QA 
 102 
 
 W425 
 
 JC-NRLF 
 
IN MEMQRIAM. 
 
 Professor J. Henry Sengei 
 
ANSWERS 
 
 TO 
 
 'ENTWORTH AND HILL'S 
 
 ARITHMETIC. 
 
T. Kr^ ' S< 
 
 WENTWORTH'S 
 SERIES OF MATHEMATICS. 
 
 First Steps in Number. 
 
 Primary Arithmetic. 
 
 Grammar School Arithmetic. 
 
 High School Arithmetic. 
 
 Exercises in Arithmetic. 
 
 Shortor Course in Algebra. 
 
 Elements of Algebra. Complete Algebra. 
 
 College Algebra. Exercises in Algebra. 
 
 Plane Geometry. 
 
 Plane and Solid Geometry. 
 
 Exercises in Geometry. 
 
 PI. and Sol. Geometry and PI. Trigonometry. 
 
 Plane Trigonometry and Tables. 
 
 Plane and Spherical Trigonometry. 
 
 Surveying. 
 
 PI. and Sph. Trigonometry, Surveying, and Tables. 
 
 Trigonometry, Surveying, and Navigation. 
 
 Trigonometry Formulas. 
 
 Logarithmic and Trigonometric Tables (Seven). 
 
 Log. and Trig. Tables (Complete Edition), 
 
 Analytic Geometry. 
 
 Special Terms and Circular on Application. 
 
ANSWEES. 
 
 Art. 
 
 45, 995; 
 
 Art. 
 
 49, 1110.87; 
 
 Art. 
 
 53, 1.2626906; 
 
 398.8 ; 
 
 1000; 
 
 6.3834733. 
 
 488.92 ; 
 1689.91. 
 
 1299.07; 
 
 770.22 ; 
 
 54, 7.603166; 
 11.4093504* 
 
 46, 1707.8; 
 
 1342.17. 
 
 6.7286717; 
 
 3271.1 ; 
 1945.66 ; 
 3440.4 ; 
 
 2018.44 ; 
 
 50, 886.353: 
 950.998 ; 
 347.0759 ; 
 724.8363 ; 
 
 10.528675 ; 
 3.2657244 ; 
 21.712055; 
 19.9922991 
 
 8440.75. 
 
 1694.6084. 
 
 22.6276131 
 
 47, 2372.64; 
 
 52, 6.6452727; 
 
 20.0826303. 
 
 8794.95 ; 
 
 7.7847491 ; 
 
 55, 4.523467; 
 
 3625.3 ; 
 
 10.6313239 ; 
 
 14.8237261 
 
 2299.86 ; 
 
 20.8266782 ; 
 
 22.1157111 
 
 2062; 
 
 1.2272041 ; 
 
 24.8583194 
 
 1897.8236 ; 
 
 1.2099648. 
 
 10.2590772 
 
 1900.01828. 
 
 53, 1.30103; 
 
 29.6490831. 
 
 48, 6.64528; 
 
 4.5861528 ; 
 
 57, 1448.95; 
 
 30,106.937; 
 
 3.5282304 ; 
 
 2393.60; 
 
 2284.57828 ; 
 
 19.0826303 ; 
 
 1870.27 ; 
 
 371.8273. 
 
 16.5414467 ; 
 
 2956.89 ; 
 
 49, 848.87; 
 
 6.0157063 : 
 
 4267.58 ; 
 
 1748.87; 
 
 4.2070434 ; 
 
 3950.41 ; 
 
 3041.87; 
 
 5.2839031 ; 
 
 6570.39 ; 
 
 959.87; 
 
 3.2384788 ; 
 
 3501.93 ; 
 
 1000.87; 
 
 8.485051 ; 
 
 4064.96. 
 
 M43594 
 
ARITHMETIC. 
 
 Art 
 
 69, 3 ; 3 ; 
 
 75, 1802; 
 
 78, 15.1683487; 95, 
 
 73; 
 
 7; 3; 
 
 814 
 
 0.3178372; 
 
 115; 
 
 3; 9; 
 
 51; 
 
 1.854102; 
 
 128; 
 
 14; 
 
 118; 
 
 0.317004; 
 
 116; 
 
 22; 
 
 2482; 
 
 0.5040172; 
 
 264; 
 
 22 
 
 15,545; 
 
 1.618034; 
 
 284; 
 
 70, 40 mi. 
 
 N.; 1388. 
 
 0.080936. 
 
 297; 
 
 $4. 
 
 
 79, 2.3561945; 
 
 320; 
 
 73, 111; 
 
 76, $106.98; 
 
 1.5707963; 
 
 354; 
 
 220; 
 
 $87.69; 
 
 0.7853981; 
 
 369. 
 
 301; 
 
 $97.87; 
 
 2.6179939; 96, 
 
 58, (59) ; 
 
 432; 
 
 $141.73; 
 
 2.0943951; 
 
 89, (90); 
 
 553; 
 
 $23.50; 
 
 1.5707963; 
 
 88, (89) ; 
 
 602; 
 
 $118.46; 
 
 1.0471975; 
 
 241, (242); 
 
 716; 
 
 $307.92; 
 
 0.5235987. 
 
 180, (181); 
 
 876; 
 
 $26.38. 
 
 80, 0.618034; 
 
 121, (121). 
 
 877; 
 
 77, 7066; 
 
 0.7961796; 97, 
 
 1,2; 
 
 9978; 
 
 6975; 
 
 1. 
 
 2,3; 
 
 4997. 
 
 7287; 
 
 81, 46. 
 
 3,5; 
 
 74, 333; 
 
 2848; 
 
 82, 19,418. 
 
 4, 4; 
 
 423; 
 
 1747; 
 
 83, 382. 
 
 2,6; 
 
 522; 
 
 7276; 
 
 84, 46. 
 
 1, 7. 
 
 5922; 
 
 6987; 
 
 85, 329.426. 98, 
 
 6689 ; 
 
 6399; 
 
 6960; 
 
 86, 4615.71. 
 
 8334.68. 
 
 6397; 
 
 7391 ; 
 
 87, 115,946. 99, 
 
 7.9585202. 
 
 7341; 
 
 3251. 
 
 88, 182,741. 100, 
 
 0.80415828 
 
 6550; 
 
 78, 0.4233109; 
 
 89, 3822.161. 101, 
 
 609 gals. 
 
 3086; 
 
 0.2617994; 
 
 90, 1,107,790. 102, 
 
 12; 
 
 3878; 
 
 4.3761829; 
 
 91, $501.02. 
 
 17; 
 
 9334; 
 
 2.1462729; 
 
 92, $72.17. 
 
 13.37; 
 
 2999. 
 
 0.088907 ; 
 
 93, $235.56; 
 
 15.8958; 
 
 75, 195; 
 
 2.976072; 
 
 $180.37. 
 
 100. 
 
 119; 
 
 1.6715398; 
 
 94, 66 yrs. ; 103, 
 
 0.5; 
 
 1822; 
 
 3.1636232; 
 
 45 yrs., 11 mos., 
 
 30 days. 
 
ANSWERS. 
 
 Vrt. Art. 
 
 103, 0.47; 116, 
 
 439.726; 
 
 122, 0.0065; 
 
 0.468; 
 
 74.2064; 
 
 0.00012. 
 
 0.4764; 
 
 469.206. 
 
 123, $98.10; 
 
 0.4764012. 117, 
 
 3.1415928; 
 
 $320.60; 
 
 104, 3005; 
 
 3.1415928; 
 
 $608.40; 
 
 2494; 
 
 78.53981625. 
 
 $784; 
 
 1997; 118, 
 
 34.5576; 
 
 $1028.40. 
 
 1484; 
 
 37.6992; 
 
 124, $0.83625; 
 
 428; 
 
 40.8408; 
 
 $19.5125; 
 
 939; 
 
 43.9824; 
 
 $0.250875; 
 
 1436; 
 
 47.124; 
 
 $4.73875; 
 
 1949. 
 
 24.596748; 
 
 $0.529625; 
 
 105, 31,385. 
 
 29.068884; 
 
 $3.62375; 
 
 106, 3.15. 
 
 38.013156; 
 
 $22.30; 
 
 107, $8138.25; 
 
 38.013156; 
 
 $23.13625; 
 
 $7245.75. 
 
 40.249224 ; 
 
 $0.39025. 
 
 108, A.D. 899 ; 
 
 42.485292. 
 
 125, 262.5; 
 
 A.D. 1087 ; 120, 
 
 31.4159265; 
 
 5467; 
 
 B.C. 399; 
 
 314.159265; 
 
 2355; 
 
 B.C. 347; 
 
 3,141,592.65; 
 
 0.48825; 
 
 B.C. 382; 
 
 $37.50; 
 
 523,456; 
 
 A.D. 70. 
 
 $21.70; 
 
 9.321102. 
 
 109, James, 1 more. 
 
 $58.75; 
 
 129, 1.570796; 
 
 116, 555; 
 
 $375; 
 
 15.70796; 
 
 369; 
 
 $217; 
 
 2.356194; 
 
 462; 
 
 $587.50; 
 
 235.6194; 
 
 342; 
 
 $337.50; 
 
 3.92699; 
 
 1684; 
 
 $512.50. 
 
 0.392699; 
 
 2560; 122, 
 
 0.236; 
 
 0.00392699; 
 
 17,312; 
 
 0.0236; 
 
 578.838326; 
 
 7122; 
 
 0.00063.; 
 
 5.78838326; 
 
 14,256; 
 
 0.078; 
 
 672.300688 ; 
 
 58.009; 
 
 0.00431 ; 
 
 67.2300688; 
 
 28.8594; 
 
 0.002331 ; 
 
 0.0672300688 
 
ARITHMETIC. 
 
 Art. 
 
 129, 
 
 Art. 
 
 7.85398; 135, 
 
 Art. 
 
 4466.88. 144, 
 
 7.02460 ; 
 
 
 786.183398; 138, 
 
 7.77546; 
 
 20,000,001.06; 
 
 
 0.786183398; 
 
 0.777546; 
 
 0.381966 ; 
 
 
 749.269692; 
 
 0.0777546; 
 
 5000.000 ; 
 
 
 0.00749269692. 
 
 52.20292; 
 
 3000.00. 
 
 130, 
 
 215.042; 
 
 5.230204; 147, 
 
 1. $626; 
 
 
 2.15042; 
 
 5.167932; 
 
 $624; 
 
 
 1612.815; 
 
 82.8089; 
 
 $628; 
 
 
 161.2815; 
 
 8532.7315. 
 
 $626. 
 
 
 178.48486. 139, 
 
 90.85041; 
 
 2. 1346. 
 
 131, 
 
 0.98994952; 
 
 230.52519; 
 
 3. 16.011 bu. 
 
 
 0.9998490152; 
 
 4.6723068; 
 
 4. $52,976,000. 
 
 
 0.99999043656; 
 
 5.5190079; 
 
 5. 767,340. 
 
