REDUCTION OF DECIMALS, page 31. I. *4375; 73; 2142857; °34375; ·1875; 076923; 0112; 275 2. 5384615; 6470588; 6315789; 185; 7167235; 3183098; 4683544; *0104895. page 34. I. 2833; 4833; '7; 4166; 8; ·9666 2. 3. 4. 5. 6. 788260449735. 29 530588194. 12.175 hours; 00138 IN.M = 1*15202 1.M.; 1 I.M. = ·86804 N.M., 1'1515, '868421. 7. 12.5925; 29d716493055; 15.74229166; 119d.221701388. 8. 81875; 19°67916; 104°26875; 82°.325. 9. 37°305; sum 78°755 or 78° 45′ 18′′. 10. 1 Kilomètre 621382 miles; 1 mile = 1.609315 kilomètres. I. 2. MULTIPLICATION BY LOGARITHMS, page 50. 3'774517 = 5950; 3'000000 = 1000; 3'0224291053; 3·884399 = 7663. 2*971331=936′12; 4'034147 = 10818; 3'4948503125; 3045714 = 1111. 3. 3.839603 = 6912; 5'532375 = 340703; 5908534 810091; 5237543= 172800; 5786113 = 611100. 4. 458667838608; 4·67760747600; 2.731378538738; 3.519872= 3310 35. 5. 3'9713879362'4; 2993736985.68; 4659678 = 45674'9; 2·892873 = 7814; 3'4454252788.85. 6. 3'100249 = 1259'64; 2'511391 = 324·631; 2'935576 = 862·137; 5′000000 = 100000. 7. 5'599311=397476; 3'590806 3897.68; 2.706547 = 508-8; 4'523226 = 33360; 8.825336066886. 8. 5'045979 = 111168; 2640978 = 437'5; 2°411417 = 257·88; 1202283. 6.080006 9. 2'953494898*45; 1*595937 = 39'44; 2·864036731°2; 9′252805=17898. 10, 1798757=62*9154; 5·260964·018237; T·559971 = ·363054. 2000000='01; 5'00000000001; I'000000='1; 5·000000=100000. 347336800297419; II. 12. 5755418 = '00005694; 46221100004189; 2629523004261. DIVISION BY LOGARITHMS, page 53 I. 191907883; 2°778875=601; 1°924279 = 84; 2·096910 = 125. 2. 4′98668096979'6; 2'698970 = 500; 1982985 = 96·158; 1775257 = 59.6015. 3. 165321245; 1278754 = 19; 0·857333=7′2; 1·822584 = 66·4636. 4. 2462138289.827; 2°525020=334′982; 2°045813=111'125; 1*361728 = 23 5. I.83275268038; 0.561751 = 364545; 030734107333; 3°509203= 3230. 6. 1'000000 = 10; 7'425115 = ·266143; 2·376859 = 238'155; 2'000000=100. 7. 2264818184; 2·380753 = 240'3; 3'946651 = 8844'04; 2'797960 = 628. 8. 194050687·1978; 2·179787 0151282; 0·176670 — 1°502; 0·833525= 6.81592. 9. 5'421422263889; 1'421442 = 26·3889; 0·421422 = 2·63889; 3'421422 = 2638 89. 10. 405710100011405; 2°537395 =344·663; 1∙166086 = 14·6584; 1'003528= 10:0816. II. 3'3398942187°23; 3004751 1011; 1172049 14861; 3028878 = 1068.76. 12. 0'000000= 1; 1'000000 = 10; 3'000000001; 3'000000 1000; 4'000000 = 10000. 13. 3077427 = 1195*16; 3'112507 = 1295*71. 14. The result of the division is 103275, and the product is identical with it, as far as the sixth decimal figure. MISCELLANEOUS EXAMPLES. For practice in Natural and Logarithmic Sines, Tangents, and Secants, page 62 (1.) Nat. sine 432651, its common log. is 9'636138, which is the log. sine required. (2.) Nat. tang. 3, its common log. is 10:477121, which is the log. tang. required. (3.) Log. 9'236713, its corresponding nat. no. is 172470, the nat. cos, required. (4.) The given log. tang. 9.850593, being subtracted from 20, gives 10'149407, the log. cotang. (5.) The nat. sine of 68° 45′ 24′′ is 932050, the log. of which, or 9'969439, is its log sine, which, being subtracted from 20, leaves 10030561 for the log. cosec. (6.) The log. sec. 11024680 subtracted from 20, leaves 8-975320, the log. cosine, the nat. no. correspoding to which, or '094476, is the nat. cosine sought. (7.) I. The quantity 9450981 is found in the tables to be the log. cosine of the arc 73° 35′ 31′′. 2. The nat. no. corresponding to the given log. is 282476, which is the nat. cos. of 73° 35′ 31, the arc A sought. (8.) 1. The square of radius, or 1, divided by the nat. sec. 2·005263, gives '498688, the nat. cosine of A, which is found in the tables of nat. cosines, to correspond to 60° 5' 12" the value of A. 2. The common log. of the nat. sec. 2·005263 is 0·302171, which is found to be the log. sec. of 60° 5' 12", the arc A sought. |