52 X 36 = 12′5; 5000 X 60 = 300000 ÷ 12°5 = 24000 lbs. of 288 28.8 cwt., the 4. 5. 4 X 8 X 12a ÷ 16 = 288 cwt., the breaking strain, and working strain. 6. 50: 58: 603 ÷ 4176: V2 4176 = 64'6 revolutions. 7. 29: 32: 10a : 110′3348, . ́. √a 110°3348 = 10'5 knots. 8. 12.25 X 75 (= 9*1875, section of plate) × 23 = 211*3125 tons; 875a × 7854 = *601321875 X 2 = 1°20264375 ÷ (°75 × 2°5) = 1·875 = ·64141; 211°3125 × 64141 = 135'5379506, &c., tons. 9. Length of crank-pin = 13a = 169 sq. inches; area of L.P. piston = 72a × 7854= 40715136; area of H.P. piston = of 40715136 1017.8784; pressure on low pressure piston = 4071-5136 × 18 = 73287 2448; pressure on high pressure piston = 1017.8784 X 54 549654336; pressure on low pressure pin = 73287°2448 ÷ 169 = 433'652 lbs.; pressure on high pressure pin = 54965°4336 ÷ 169 = =325°23, &c., lbs. 10. 7'1 × 12 ÷ 62°5 = 1°3632 evaporation in cubic feet of water; 1′3632 × 512 = 697'9584 cubic feet of steam; 697′9584: 3'1 :: 3600: 15'99 seconds. 11. Top 1692; bottom 18.60; mean 17.76 lbs. EXAMINATION PAPER-No. XIV, Page 470. 1. 482876; 112° X 28 = 3136; 48 X 200 9600; 167°59 Fahrenheit. The 4. 122 X 7854 X 2 = 226·1952 ÷ ('25 × 6 =) 1°5 = 150°797, number of slots. slots are placed there to prevent the water getting into the cylinder when priming. 5. 83 X 7854 × 145′′ = 7288°512; 30 X 10 X 5=1500; 7288°512 + 1500=8788*512 3.62441°25 lbs. 6. 483 X 7854 (= 1809'5616) X 29 = 52477 2864; 100 : 24: 52477°2864 : 12594'548736 (12 X 10 =) 120 = 104°9545, &c., lbs. per square inch on the guide. 7. 5–875 = 4*125; Sooo X •8752 = 5359'375 – 4125 = I299'242; 6* X 854 = 28.2744; 1299°2424 ÷ 28′274445'95 lbs. 8. 29.00 204 = 14°21 lbs. pressure. 9. P1 = 1325; P2 = 17°75; .'. (13°25 + 17°75) × 66a X 3'5 X 60 = 28357560÷ 140000 202-554 tons. 10. 66 7854 X 7 X 60 X 18′36 = 26381575'9468833000 = 799°44169, &c., H.P. 11. 202 55410 20°2554 tons of coal; 20:2554 X 2240 = 45372 0960 lbs. 24= 1890'504, which divided by 79944 = 2.365 lbs. of coal per I.H.P. EXAMINATION PAPER-No. XV, Page 472. 1. 34+8=11th = 11h75; 3'25 × 8.5 = 27·625; 27·625 ÷ 11'75 = 2°35106h= 2h 21m 38.8. 2, 5 × 75 = 37°5; 4'14 X 2 = 8°28; .*. 37°58′28=4′529 tons. 3. 75'573.252.25 X 3'1416 7′0686 inches. 4. Total distance run 2165 miles; 31202165 = 955 miles yet to go; coals burnt 490 tons; 800- 490 310, coals left for remainder of voyage; 2165 955 490 216.14 tons,.. 310-216'14 93.86 tons remaining at the end of the voyage. 5. 072 X 072 X 7854 (= 004071536) 750054286; 1000054286 184'1 thickness. |