 
 1.0000003360552; 
 
 6.1370379; 
 
 6. 252,321.5. 
 
 
 1.979894; 
 
 3.136364; 
 
 7. $73.20. 
 
 
 1.999975782; 
 
 4.183564; 
 
 8. $43.42. 
 
 
 2.0000040662; 
 
 4.7108292; 148, 
 
 1.7 8 ; 8 3 ; 
 
 
 2.999824; 
 
 366.509528. 
 
 C9. 
 ^ > 
 
 
 4.99985252; 140, 
 
 0.4853772; 
 
 5 6 . 
 
 
 381.924; 
 
 0.3000228; 
 
 2. 3.01 3 ; 
 
 
 0.38196664319; 
 
 0.61685316; 
 
 0.67 10 ; 
 
 
 0.61803335681. 
 
 0.2371908; 
 
 0.208 4 . 
 
 133, 
 
 63,231.52; 
 
 1.679724; 
 
 3. 2.003 6 ; 
 
 
 654.6528; 
 
 1.038276; 
 
 20.03 4 ; 
 
 
 450.8847; 
 
 2.1347172; 
 
 20.03 3 . 
 
 
 309.89508. 
 
 1.649826. 153, 
 
 321; 
 
 134, 
 
 2,914,700; 141, 
 
 34.109310; 
 
 423; 
 
 
 278,560; 
 
 20.103747; 
 
 282; 
 
 
 99.9999; 
 
 2.296; 
 
 141 ; 
 
 
 7854. 
 
 4.74165; 
 
 212; 
 
 135, 
 
 1584; 
 
 11.647195; 
 
 10.41 ; 
 
 
 3696; 
 
 0.110999; 
 
 12.004 ; 
 
 
 897.6; 
 
 8.362134; 
 
 1.21; 
 
 
 3025.44; 
 
 74538. 
 
 0.144. 
 
ANSWERS. 
 
 158, 1. 0.04286; 160, 
 
 4. 
 
 2.23613. 
 
 Art. 
 
 167, 6. 19||f ; 
 
 0.000027 ; 165, 
 
 1. 
 
 2. 
 
 i; 
 
 36,666.66667. 
 
 2. 
 
 684. 
 
 0.5. 
 
 2. 23.33333; 
 
 3. 
 
 1095. 
 
 7. 2; 
 
 1571.42857; 
 
 4. 
 
 330. 
 
 2 T7r; 
 
 18.57143. 
 
 5. 
 
 236.4. 
 
 i; 
 
 3. 24.28571; 
 
 6. 
 
 6048. 
 
 0.1126; 
 
 0.00064; 
 
 7. 
 
 6700. 
 
 0.01; 
 
 0.01182. 
 
 8. 
 
 30.12. 
 
 0.00011. 
 
 4. 0.01545; 
 
 9. 
 
 0.9072. 
 
 168, 1. 3.637813. 
 
 0.05833 ; 
 
 10. 
 
 44.1. 
 
 2. 0.00129. 
 
 0.0025. 
 
 11. 
 
 215,240. 
 
 3. 2.030. 
 
 5. 91.66667; 
 
 12. 
 
 8516.6. 
 
 4. 0.00007294. 
 
 1.41667; 
 
 13. 
 
 217. 
 
 5. 38.144. 
 
 14.16667. 
 
 14. 
 
 3040. 
 
 6. 0.00005677. 
 
 6. 2266.66667; 
 
 15. 
 
 259. 
 
 7. 6120.968. 
 
 1133.33333; 
 
 16. 
 
 324. 
 
 169, 1. 1; 
 
 0.12364. 
 
 17. 
 
 22.5. 
 
 10; 
 
 7. 320; 
 
 18. 
 
 33.75. 
 
 100; 
 
 32; 167, 
 
 1. 
 
 2; 
 
 1000; 
 
 3.2. 
 
 
 4; 
 
 10,000 ; 
 
 8. 0.032; 
 
 
 5; 
 
 100,000 ; 
 
 1.17778; 
 
 
 0.5; 
 
 1,000,000. 
 
 0.00012. 
 
 
 0.4015; 
 
 2. 1; 
 
 160, 1. 3.35977; 
 
 
 0.90202. 
 
 TV; 
 
 1.75499; 
 
 2. 
 
 0.70710. 
 
 T^O; 
 
 94.66644 ; 
 
 3. 
 
 0.70710. 
 
 TtfW ' 
 
 184.98040. 
 
 4. 
 
 3.14159; 
 
 Tin5iF"o i 
 
 2. 1.76470; 
 
 
 0.31831. 
 
 i _ . 
 
 1.73410; 
 
 5. 
 
 0.54023 ; 
 
 yirir ^ TTr ; 
 
 1.73210; 
 
 
 0.60919; 
 
 3. 1; 
 
 1.73200. 
 
 
 0.5; 
 
 1; 
 
 3. 0.0000254; 
 
 
 0.33333. 
 
 1; 
 
 4. 1.41423; 
 
 6. 
 
 U$f ; 
 
 1 ; i 
 
ARITHMETIC. 
 
 Art. 
 
 169, 4. 10,000: 
 
 TT7 innr '> 
 100; 
 
 5. T V; 6.10; 
 
 10; yV; 
 
 _ i iQ. 
 
 7. 1.030301; 
 1.01; 
 0.99009. 
 
 100. 
 
 10. 1. 
 
 
 EXERCISE I. 
 
 
 Page 63. 
 
 
 17. 73.603891. 
 18. 1426.8527. 
 
 21. 19.0554; 
 21.8365. 
 
 23. 0.45763; 
 99.99824. 
 
 19. 61.942. 
 
 22. 24.7183; 
 
 24. 8.5125. 
 
 20. 11.5111; 
 7.51917. 
 
 0.8531. 
 
 25. 24.9914. 
 
 
 Page 64. 
 
 
 26. 20.6445; 
 
 31. 9.0601; 0.002025; 37. 
 
 0.02295; 
 
 0.2412; 
 0.0224. 
 
 0.00006561; 
 132.682214448064; 
 
 2.25; 
 0.1794. 
 
 27. 10.30005; 
 241.46387 ; 
 
 0.438976. 38. 
 32. 0.000512. 
 
 11,875; 
 2894.53125; 
 
 0.01004. 
 
 33. 48.64; 0.01078; 
 
 7.8125. 
 
 28. 0.000006; 
 
 8.8089. 39. 
 
 0.10720; 
 
 453.646; 
 0.43104. 
 29. 0.343; 
 0.03555. 
 30. 1.13925. 
 
 34. 149.7; 3.593; 7557. 
 35. 10.932; 0.4575; 2760. 
 36. 39,840; 1000; 40. 
 10,000,000. 
 
 20.41482; 
 0.17857. 
 0.06905; 
 58,257.40365; 
 338,983.05084. 
 
 EXERCISE II. 
 
 1. 7.375. 3. 10. 6. 5. 9. 0.06. 12. 0.00112914. 
 
 2. 6. 4. 5.555. 7. 20. 10. 0.202272. 13. 3. 
 
 5. 1. 8. 9. 11. 0.0078. 
 
ANSWERS. 7 
 
 Page 65. 
 
 14. 13. 17. 0.0505. 20. 0.7557. 23. 2760. 
 
 15. 19.04. 18. 0.00046. 21. 0.010932. 24. 116. 
 
 16. 120. 19. 0.0003593. 22. 0.00004575. 25. 2.52. 
 
 EXERCISE III. 
 
 1. 909. 4. 2.27083 mi. 6. 21.36288 ; 7. 96.248 in. 
 
 2.42. 5. 3.4167 hrs. 6.36618. 8.336.13445. 
 
 3. 935. 
 
 
 
 
 Page 66. 
 
 
 9. 350.25 Ibs. 
 
 14. $5934. 
 
 17. 8857.98276 min. 
 
 10. 260,078. 
 
 15. 61. 
 
 18. 14,925.37313. 
 
 11. 601. 
 
 16. 37.56097 min. ; 
 
 19. $31.45. 
 
 12. $2184.91. 
 
 49.67741 min. 
 
 20. $196.80. 
 
 13.4032; $3.24. 
 
 
 21. 66,662.97. 
 
 
 Page 67. 
 
 
 22. 8590.10270. 
 
 26. 3 dys. ; 
 
 28. B., $46.36; 
 
 23. 7.48051 ; 
 
 6 dys. ; 
 
 0., $41.48. 
 
 9.30917; 
 
 6 dys. 
 
 29. $63.20. 
 
 1.24445; 
 
 27. H., $0.54; 
 
 30. 420 ; 50. 
 
 3.38375. 
 
 T., $0.90; 
 
 31. 6000. 
 
 24. $8383.67. 
 
 R, $0.36. 
 
 32. 24,780 Ibs. ; 
 
 25. 7068. 
 
 
 25,620 Ibs. 
 
 33. 708 Ibs., dry ; 
 732 Ibs., wet. 
 
 34. 15.245 cu. in. ; 
 113.34863 Ibs. 
 
 35. 1.81357. 
 
 43. 39.3708. 
 
 36. 7.49064. 39. 671,400,000 mi. : 
 
 37. 7.50334. l,080,684,000 kro . 
 
 38. 11,190,000 mi. ; 40. 449.43724. 
 18,011,400 km . 41. 431.03448. 
 
 42. 0.2178. 
 Page 69. 
 
 44. Divided by 2. 
 
 45. It is increased by two times the number ; not any. 
 
ARITHMETIC. 
 
 46. It is multiplied by the square of the number ; not any. 
 
 47. It is multiplied by the number ; it is divided by the 
 
 number. 
 
 48. 1.21 sec. ; 343.4 sec. ; 
 475.3 sec. ; 723.4 sec. ; 
 183.7 sec. ; 1291.1 sec. : 
 
 49. Earth, 91,501,150; 
 Mercury, 35,357,660 ; 
 
 Venus, 66,116,960 ; 
 Mars, 139,255,740 ; 
 
 2470.6 sec. ; 14,270.5 sec. ; 
 
 4528.7 sec. ; 77,469,335 sec. 
 9093 sec. ; 
 
 Asteroids, 248,560,000 ; 
 Jupiter, 475,619,560 ; 
 Saturn, 871,824,200; 
 Uranus, 1,750,483,800; 
 
 Neptune, 2,747,209,400. 
 
 
 
 
 Page 73. 
 
 
 
 1. 
 
 5.427 km ; 
 
 5. 
 
 1.23 km ; 
 
 10. 
 
 391.94845"' 
 
 
 5,427,000 mm ; 
 
 
 123,000 cm 
 
 
 16 m . 
 
 
 542,700 cm . 
 
 6. 
 
 12.30 m ; 
 
 11. 
 
 $11.59. 
 
 2. 
 
 6.853 m ; 685.3 cnt ; 
 
 
 12,300 mm . 
 
 12. 
 
 $45. 
 
 
 0.006853 ku \ 
 
 7. 
 
 172.718 m . 
 
 13. 
 
 42.05 m . 
 
 3. 
 
 4970 cm ; 
 
 8. 
 
 862.05 m ; 
 
 14. 
 
 $3.12. 
 
 
 49 ; 700 ram ; 
 
 
 0.00083 m . 
 
 15. 
 
 $0.014. 
 
 
 0.0497 km . 
 
 9. 
 
 365.6 m ; 
 
 16. 
 
 533.33 m . 
 
 4. 
 
 l,240,000 cm ; 
 
 
 1.852272"'; 
 
 17. 
 
 0.07. 
 
 
 12,400,000 mm . 
 
 
 0.364896 m . 
 
 18. 
 
 $147. 
 
 Page 75. 
 
 1. 185.4276 ha ; 
 1.854276 qkm . 
 
 2. 278.56 ha . 
 
 3- 1 
 
 l,743,100 qmm . 
 4. 174.675 qkm . 
 
 5. l,361,400 qra 
 
 6. 22,500 qm . 
 
 s;e 76. 
 
 7. 137 qcm . 
 
 8. 357.1 qmm . 
 
 Page 77. 
 1. 2,250,000 ccm 2. 2.162875 cbm . 
 
ANSWERS. 
 
 1. 1700 1 ; 
 157.854 1 . 
 
 2. 9500 ccm ; 15 C< 
 
 3. 125,000 ccra ; 
 0.125 cbm . 
 
 Page 78. 
 
 4. 4.3188 hl ; 
 0.43188 cbm 
 
 5. 375 1 ; 375,000 ccm . 
 
 6. 734.15965 1 1 ; 
 7.3415965P 1 ; 
 0.734159651 cbm . 
 
 7. 8.573412867 cbm . 
 
 8. 734,578.912 ccm ; 
 734.578912 1 . 
 
 9. 1.7315 cbm ; 
 l,731,500 ccm . 
 
 1. 1730; 
 341. 
 
 2. 100. 
 
 Page 79. 
 
 3. 13.756 g ; 4. 346.P. 
 
 0.013756 kg . 5. 376.15 kg . 
 
 EXERCISE IV. 
 
 1. 109.59 m . 
 
 2. $254.12. 
 
 3. 57.625 ra . 
 
 4. 3.437 m . 
 
 5. ll,282 km . 
 
 6. 3312 km ; 2860 km ; 
 1600 km ; 3180 km . 
 
 15. 3.1416 m . 
 
 16. 260,752.8 mm : 
 ll,655.3 mm ; 
 103,044.5""" 
 326. 7 mm ; 
 370. 7 mm ; 
 525.0 ffira ; 
 123. 5 mm . 
 
 Page 80. 
 
 7. 5527.9 km ; 
 6712.45 km ; 
 15,478.12 km ; 
 21,953.66 km ; 
 288,240.5 km 
 
 8. $4.11; $14.15. 
 
 Page 81. 
 
 17. 925,142,191,327 m 
 
 18. 40,005.1344 kn \ 
 
 19. 4.1155 m ; 
 4.1155 m ; 
 69.9635 m . 
 
 20. 17 nearly; 
 18 nearly; 
 4197 nearly. 
 
 6. 677,800 mg . 
 
 7. 5800. 
 
 9. $113.63; 
 
 $229.17. 
 
 10. $745.88. 
 
 11. $64.88. 
 
 12. $128.50. 
 
 13. $968.50. 
 
 14. $47.32. 
 
 21. 0.31831. 
 
 22. 100 cm . 
 
 23. 1.7507 m . 
 
 24. 0.94538 m . 
 
 25. 636.62 m . 
 
 26. 6.3662 cm . 
 
 27. 23.87325 m 
 
10 
 
 ARITHMETIC. 
 
 1. 323 qcm . 
 
 2. ll,200 ha ; 
 ll,144.659 ha . 
 
 EXERCISE V. 
 Page 82. 
 
 3. 14.222 ha ; 
 14.166 ha . 
 
 4. 0.169 ha . 
 
 Page 83. 
 
 24. 99.84 m 
 
 25. 54 m . 
 
 31. 19. 
 
 32. $35. 
 
 38. $120, 
 
 39. $234.60. 
 
 Page 85. 
 
 26. 43.76 m . 
 
 27. 25 m ; $46.88. 
 
 5. 15.639 qm ; 
 33.914 qm ; 
 40.152 qin . 
 
 6. 2.49126761 ha ; 
 
 7. $956.66 ; 
 
 8. 572.5566 qcm ; 
 
 2.4909024 ha ; 
 
 $956.51 ; 
 
 0.7854 qm . 
 
 2.4907176 ha ; 
 
 $956.44; 
 
 9. 48.275 ha . 
 
 7.47288761 ha . 
 
 $2869.60; 
 
 10. 754.7694 qcm . 
 
 7. $168.16; 
 
 $59,167.61 ; 
 
 11. 18 cm ; 
 
 $168.14; 
 
 $59,158.93; 
 
 36 m . 
 
 $168.12; 
 
 $59,154.54 ; 
 
 12. 468 qm ; 
 
 $504.42; 
 
 $177,481.08. 
 
 300 qm . 
 
 
 Page 84. 
 
 
 13. 153.9384 qcm 
 
 17. 7696.92 qcm . 
 
 21. 1809.5616 qm . 
 
 14. 1017.8784 qcm 
 
 18. 48.275 ha . 
 
 22. 5026.56 qm ; 
 
 15. 199.5119 qm 
 
 19. 153.9384 qcm . 
 
 706.86 qm ; 
 
 16. 226.1952 qcm . 
 
 20. 1.505 qm . 
 
 4319. 7 qm . 
 
 28. 33.25 m ; $70.66. 
 
 29. 44.8 m ; 40 cm ; $56. 
 
 Page 86. 
 
 33. $73.88. 35. $36.14. 
 
 34. $14. 36. $19.95. 
 
 Page 87. 
 
 40. 1.6. 42. 96. 
 
 41. 3.75. 43. 5.5. 
 
 37. $43.20. 
 
 44. 72; $18. 
 45.42; $5.88. 
 
ANSWERS. 
 Page 88. 
 
 46. $1.49. 
 
 47. $19.21? 
 
 48. $7.56. 
 
 49. $0.97. 
 
 50. $3.85. 
 
 51. $129.02. 
 
 11 
 
 52. $55.20. 
 
 53. $118.04. 
 
 EXERCISE VI. 
 
 Page 89. 
 1. 378 ccm . 2. 73.416 s . 3. 1375.6064 hl . 4. lll,424.1184 k *. 
 
 Page 90. 
 
 5. $4258.69. 8. 280.68 hl ; 11. 0.785 1 . 
 
 6. 1079.757 1 ; 173.086 hl ; 12. 4.132 1 ; 
 1079.757 k -. 364.884 hl . 0.392 1 . 
 
 7. 445,341 ccm ; 9. 2.3701 m ; 13. 523.6 ccm ; 
 445.341 1 ; 9.2201 hl . 0.0012 ccm . 
 4.45341 hl . 10. 298.452 ccm . 14. 3811.2 ccra , or 3.8112 1 . 
 
 15. 1749.561 1 , or 
 17.49561 hl . 
 
 Page 91. 
 
 16. 145,782 l . 
 
 17. 223.42 min. 
 
 18. 40.459 min. 
 
 19. 0.903178 cbm . 
 
 EXERCISE VII. 
 
 1. 100 k ; 73.8 kR ; 3. 264.404 k *. 5. 259.380 kg . 
 1000 k ; 0.001 kg . 4. 274.980 k s. 6. 955.24 kg . 
 
 2. $5. 
 
 Page 92. 
 
 7. 7235 k *, or 7.235'; 8. 2S.75 k *. 9. 24. 
 
 8464.95 k s, or 8.46495*. 10. 363.33 m *. 
 
 EXERCISE VIII. 
 Page 93. 
 
 1. 0.833. 3. 79.249 kJ? ; 79.443 k{? ; 4. 64.1806 K ; 
 
 2. 678.11 k . 79.831^; 81.286 k ; 66.6779^. 
 
 82.159^. 
 
12 
 
 ARITHMETIC. 
 
 Page 94. 
 
 5. 2.608. 8. 
 
 8.953. 10. 1.0258 
 
 ; 13. 7.3. 
 
 6. 5.1635 k *. 9. 
 
 7.309 ; 1.0257. 
 
 14. 2.317. 
 
 7. 12.242 k * ; 
 
 283.615 kg ; 11. 4.315. 
 
 15. 2.789. 
 
 12.215 k *. 
 
 295.765 k *. 12. 1.723 ; 
 
 16. 3.04. 
 
 
 2.098. 
 
 
 
 Page 95. 
 
 
 17. 17.8 ccm ; 
 
 18. 13.616 ; 13.588 ; 
 
 19. 7.5. 
 
 1.893. 
 
 13.592; 13.599. 
 
 
 
 EXERCISE IX. 
 
 
 1. 2.67 kg ; 18.67 kg ; 
 
 2. 161.5 kg . 4. 40 1 ; 
 
 5. 90 l ; 
 
 1.14 kg ; 0.38 kg ; 
 
 3. 20 1 ; 13.33 1 
 
 ; $4.44. 
 
 2.67 kg ; 18.67 k *; 
 
 140 1 ; 560 1 . 
 
 6. $0.06 ; 
 
 93.33 k *. 
 
 3740 1 . 
 
 $0.065. 
 
 
 Page 96. 
 
 
 7. $11.50. 10.11. 
 
 .2 min. 13. 40 min. 
 
 16. 61 times. 
 
 8. 7. 11. 6.588 min. 14. 2.533 1 a min 
 
 . 17. 852.6 k *. 
 
 9. $26.25. 12. 2.4984 dys. 15. 265.26. 
 
 18. $159.86. 
 
 
 EXERCISE X. 
 
 
 
 Page 97. 
 
 
 1. 46,609 m . 
 
 5. $900,662.50. 
 
 7. 41.145 m . 
 
 2. 5013. 
 
 6. $23,062,338; 
 
 8. 12.16 m 
 
 3. 840. 
 
 $7,391,775. 
 
 9. 0.028 cm . 
 
 4. $2,876,626.20. 
 
 
 10. 2304.338 kn . 
 
 Page 98. 
 
 11. 6.24 km . 13. 100 ha ; 14. 54,200,000 ha . 17. 1690. 
 
 12. 19,277.2. 10,000 a ; 15. $20,991.60. 18. $0.136. 
 
 l,000,000 qm . 16. 716. 19. $300. 
 
 20. 0.997 2 x 14.0715 ha - 13.987 ha . 
 
ANSWERS. 
 
 13 
 
 
 
 Page 99. 
 
 
 21. 
 
 121,000; 
 
 24. 0.15869 cbm . 
 
 27. 3.646 cbm . 
 
 
 181.5", 
 
 25. 10.547. 
 
 28. 196. 
 
 22. 
 
 0.283608 a . 
 
 26. 5250 1 ; 2.38 m 
 
 29. 1.6387 cbm . 
 
 23. 
 
 14.6965 s . 
 
 
 
 
 
 Page 100. 
 
 
 
 30. 4200. 
 
 
 32. 1331 ccm ; 18,782. 
 
 
 31. 1372.55 1 ' 1 ; 
 
 $4952.50; 
 
 33. 29.532 cbm . 
 
 
 $148.58. 
 
 
 34. 1.273 kg . 
 
 Page 101. 
 
 35. $0.602. 41. $1.48. 
 
 36. 3243. 42. 9 m . 
 
 37. 0.0434578 kg . 43. 0.86207 m . 
 
 38. 1.911'. 44. $8. 
 
 39. 1.16 ccm ; 0.14 ccm ; 0.088 ccm ; 45. 6.06 ccm . 
 0.113 ccm ; 0.095 ccm ; 4.167 ccm . 46. 154.943 qcm . 
 
 40. $0.548. 47. 32.5624 kg . 
 
 48. 33.696 k *. 
 
 49. 18,966. 
 
 50. 0.4615 cbm ; $14.28. 
 
 Page 102. 
 
 51. 3624.145 k *. 
 
 52. 258.74 1 ; 12. 
 
 53. 20.48 cbm . 
 
 54. $993.30. 
 
 55. 56,000. 
 
 56. 101.118 1 . 
 
 Page 103. 
 
 57. 67.259 kg ; 16.72 cm . 61. 10,472'. 
 
 58. 7; 5 1 . 
 
 59. 0.42568 cbm ; $0.518. 
 
 60. 6.603 m . 
 
 62. 666.37 qm . 
 
 63. 0.032 mm . 
 
 64. 1.264; $2,173,913.04. 
 
 
 Page 10 i. 
 
 65. 3846.15 m 67. 1194; $188.81. 
 
 66. 1128.7878 kg . 68. 0.89079 1 ; 434.2K 
 
 69. 196.875 kg . 
 
 Page 105. 
 
 70. $71.96; 1504.11134 kg . 72. $25,608.96. 74. $0.191. 
 
 71. $0.28. 73. 83.333 m . 75. $1378.13. 
 
 
14 
 
 ARITHMETIC. 
 
 EXERCISE XL 
 
 1. 2 X 2 X 37 ; 4. 
 2 3 X 3 X 11 ; 
 
 2 X 89 ; 3 X 61 ; 
 1X173; 11X17; 
 2X 173; 7x7x7. 
 
 2. 2x3x5x7; 
 1 X 353 ; 
 
 2 5 X 3x 5x 11; 5. 
 
 3x7x11; 
 
 2 3 x3x7xllxl7; 
 
 37x37; 
 
 2 3 x 3 2 x 19. 
 
 3. 13 X 19 ; 3 X 109 ; 
 1X179; 1x83; 
 5 3 Xl7; 
 
 13 X 181 ; 
 1 X 2333. 
 
 Page 110. 
 
 3X5X11; 
 
 2 3 X 3 X 7 ; 
 
 2 2 X 3 X 179 : 
 2x3x2777: 
 3x107; 
 3x11x47; 
 2x19. 
 2x41; 
 3x43; 
 
 2 3 X 3 2 ; 
 2x3x 11; 
 2 2 X 17 ; 
 5x13; 
 
 2 2 x 19 ; 
 2x43; 
 2 3 Xll; 
 2x71; 
 
 6. 2 X 163 ; 2 4 X 23 ; 
 2 4 X 29 ; 2 2 X 73 ; 
 2 X 181 ; 5 X 73 ; 
 2 X 5 X 73 ; 
 2x3x7. 
 
 7. 2 2 x7x31; 3 3 X37; 
 2x3 X 137; 
 2x673; 3 3 X283; 
 2 X 3 X 1039 ; 
 
 2 X 3 2 X 13 ; 
 
 8. 3X 193; 1X577; 
 2 2 x53;2x3 2 x7; 
 2 7 2 13 
 2x3 2 x5x7xl3. 
 
 9. 7x1171; 
 5 5 ; 7 4 ; II 3 ; 
 
 3 2 x7x 11x113; 
 
 3 x 7 x 11 X 109, 
 
 EXERCISE XII. 
 
 1. 2 2 x 3x7x0.1; 
 2 2 xl9x0.1; 
 2 2 x3 3 x0.01; 
 2 4 x3 2 X 0.001; 
 
 2 2 x3 2 x 0.001; 37x0.001; 
 3x5x11x13x0.01. 
 
 2. 2x73x0.1; 
 3 2 x29x0.01; 2 2 x53x0.1; 
 2x3x7x11x17x0.01; 
 2 2 x7xllxl7x0.0001; 
 2 2 x 13x0.00001. 
 
 3. 3xl7 2 x0.01; - 
 3x7x23x0.1; 
 3 2 X 11x101x0.01; 
 2 3 x3 2 x7x0.01; 
 3 3 x5xllx0.001; 
 2 3 X3 3 X 0.001. 
 
 4. 11x317x0.01; 
 2 2 x3 4 x0.1; 
 3x5x11x31x0.001; 
 2 3 x89x0.1; 
 41x73x0.001. 
 
ANSWERS. 
 
 15 
 
 EXERCISE 
 
 XIII 
 
 
 
 
 Page 112. 
 
 1 
 
 .3. 
 
 7, 
 
 ,2. 
 
 
 12. 14. 
 
 
 17. 6. 
 
 22. 
 
 11. 
 
 2 
 
 . 13. 
 
 8 
 
 ,3. 
 
 
 13. 12. 
 
 
 18. 14. 
 
 23. 
 
 21. 
 
 3 
 
 .4. 
 
 9 
 
 . 5. 
 
 
 14. 21. 
 
 
 19. 16. 
 
 24. 
 
 16. 
 
 4 
 
 . 9. 
 
 10. 14. 
 
 15. 4. 
 
 
 20. 24. 
 
 25. 
 
 17. 
 
 5 
 
 .27. 
 
 11, 
 
 , 6. 
 
 
 16. 9. 
 
 
 21. 42. 
 
 26. 
 
 101. 
 
 6. 2. 
 
 EXERCISE 
 
 XIV 
 
 
 
 
 Page 115. 
 
 1 
 
 .37. 
 
 5 
 
 . 135. 
 
 
 9. 809. 
 
 
 13. 97. 
 
 17. 
 
 1. 
 
 2 
 
 . 105. 
 
 6 
 
 .352. 
 
 
 10. 113. 
 
 
 14. 93. 
 
 18. 
 
 56. 
 
 3 
 
 ,8. 
 
 7 
 
 .345. 
 
 
 11. 127. 
 
 
 15. 108. 
 
 19. 
 
 387. 
 
 4 
 
 . 151. 
 
 8 
 
 . 107. 
 
 
 12. 99. 
 
 
 16. 59. 
 
 20. 
 
 2138. 
 
 EXERCISE 
 
 XV 
 
 
 
 
 Page 116. 
 
 1 
 
 .57. 
 
 3 
 
 .247. 
 
 
 5: 107. 
 
 
 7.37. 
 
 9. 
 
 111. 
 
 2.23. 
 
 4 
 
 .327. 
 
 
 6. 449. 
 
 
 8. 119. 
 
 10. 
 
 227. 
 
 EXERCISE 
 
 XVI. 
 
 Page 118. 
 
 
 1.42. 
 
 11. 
 
 297. 
 
 21. 
 
 630. 
 
 31. 
 
 288. 
 
 41. 7560. 
 
 
 2.24. 
 
 12. 
 
 1001. 
 
 22. 
 
 32,400. 
 
 32. 
 
 36,036. 
 
 42. 2400. 
 
 
 3.30. 
 
 13. 
 
 385. 
 
 23. 
 
 780. 
 
 33. 
 
 3570. 
 
 43. 32 
 
 ,844. 
 
 
 4.36. 
 
 14. 
 
 432. 
 
 24. 
 
 3600. 
 
 34. 
 
 5040. 
 
 44. 40,480. 
 
 
 5. 105. 
 
 15. 
 
 660. 
 
 25. 
 
 600. 
 
 35. 
 
 27,324. 
 
 45. 23 
 
 ,400. 
 
 
 6. 120. 
 
 16. 
 
 7920. 
 
 26. 
 
 210. 
 
 36. 
 
 2340. 
 
 46. 576,576. 
 
 
 7. 168. 
 
 17. 
 
 6720. 
 
 27. 
 
 2520. 
 
 37. 
 
 27,720. 
 
 47. 181,875. 
 
 
 8.60. 
 
 18. 
 
 1296. 
 
 28. 
 
 2310. 
 
 38. 
 
 228,150. 
 
 48. 50 
 
 ,592. 
 
 
 9. 96. 
 
 19. 
 
 1800. 
 
 29. 
 
 756. 
 
 39. 
 
 13,800. 
 
 49. 29,029. 
 
 10. 231. 
 
 20. 
 
 4704. 
 
 30. 
 
 6630. 
 
 40. 
 
 2736. 
 
 50. 10 
 
 ,241. 
 
16 ARITHMETIC. 
 
 EXERCISE XVII. 
 
 Page 119. 
 
 1. 4664. 6. 27,869. 11. 7,577,304. 16. 37,219. 
 
 2. 11,803. 7. 92,796. 12. 12,397. 17. 163,601,937. 
 
 3. 141,036. 8. 14,385. 13. 164,808. 18. 250,641,677. 
 
 4. 41,123. 9. 5967. 14. 3,295,313. 19. 34,573. 
 
 5. 23,069. 10. 61,318. 15. 260,117. 20. 79,781. 
 
 EXERCISE XVIII. 
 
 Page 122. 
 
 1. If. 4. 9 T 8 T . 7. 14|f . 10. 26^- 2 T - 13 - 18^- 
 
 2. 2|. 5. 13 f V 8. 37. 11. 3f. 14. 18|*. 
 
 3. 61 6. 11. 9. 50ff. 12. 13. 15. 359." 
 
 EXERCISE XIX. 
 
 Page 123. 
 
 W- 
 
 EXERCISE XX. 
 
 Page 124. 
 
 l.f. 6.f. 11. f 16. V 21-TVr- 26. |f 
 
 2.f 7. |J. I 2 - If 17. T V 22.fif. 27. ff 
 
 3. ii|. 8. -\- i3 - H- 18 ' If 23 ' Iff- 28 ' 2 3 9 4 3 9 8 2 3 ! 2 -- 
 
 4. if 9. T 8 g-. 14. 1. 19. if. 24. -j^-. 29. -f^. 
 
 5. if. 10. f^. 15. iff. 20. -^- 2 T - 25 ' *i 30 ' f 
 
ANSWERS. 17 
 
 
 EXERCISE XXI. 
 
 
 
 
 Page 125. 
 
 
 
 Mi 
 
 2. Of. 
 3.4. 
 4. 15. 
 
 5. 3. 8. f . 11. l^f 14. 3 T V 
 6. 10. 9. 15. 12. 2f . 15. 4^. 
 7. LI. 10. 1-^. 13. 3-1-. 16. 5. 
 
 17. 
 18. 
 19. 
 20. 
 
 4 
 
 13. 
 
 
 EXERCISE XXII. 
 
 
 
 
 Page 126. 
 
 
 
 2 ^ 
 3. ^V 
 
 4.6. 
 
 5. lOf 8. f 11. IsV 14. f 
 6. 451 9. 11. 12. 48 T %. 15. 1-l^f . 
 7. 2. 10. 3f . 13. 1|. 16. llf 
 
 17. 
 18. 
 19. 
 
 8 f 
 I. 3 
 
 
 Page 127. 
 
 
 
 20. 6^. 
 
 21. f w 
 
 22. f . 
 
 23. _U. 25. f. 27. 52^ 4 T . 29. 32 T V 
 24. 8. 26. 2}f . 28. 20^-. 30. |f . 
 
 31. 
 32. 
 33. 
 
 1 
 
 
 EXERCISE XXIII. 
 
 
 
 2 ^ 
 3 -$- 
 
 4.2l 
 
 5. s 8 . i4 n. 27 14. 9 
 
 o o o 6 o 14 
 
 6. 2. 9. 2. 12. If 15. li. 
 7. |i 10. 1. 13. 7-1. 16. 3. 
 
 17. 
 18. 
 19. 
 
 2 
 6^-. 
 
 
 EXERCISE XXIV. 
 
 
 
 
 Page 129. 
 
 
 
 1. 
 2. 
 
 14.0 20031 5 324 K 288 255 130 152 
 
 
 
 3. .10.0_10.A_200._!Afi. g^ 315 19690 90 665 
 7. 
 
 8" tf, f , I- 9- H- A- H- 10 ' T 4 T- T ? 8- fV> A- 
 
18 ARITHMETIC. 
 
 EXERCISE XXV. 
 
 
 
 
 
 
 Page 131. 
 
 
 
 1. 
 
 2. 
 
 9. 
 
 2 T V 
 
 17. 
 
 113^. 25. Hf. 
 
 33. 
 
 341i| 
 
 2. 
 
 li 
 
 10. 
 
 21 T 3 T . 
 
 18. 
 
 llf 26. 114 1-. 
 
 34. 
 
 Hi 
 
 3. 
 
 H- 
 
 11. 
 
 l*i 
 
 19. 
 
 2ff . 27. 10|ff . 
 
 35. 
 
 1^4- 
 
 4. 
 
 4. 
 
 12. 
 
 If- 
 
 20. 
 
 3_i_. 28. ll^f. 
 
 36. 
 
 346^ 
 
 5. 
 
 4. 
 
 13. 
 
 i- 
 
 21. 
 
 85^-. 29. 14f|. 
 
 37. 
 
 29^\ 6 5 
 
 6. 
 
 4. 
 
 14. 
 
 li 
 
 22. 
 
 199^. 30. 18^. 
 
 38. 
 
 istfi 
 
 7. 
 
 6|. 
 
 15. 
 
 tf 
 
 23. 
 
 12 T V 31. 8if . 
 
 39. 
 
 294fg 
 
 8. 
 
 * 
 
 16. 
 
 19jf. 
 
 24. 
 
 8^-. 32. lOfi 
 
 40. 
 
 465fi 
 
 EXERCISE XXVI. 
 
 
 
 
 
 
 Page 133. 
 
 
 
 i. 
 
 61 
 
 10. 
 
 4*. 
 
 18. 
 
 41. 26. 4|^. 
 
 34. 
 
 H4 
 
 2. 
 
 i 
 
 11. 
 
 4f 
 
 19. 
 
 2 T V. 27. lOfff. 
 
 35. 
 
 101 T 3 , 
 
 3. 
 
 T9- 
 
 12. 
 
 H- 
 
 20. 
 
 4f . 28. ftft. 
 
 36. 
 
 2 AV- 
 
 4. 
 
 6V 
 
 13. 
 
 
 
 21. 
 
 3M- 29 - 2HM- 
 
 37. 
 
 4if- 
 
 5. 
 
 H- 
 
 14. 
 
 6-jV 
 
 22. 
 
 57^0.. so. 1193 T V. 
 
 38. 
 
 TT9- 
 
 6. 
 
 H- 
 
 15. 
 
 2||. 
 
 23. 
 
 6^V 31. H93 T 7 -^-. 
 
 39. 
 
 y-1-6-. 
 
 7. 
 
 61. 
 
 16. 
 
 3H- 
 
 24. 
 
 6f. 32. 1193H- 
 
 40. 
 
 TrV- 
 
 8. 
 
 21. 
 
 17. 
 
 1 2 
 
 25. 
 
 lOii. 33. 248||. 
 
 41. 
 
 218 
 
 T9TT- 
 
 9. 
 
 7f 
 
 
 
 
 
 42. 
 
 ToTF- 
 
 EXERCISE XXVII. 
 
 
 
 
 
 
 Page 134. 
 
 
 
 1. 
 
 iff- 
 
 6. 
 
 25^7_ 
 
 10. 
 
 g463 14 g ~^ 1 
 
 18. 
 
 ll ff l 
 
 2. 
 
 3ifJ 
 
 . 7. 
 
 344jf. 
 
 11. 
 
 441 15 151 
 2000' Tow" 
 
 19. 
 
 
 3. 
 
 If 
 
 8. 
 
 186 T 2 T 8 T 
 
 12. 
 
 1_1_ 16. 4 73_ 
 
 20. 
 
 25 -5c 
 
 4. 
 
 27-f-g 
 
 9. 
 
 if 
 
 13. 
 
 8 i-io- 17 - 137 ift- 
 
 21. 
 
 II^'T 
 
 5. 
 
 0. 
 
 
 
 
 
 22. 
 
 STOTT 
 
Page 136. 
 
 
 
 9. If. 12. J ? . 
 
 15. 3f 
 
 19. f 
 
 10. If 13. f 
 
 16. 2|f. 
 
 20. 20. 
 
 11. lO^V 14. $. 
 
 17. 185. 
 
 21. -g 9 3 
 
 
 18. 53 
 
 22. 1.' 
 
 ANSWERS. 19 
 
 EXERCISE XXVIII. 
 l-*f 5. If 
 
 2. T . e, 1-J-J-. 
 
 3. If. 7. 4 T V 
 
 4. T V 8 - 2AV 
 
 EXERCISE XXIX. 
 Page 137. 
 
 1. f . 8. 3$. 14. f . 20. f 26. f 32. 1. 
 
 2.2$. 9. T V 15.2. 21. T L 27. If 33.^. 
 
 3. f 10. 2$. 16. f 22. ,,V 28. T \. 34. 2f|. 
 
 4. If. 11. 3^. 17. T V 23. ffa. 29. HG$Jf 35. $$f$$. 
 
 6. 1. 13. m. 19. 1. 25. 76 31> L 37. 7 
 
 j* 7U o yuo 
 
 7. ^ 38. |f|. 
 
 EXERCISE XXX. 
 Page 138. 
 
 i. i e. s^Vu- n - i^Mto- 16 - so^vv 21- if!- 
 
 12. 104A 7 ^. 17. 125MI. 22. 6^V. 
 
 4. lOiff. 9. 7^. 14. lOOrdnp 19. ^. 24. 
 
 5. 50fi. 10. 20^-Vo- I 5 - Mfa. 20. 1^. 
 
 EXERCISE XXXI. 
 
 1. 0.875. 8. 9.0048046875. 15. 0.01875. 
 
 2. 0.9375. 9. 11.00475. 16. 7.75. 
 
 3. 0.28125. 10. 0.072. 17. 1.2. 
 
 4. 0.36. 11. 0.00425. 18. 0.328125. 
 
 5. 0.078125. 12. 0.9296875. 19. 14.8. 
 
 6. 4.01375. 13. 0.0208. 20. 0.69384765625. 
 
 7. 5.00015625. 14. 0.04296875. 
 
20 
 
 ARITHMETIC. 
 
 EXERCISE XXXII. 
 Page 139. 
 
 1. 33.58125 ; 
 
 2. 104.993809^1; 
 3.65.324375; 
 
 4. 46.2625; 46|i. 
 5.9.16875; 9 T 2 eV 
 
 6. 3.71875 ; 3ff . 
 
 7. 6.2625 ; 6fi~ 
 
 8. 2.775 ; 2 
 
 9. 44.5125; 
 10.82.8192; 
 
 11. 3.1875; 3 T V 
 12.0.388125; ^Vo 
 
 13. 7.91875 ; 7 j^, 
 
 14. 296.875 ; 296f 
 
 
 EXERCISE 
 
 XXXIII. 
 
 
 Page 
 
 141. 
 
 1. 0.5. 
 
 7. 0.00081. 
 
 12. 0.380952. 
 
 2. 0.45. 
 
 8. 1113095238 
 
 . 13. 0.39. 
 
 3. 3.416. 
 
 9. 910l85. 
 
 14. 0.5285714. 
 
 4. 0.183. 
 
 10. 111142857. 
 
 15. 2.22745098039215686. 
 
 5. 3.35416. 
 
 11. 0.267857142 
 
 . 16. 5.230769. 
 
 6. 2135. 
 
 
 17. Seven. 
 
 
 Page 
 18. Five. 
 
 142. 
 19. Two. 
 
 
 EXERCISE 
 
 XXXIV. 
 
 
 Page 
 
 143. 
 
 1 2 7 *7 Q 1 6 7 1 *^ 7 9 "I Q ~| 5 9 
 
 O 4 2 1 Q13 14.4117 OO Q , 643 
 9 9"0'' T' ~3"7~0~' 2220' 
 
 3. 53^^. 
 
 9. 1 T 5 2-. 
 
 15 - Hti 21 - 5 fH- 
 
 4. 7fff$. 
 
 10. m- 
 
 16 - 5 AW9 8 5- 22 - iyMfi 
 
 5. 2|| jjjj. 
 
 nQ 9 
 * TT~0"' 
 
 17. ff . 23. ^. 
 
 6 - ITi-HlT- 
 
 19 ^91 
 1/5. OTTTTT. 
 
 
ANSWERS. 21 
 
 EXERCISE XXXV. 
 Page 144. 
 
 1. y ^ G, C. M. ; 14 L. C. M. 7. 5fi- G. C. M. ; 14,140 L. C. M. 
 2.^ 60 8.^W u 2520 
 
 3.& 10,530" 9.^ 85 5 
 
 " 20& " 10.2 Y \ V 460 
 
 4620 11. 6y\ " 8085 
 
 Page 145. 
 13. 2737. 14. 77. 15. 
 
 EXERCISE XXXVI. 
 
 ; rfffc; ^^o- 
 
 22*; 3; T \; 1^ ; T \; H; -/ ; 12; 
 8.60f; 2861; |. 25 8 ; ||i ; T V ; T 4 T ; &. 
 9.3; 4; If; 1J; 1^. 
 
 Page 146. 
 
 10. *; 4; 1; l&l.tt; l^V 12- A- 13 ' 
 
 11. 10^. 14. 
 15.0.5; 0.75; 0.625; 0.1875; 0.5625; 0.9375; 0.428571 
 
 0.25 ; 0.125 ; 0.875 ; 0.3125 ; 0.6875 ; 0.16 ; 0.5 ; 0.27 
 0.3; 0.375; 0.0625; 0.4375; 0.8125; 0.83; 0.175. 
 
 1^* ITS TOTIT T0" ' "2T ' 9T93" ' 
 
 17. 5f or 5.6. 19. 6.7. 21. 121| or A|A. 
 
 18. 36|tf. 20. 401. 22. 47.917. 
 
 23. 0.86; 0.27; 0.283; 0.384615; 
 0.1142857; 0.736842105263157894; 0.1320754716981. 
 
 24. ^V 26 - 0.09375; 0.00009375; 0.2297 ; 0142857. 
 
 25. - 27. 
 
22 ARITHMETIC. 
 
 Page 147. 
 
 28. ft. 29. 3^fi 34. 7$H$ ; 6ft ; 5^ ; 21 T \V 
 
 30. G. C. M. 49 ; 35. -1 39. 4 f . 
 
 L. C. M. 3889277. 36. 10/yV. 40. li^ff . 
 
 31 - tt, T 9 T> tf> M. 37. f . 41. 5 T V-' 43. T yt. 
 
 32. 22|f 33. T if g. 38. 6.33403. 42. f . 44. f 
 
 45. 0.731343283582089552238805970149253 ; 
 
 0.378; 0.84931506. 46. 30, 45, 75 (the smallest). 
 
 EXERCISE XXXVII. 
 
 1. 132 in. 2. 23,166 ft, 3. 5499 in. 4. 5,294,820 ft 
 
 5. 1309 mi. 192 rds. 4 yds. 2 ft. 8 in. 6. 443,646 in. 
 
 7. 1,754,676 in. 8. 45,112,320 in. 
 
 9. 102 mi. 114 rds. 3 yds. 1 ft. 
 
 10. 4 mi. 89 rds. 5 yds. 1 ft. 2 in. 
 
 11. 137 mi. 36 rds. 3 yds. 1 ft. 
 
 12. 3 mi. 217 rds. 4 yds. 1 ft. 3 in. 
 
 13. 7920 in. 14. 3238 fath. 4 ft. 1 in. 
 15. 5 ft. 4 in. 16. 27-^- mi. 
 
 EXERCISE XXXVIII. 
 Page 152. 
 
 1. 120,058,848 sq. in. 4. 1148 sq. rds. 2 sq. yds. 
 
 2. 944 sq. yds. 103 sq. in. 5. 23,048,771 sq. in. 
 
 3. 73,830,400 sq. rds. 6. 43,560 sq. ft. 
 
 7. 15 A. 148 sq. rds. 2 sq. yds. 2 sq. ft. 40 sq. in. 
 
 8. 3 A. 28 sq. rds. 9 sq. yds. 
 
 9. 14 sq. rds. 10 sq. yds. 7 sq. ft. 110 sq. in. 
 
ANSWERS. 23 
 
 EXERCISE XXXIX. 
 Page 153. 
 
 1. 202 cu. ft. 4. 9 cu. yds. 11 cu. ft. 88 cu. in. 
 
 2. 1,175,183 cu. in. 5. 19 cu. yds. 20 cu. ft, 706 cu. in. 
 
 3. 43 cu. ft. 21 cu. in. 6. 9| ft. 
 
 7. $101.86. 
 
 EXERCISE XL. 
 Page 154. 
 
 1. 59 pts. 4. 233 qts. 1 pts. 7. 0.8036 bu. 
 
 2. GO bu. 5 qts. 5. 465 qts. pts. 3 T 7 T gi. 8. 109,792 pts. 
 
 3. 790 gi. 6. 1.244 cu. ft. 9. 96 bbls. 23 gals. 
 
 EXERCISE XLI. 
 Page 155. 
 
 1. 4 Ibs. 9 oz. 9 dwts. 11 grs. 5. 123 Ibs. 7 oz. 5.2 drs. 
 
 2. 15 1. 1. 9 1. cwt. 44 Ibs. 6. 32,316 grs. 
 
 3. 4 t. 5 cwt. 53 Ibs. 3 oz. 7. 905 Ibs. 4 oz. 11 dwt. 16 grs. 
 
 4. 150 Ibs. 8 dwts. 13 grs. 8. 613 Ibs. 7 drs. 
 
 9. 45 t. 27 Ibs. 13 oz. 5 drs. 
 10. 176 t. 5 cwt.- 48 Ibs. 5 oz. 13 drs. 
 11. 7680 TV 12. 16 fl.oz. 5 fl. drms. 20 n^. 
 
 EXERCISE XLII. 
 Page 15G. 
 
 1. 22,645 sec. 4. 8 dys. 14 lirs. 13 min. 12 sec. 
 
 2. 544,324 min. 5. 151 ; 118; 286; 151 dys. 
 
 3. 33 dys. 17 hrs. 27 min. 6. 151,200 min. 
 
 7. 468,000 sec. 
 
 8. 1600, 1656, 1880, 1924, 2000. 
 
24 ARITHMETIC. 
 
 EXERCISE XLIII. 
 
 Tage 157. 
 1. 9025". 2. 54 ? 202". 3. 15 46'. 4. 58 57' 1". 
 
 5. 90, 120, (180), 45, 30, 0' 
 
 6. 2815 geog. mi. ; 3244.75f stat. mi. 
 
 EXERCISE XLIV. 
 
 Page 158. 
 
 1. 140,000 d. 7. 303 10 s. 3 d. 2 far. 
 
 2. 76,750 far. 8. 2813 g. 20 s. 10 d. 
 
 3. 119 Is. 9. 1193 crowns 6 d. 3 far. 
 
 4. 2268 half sov. 2 s. 7 d. 10. $3.86. 
 
 5. 6495 g. 10 s. 11. $4.76. 
 
 6. 1,801,919 14s. 12. $3.67. 
 
 13. 61 2s. 6 d. 
 
 EXERCISE XLV. 
 
 Page 160. 
 
 1. 15 C. ; 12 R. 8. - 22 F. ; - 24 R. 
 
 2. 25 C. ; 20 R. 9. llf F. ; - 9| R. 
 
 3. 510 C. ; 408 R. 10. 41 F. ; 5 C. 
 
 4. - 40 C. ; - 32 R. 11. 59 F. ; 15 C. 
 
 5. - 20 C. ; - 16 R. 12. - 13 F. ; - 25 C. 
 
 6. 50 F. ; 8 R. 13. 394 F. ; 3| R. 
 
 7. 71| F. ; 17f R. 14. - 17| C. ; - 14| R. 
 
 EXERCISE XLVI. 
 
 Page 162. 
 
 1. 3 dys. 4 hrs. 34 min. 36 sec. 3. 92 12 s. 1 d. 3 far. 
 
 2. 245cu.yds.4cu.ft.1514cu.in. 4. 35 mi. 126 rds. 4yds. 1 in. 
 
 5. 151 A. 55 sq. rds. 29 sq. yds. 7 sq. ft. 34 sq. in. 
 
 6. 23 bu. 6 qts. 1 pt. 9. 84 Ibs. 2 oz. 14 dwt. 
 
 7. 212 t. 6 cwt. 3 oz. 10 drs. 10. 41 gals. 1 pt, 
 
 8. 243 gals. 1 qt. 1 gi. 11. 132 30' 45". 
 
ANSWERS. 25 
 
 EXERCISE XLVII. 
 
 Page 163. 
 
 1. 34 Ibs. 9 oz. 18 dwt. 11 grs. 3. 7 cu. yds. 3 cu. ft, 1528 cu. in. 
 
 2. 1 pk. 4 qts. 1 pt. 4. 27 18 s. 2f d. 
 
 5. 7 gals. 2 qts. 1 pt. 
 
 6. 8 t. 5 cwt. 98 Ibs. 5 oz. 11 drs. 
 
 7. 6 A. 9 sq. rds. 174 sq. ft. 26 sq. in. 
 8. 31 37' 45". 9. 298 dys. 21 hrs. 
 
 10. 202 rds. 4 yds. 3 in. 
 
 EXERCISE XLVIII. 
 Page 164. 
 
 1. 249 4 d. 3. 33 Ibs. 8 oz. 4 dwt. 4 grs. 
 
 2. 1391 gals. 1 qt. 4. 55 t. 6 cwt, 70 Ibs. 
 
 5. 2740 bu. 2 pks. 
 
 Page 165. 
 
 6. 108 wks. 1 dy. 12 hrs. 24 min. 
 
 7. 32 cu. yds. 7 cu. ft, 498 cu. in. 
 
 8. 3 sq. mi. 553 A. 27 sq. rds. 3 sq. yds. 2 sq. ft. 36 in. 
 
 9. 5 mi. 258 rds. 3 yds. 
 
 10. 10 yrs. 67 dys. 23 hrs. 45 min. 36 sec. 
 
 11. 38,508 mi. 19 rds. 3 yds. 
 
 12. 2147 Ibs. 943l97 grs. 
 
 EXERCISE XLIX. , 
 Page 166. 
 
 1. 1 mi. 207 rds. 2 yds. 8 in. 2. 137. 
 
 3. 8 wks. 1 dy. 7 hrs. 50 min. 2|f-- sec. 
 
 4. 77. 5. 325. 
 6. 7 sq. mi. 264 A. 39 sq. rds. 7. 7. 
 
26 ARITHMETIC. 
 
 EXERCISE L. 
 
 Page 107. 
 
 1. 256 rds. 3. 62 Ibs. 8 oz. 
 
 2. 30 sq. rds. 4. 13 ,9. 4 d. 
 
 5. 261 rds. 4 yds. 1 ft. 6 in. 
 
 6. 101 sq. rds. 24 sq. yds. 6 sq. ft. 108 sq. in. 
 
 7. 26' 40". 10. 2 qts. 1 pt. 
 
 8. 121 dys. 16 hrs. 11. 320 dys. 6 hrs. 
 
 9. 5 qts. 12. 3 oz. 18 dwt. 
 
 EXERCISE LI. 
 . 168. 
 
 1. 23 A. 40 sq. rds. 16 sq. yds. 1 sq. ft. 28f sq. in. 
 
 2. 10 hrs. 30 min. 38f sec. 
 
 3. 15 dys. 10 hrs. 38 min. 51 sec. 
 
 4. 34 rds. 2 yds. 4 T \ in. 
 
 5. 57 rds. 2 yds. 2 ft. 7.5936 in. 
 
 6. 5 t. 6 cwt. 94 Ibs. 
 
 7. 8 oz. 6 dwt. 2| grs. 
 
 8. 1 Ib. 6 oz. 13 dwt. 8 grs. 
 
 9. 3 mi. 198 rds. 4 yds. 4| in. 
 
 10. 2 wks. 2 dys. 3 hrs. 35 min. 
 
 11. 12 dys. 10 hrs. 31 min. 30 sec. 
 
 12. 86 rds. 4 yds. 1 in. 
 
 13. 4 cwt. 72 Ibs. 4 oz. 9| drs. 
 
 EXERCISE LII. 
 
 Page 169. 
 
 i-Hi 4 -i 7 -A- 10 -i 13 -8f^- le.^ 
 
 2. Hi 5 - *i 8 - rb- n - 2V 14 - *i- i r 
 
 3. A A. 6. T V 9. ff 12- fV 15 'Mi 
 
ANSWERS. 27 
 
 EXERCISE LIII. 
 Page 170. 
 
 1. 0.815625. 3. 0.445 A. 5. 0.242. 7. 0.0311. 
 
 2. 0.73 mi. 4. 0.3174. 6. 0.501. 8. 0.303. 
 
 9. 0.148. Pa 8 e 17L 10. 0.243. 
 
 11. 5.128 (reckoning 365 days). 
 12. 1.139. 13. 0.15433. 14. 0.03. 15. 0.4388. 
 
 
 EXERCISE LIV. 
 
 
 Page 172. 
 
 1. 18 45'. 
 
 4. 51 23' 45". 
 
 2. 32 45'. 
 
 5. 93 7' 30". 
 
 3. 77 32' 30". 
 
 6. 62 3'. 
 
 7. 272 30'. 
 
 8. 228 48' 45" 
 
 9. 37 min. 20 sec. 
 
 10. 4 hrs. 42 min. 14. 6 hrs. 43 min. 3.6 sec. 
 
 11. 3 hrs. 46 min. 24f sec. 15. 8 min. 8 T 2 ? sec. 
 
 12. 7 hrs. 14 min. lOf sec. 16. 5 hrs. 40 sec. 
 
 13. 8 hrs. 58 sec. 
 
 EXERCISE LV. 
 
 Page 174. 
 
 1. (1) 12 h. 53 m. 34if s. P.M. (7) 2 h. 22 m. 8 s. P.M. 
 
 (2) 12 h. 49 m. 43ff s. P.M. (8) 4 h. 51 m. 36 s. P.M. 
 
 (3) 1 h. 55 m. 56 s. P.M. (9) 5 h. 53 m. 16^ s. P.M. 
 
 (4) 7 h. 45 m. 35 s. P.M. (10) 6 h. 9m. 40 s. A.M. 
 
 (5) 3 h. 50 m. 15 s. A.M. (11) 7 h. 3 m. 59-f s. A.M. 
 
 (6) 5 h. 58 m. 59 s. A.M. (12) 7 h. 6 m. 20 s. A.M. 
 
 2. (1) 11 h. 13 m. 54-ff s. P.M. (7) 12 h. 42 m. 28 s. A.M. 
 
 (2) 11 h. 10 m. 8|f s. P.M. (8) 3 h. 11 m. 56 s. A.M. 
 
 (3) 12 h. 16 m. 16 s. A.M. (9) 4 h. 13 m. 36 T \ s. A.M. 
 
 (4) 6 h. 5 m. 55 s. A.M. (10) (4 h. 30 m.) 
 
 (5) 2 h. 10 m. 35 s. P.M. (11) 5 h. 24 m. 194 s. P.M. 
 
 (6) 4 h. 19 in. 19 H. P.M. (12) 5 h. 26 m. 40 s. P.M. 
 
28 ARITHMETIC. 
 
 3. (1) 6 h. 57 m. 38|f s. A.M. (7) 8 h. 26 m. 12 s. A.M. 
 
 (2) 6 h. 53 m. 52|| s. A.M. (S) 10 h. 55 m. 40 s. A.M. 
 
 (3) (8 A.M.) (9) 11 h. 57 m. 20-& B. A.M. 
 
 (4) 1 h. 49 m. 39 s. P.M. (10) 12 h. 13 m. 44 s. A.M. 
 
 (5) 9 h. 54 m. 19 s. P.M. (11) 1 h. 8 m. 3f s. A.M. 
 
 (6) 12 h. 3 m. 3 s. A.M. (12) 1 h. 10 m. 24 s. A.M. 
 
 EXERCISE LVL 
 
 Page 174. 
 
 1. (1) 71 3' 30" W. (5) 112 30' W. (8) 76 50' W. 
 
 (2) 69 50' W. (6) 73 44' 45" W. (9) 90 W. 
 
 (3) 81 7' W. (7) 83 3' W. (10) 89 33' W. 
 
 (4) 92 12' W. (11) 77 4' W. 
 
 EXERCISE LVIL 
 
 Page 175. 
 
 1. 7.875 gals. 2. 4 7 s. 6 d. 3. 7 gals. 2 qts. 1.5 pis. 
 
 4. 1 4 s. Z$ d. ; 1 10 s. 5f d. ; 
 
 3 13s. 7f$eZ.; 495. 8|f d. 
 
 5. 17,983.504 sq. yds. 11. 0.1051136 mi. 
 
 6. -l- turpentine ; | pt. 12. 66,036 in. 
 
 7. 9104 yds. 2 ft. 5.952 in. 13. 4320 cu. in. 
 
 8. 4-iff ft. 14. 16871 Ibs. 
 
 9. 4.32 oz. ; 1890 troy grs. 15. 0.84375 t. 
 10. 1, 16. 472i Ibs. 
 
 17. 19 bu. 2 pks. 5.6 qts. 
 
 Page 176. 
 18. 312| bu. 19. 144 bottles. 20. 156 mi. 72 rds.; 8^^f hrs. 
 
 21. 24 hrs., nearly. 25. $350. 29. 94.5 mi. 
 
 22. $209.83. 26. 0.0184 mi. 30. 13| gross. 
 
 23. $46.94. 27. 0.9703125 A. 31. $2554.50. 
 
 24. $120.59. 28. 3 qts. 
 
 32. The former, by 2 ft, 8.08 in. 35. 0.192. 
 
 33. 0.07056 t. 36. 0.09375. 
 
 34. 0.03 sq. ch. 37. 11 hrs. 6 min. 40 sec. 
 
ANSWERS. 
 
 29 
 
 38. A. 
 
 41. 58 min. 14.91 sec. 
 
 42. 3 hrs. 12 min. 24 sec 
 
 43. 2 ft. 11.6125 in. 
 
 44. 4 t. 1 cwt. 80 T 7 r Ibs. 
 45.35. 
 
 46. The former ; f$. 
 
 Page 177. 
 
 39. 3|fmi. 40. $291.67. 
 
 . 47. 4436 mi. 99 rds. 1 yd. 6 in. 
 
 48. $15,832.30. 
 
 49. 8938iff. 
 
 50. 88 yds. = -^ mi. ; 
 
 3 min.- ^hr. 
 
 51. 42 min. 4 sec. 
 
 1. 43- mi. 
 
 2. 10,800 mi. 
 
 EXERCISE LVIII. 
 
 Page 178. 
 
 3. 4655.637 mi. 
 
 Page 179. 
 
 6. 4ff mi. 10. 4ff sec. 
 
 7. 6 9 in. 11. 1 min. 43 T %\ sec. 
 
 8. 2 min. 12. -^ day ; T \ A. 
 
 9. 2J- min. Page m 
 
 17. $3922.20. 
 
 18. 1 T \\ pts. 
 
 19. 1040|f- mi. 
 
 4. 1173 ft. 
 
 5. 4A- mi. 
 
 13. 1 A. 120 sq. rds. 
 
 14. 156| gals. 
 
 15. $5035.20. 
 
 16. 12 hrs. 
 
 20. 24 mi. ; 1 hr. 44 min. 10 sec. 
 
 21. If dys. 
 
 22. 2if dys. 
 
 23. 1 hr. 58 min. 7^- sec. 
 
 24. 5 T ^ T hrs. 
 
 25. l-/ dys. 
 
 26. 2|f dys. 
 
 31. 2 
 
 Page 181. 
 
 all. 
 
 32. 992 bu. 
 
 33. 18 girls ; 
 32 scholars. 
 
 34. 26 boys ; 
 
 22 girls. 
 
 4f|,A 
 
 Page 182. 
 
 35. 35. 36. 120. 37. 35. 
 38. 18 dwt. 8 grs. troy ; 
 oz. av. 
 
 . 
 
 27. T * 7 hr. 
 
 28. 56J min. ; 125 gals. 
 
 29. 1 hr. 42 min. 51f sec. 
 
 30. 1 hr. 3 min. 34ff sec. 
 , B ; 
 
 40. l-j%. 
 
 41. $ 13,200. 
 
 42. 14, ||, ||. 
 39. A, $21,000 ; B, $15,000 ; C, $9000. 
 
30 ARITHMETIC. 
 
 Page 183. 
 
 43. $0.75. 46, lOfjftjj- Ibs. 49. 27 min. 52. 11 dys. 
 
 44. $2665. 47. $1.44. 50. $9.336. 53. 324. 
 
 45. $25.42. 48. T ig\. 51. 611 A. 54. 90. 
 
 Page 184. 
 55. 300. 56. 7 mos. 57. 34fff 58. 16. 59. 500. 
 
 Page 185. 
 
 60. 20. 62. 4 clys. 64. 2 dys. 66. 6f yds. 68. 1396 T 4 T . 
 
 61. 11,268. 63. 84. 65. 15. 67. 2| ft. 69. 67|. 
 
 70. C the fastest; A 41 sec., B 19 T V sec. 
 
 Page 186. 
 71. $89.40. 72. $ 7573.36. 73. $ 1830.70. 
 
 EXERCISE LIX. 
 Page 187. 
 
 1 9 ft, 3. 13 A. 5.792 sq.ch. 5. 418 yds. = 76 rds. 
 
 2. 60 rds. or 990 ft. 4. 3 ft. 6. 12 sq. ft. 
 
 Page 188. 
 
 7. 5 sq. ft. 21 sq. in. 10. 27,648. 13. 344| sq. yds. border ; 
 
 8.36. 11. 2 sq.ft. 81 sq. in. 411-1 sq. yds. path ; 
 
 9. 15. 12. $ 15.20. 3500 sq. yds. grass. 
 
 14. 28.2744 sq. ft. 16. 16,060.6446 sq. ft. 
 
 15. 502,656 sq. yds. 17. 132.7326 sq. ft. 
 
 Page 189. 
 
 18. 258.5248 sq. ft, 22. 60| yds. ; 63 yds. ; none ; | yd. 
 
 19. 28.2744 sq. in. 23. 59|f yds. or 60 yds. 
 
 20. 452.3904 sq. in. 24. 17-J- sq. yds. 
 
 21. 4 sq. ft. 52.32 sq. in. 25. $43.70. 
 
ANSWERS. 31 
 
 Page 190. 
 
 26. $45.00 or $46.67. 29. Lengthwise. 32. $46.50 
 
 27. $ 123.375. 30. 81| sq. yds. 33. $4.26. 
 
 28. $194.79. 31. 199^ sq. yds. 
 
 Page 191. 
 34. $41.03. 35. $12.75. 36. $33.75. 37. $62.50 
 
 Page 192. 
 
 38. 131; 40. 78. 43. 33. 46. 325. 49. $9.94. 52. $32.84. 
 14|. 41. 162. 44. 140. 47. $2.36. 50. $1.80. 53. $10.71. 
 
 39. 233. 42. 207. 45. 300. 48. $14.85. 51. $3.92. 
 
 Page 193. 
 
 54. 187. 56. 302. 58. $0.80. 60. $1.38. 
 
 55. 83. 57. 123. 59. $1.22. 61. $0.79. 
 
 Page 194. 
 62. 810. 63. 3^ in. 64. 24| thousand. 
 
 EXERCISE LX. 
 Page 194. 
 
 1. 16 cu. ft. 72 cu. in. 3. 15 cu. yds. 16 cu. ft. 1512 cu. in. 
 
 2. 38,016 cu. ft. 4. 120f cu. yds. 5. 52| cu. ft. 
 
 Page 195. 
 
 6. 63 cu. in. 8. $855. 10. 2 ft. 8 in. 12. 259,200. 
 
 7. 1512. 9. If yds. 11. 13i ft. 13. 58 ft. 
 
 14. 72 sq. ft. 48| sq. in. 16. 14,088.9375 or 14,088|f t. 
 
 15. 36 sq. ft, 36 sq. in. 17. 14,400. 
 
 Page 196. 
 
 18. $194.79. 20. 45^- Ibs. 22. 8 ft. 24. 7fi- ft. 
 
 19. 13i ft. 21. 6|. 23. $13.67. 25. 2| ft. 
 
32 ARITHMETIC. 
 
 Page 197. 
 
 26. 76-f bu. 29. 16| ft. 31. $1440. 33. 5ff t. 
 
 27. 156 bu. 30. 107.1 bu. 32. 26^. 34. 4278f gals. 
 
 28. 6i ft. 
 
 Page 198. 
 
 35. 132^- gals. 39. 4.90875 gals. 43. 0.267. 
 
 36. 7ff gals. 40. 2.18 qts. 44. 28.51. 
 
 37. 840 cu. ft. 41. 696.9116 cu. in. 45. 0.859. 
 
 38. 1484.406 gals 42. 15.708. 
 
 Page 199. 
 
 46. 1.728 cu. in. 53. 3f| cu. in. 58. 1162f 
 
 47. iff oz. 54. 2.987 cu. in. 59. 704,000. 
 
 48. 16f oz. 55. 93f . 60. 4-JL Ibs ; 
 
 49. |4 pts. 56. 1 t. 31^ Ibs. ; 1.44 sp. gravity. 
 
 50. 253^2- g rs - 1 t- 8 cwt. 43f Ibs. 61. 36^ t. ; 
 
 51. G.912. 57. 3|fff in - 17,600. 
 
 52. 6.983. 
 
 EXERCISE LXI. 
 
 Page 202. 
 
 1. 90.816 1 . 4. 111.2945 km . 7. 192.496 ks . 
 
 2. 3.73248 kg . 5. 4.890 ha . 8. 8.98416 hl . 
 
 3. 38.6325 cbm . 6. 36.240 8t . 
 
 9. 9 mi. 100 rds. 4 yds., nearly. 
 
 10. 7 A. 66 sq. rds. 2 sq. yds., nearly. 
 
 11. 15 cu. yds. 23 cu. ft., nearly. 
 
 12. 107 qts. liquid, or 92 qts. dry, nearly. 
 
 13. 535 gals., or 57 bu., nearly. 
 
 14. 13 Ibs. 4 oz. 15 dwts. 
 
 15. 6 cds. 80 cu. ft., nearly. 
 
 16. 74.75 sq. yds. 
 
 17. 1 t. 2 cwt. 7 Ibs., nearly. 
 
ANSWERS. 33 
 
 18. 1 A. 136 sq. rds. 16 sq. yds. 23. 1312. 
 
 19. 1.275 cbm . 21. 2.795 mi. 24. $1.47. 
 
 20. 0.981 cu. yds. 22. 444.5625 Ibs. 25. $8.40. 
 
 26. 206.029 Ibs. or 93.437 kg . 
 
 27. Water: 226.233 Ibs, 102.6 1 *; oil: 201.7575 Ibs, 91.5 kg . 
 
 Page 203. 
 
 28. 349 Ibs, 158.277 kg . 32. 45.721. 
 
 29. 297.1738 Ibs, 134.9169 kg . 33. 1 hr. 11 min, nearly. 
 
 30. 10.0277 kg , 22.111 Ibs. 34. 17 t. 16cwt. 64 Ibs. 
 
 31. $20.87. 35. 13,616.64 g . 
 
 36. 15.786. 37. $3.92. 38. 13,777.796*. 
 
 EXERCISE LXII. 
 Page 205. 
 
 1.6:9. 2.9:12. 3.8:9. 4.8:14. 5. $7: $9. 
 6. 8 ft. : 11 ft. 7. 5 : 3. 8. f yd. : f yd. 
 
 EXERCISE LXIII. 
 
 Page 208. 
 1. 16 dys. 2. 11 T V 3. 2320. 4. $5.89. 5. 40. 
 
 Page 209. 
 
 6. 2 T V sq. ft. 9. 139 ft. lly 6 ^- in. 12. 39f sec. 
 
 7. 2f| hrs. 10. 8. 13. 34^ sec. 
 
 8. 17 ft. 1 T V in. 11. If hrs. 14. 9 min. 59| sec. 
 
 15. 5 wks. 3 dys. 21 hrs. 20 min. 18. 1 t. 4 cwt. 45 Ibs. 
 16.2673. 17. $7435.78. 19. 32f 
 
 Page 210. 
 
 20. 0.8 Ibs. 23. $4165. 26. 8|f mo. 29.50. 
 
 21. 2565 francs. 24. 13 yds. 27. Iff in. 30. 21,000. 
 
 22. 2306.85 Ibs. 25. 89^1 cu. in. 28. T ^ in. 31. 2ff . 
 
34 
 
 ARITHMETIC. 
 
 EXERCISE LXIV. 
 
 Page 212. 
 4. 124 Ibs. 6. 14 dys. 
 
 2. $26.44. 
 
 5. 1368 bu. 
 
 7. 540. 
 
 3. $23,356.67. 
 
 
 
 
 Page 213. 
 
 
 8. 6027. 
 
 13. lOf 
 
 17. 60 m . 
 
 9. $1.575. 
 
 14. 38 ft. 1.5 in. 
 
 18. 1134.2776 kg . 
 
 10. 56,875 gals. 
 
 15. 150 yds. 
 
 19. 242.5 cu. ft. 
 
 11. 188|f yds. 
 
 16. 5f-f- in. 
 
 20. 3.8 cu. ft. 
 
 12. 3 hrs. 
 
 
 
 EXERCISE LXV. 
 
 Page 215. 
 
 1. $3000, $4000, $5000. 
 
 2. 150 t, 200 t, 225 t., 240 t. 
 
 3. 1155 Ibs, 1848 Ibs, 3850 Ibs.; 
 3560 Ibs, 2225 Ibs, 1068 Ibs. 
 
 4. $2000; $1600. 
 
 5. 700 Ibs.; 21 Ibs. 
 
 Page 216. 
 
 6. 730ff Ibs. ; 206^ Ibs. 
 
 7. 37,500 kg saltpetre, 
 6250 kg charcoal, 
 6250 kg sulphur. 
 
 8. 10f . 
 
 9. 746.46 ; 210.54. 
 
 10. 66| Ibs, 33^ Ibs. 12. $45.60. 
 
 11. 23.203 g oxygen, 76.797 g nitrogen. 
 
 EXERCISE LXVI. 
 
 1. $1333.33^, A's; $666.66f, B's. 2. $863.28^ $836.71f 
 
 3. $948, A's; $752, B's; $816, C's. 
 
 Page 217. 
 
 4. $710, A's; $1196.25, B's. 
 
 5. $882, A's; $759.50, B's; $525, C's. 
 
 6. $37.50; $60; $35. 
 
 7. $656, A's; $287, B's. 
 
ANSWERS. 35 
 
 8. $1837.50, A's; $3311, B's. 
 
 9. 36 15s.; 14 14 s. ; 14. 
 10. $1811.25, A's; $1794, B's. 
 
 EXERCISE LXVII. 
 Page 220. 
 
 1. 13,257. 3. 1500 Ibs. saltpetre, 4. 19.2 t. 7. 660. 
 
 2. 25.55 t. 200 Ibs. sulphur, 5. 350.46 cu. ft. 8. 12% 
 300 Ibs. charcoal. 6. 6052. 
 
 Page 221. 
 
 9. 66. 13. 1 T \% loss. 17. $2750. 21. $216. 
 
 10. 20ff % . 14. T f T of 1 % 18. 8% . 22. 13fi% . 
 
 11. 3f|%. 15.6ft. 19.15%. 23. 9f%gain. 
 
 12. $12,500. 16. 5if%. 20. 7fi-% water, 92f alcohol. 
 
 Page 222. 
 
 24. $3.93f. 26. $4.16f. 28. 14f oz. 
 
 25. 7^% gain. 27. 6f%. 29. $7.50. 
 30. 5.4 t, silver, 714.6 t. lead. 31. 3038.936 t. 
 
 Pages 223-224. 
 32.30%. 33.28^%. 34. 35 T 5 T %. 35.100$. 36.5^%. 
 
 37. 3,510,000 ; 13 : 87. 39. $6400 ; $7200. 
 
 38. 14f % ; 12|%. 40. 30 cents ; 26f cents. 
 
 41. $143. 44. 2||%. 47. 25%. 
 
 42. 99^% . 45. 2H% - 48. If Ibs. 
 
 43. 2i|%. 46. 16|%. 49. 0.00125. 
 50 - TTo 5 8 7 gals, oxygen, 100 gals, nitrogen. 
 
 51. 0.00129. 52. 96i||. 53. ft of 1 % . 54. 5f| in. 
 
 Page 225. 
 55. 492-^f- ft. 
 
36 ARITHMETIC. 
 
 EXERCISE LXVIII. 
 Page 226. 
 
 1. 13.06. 4. $40; 2560 bu. 9. $210. 
 
 2. $64.88. 5. $5047.64. 7. $12,445.31. 10. $6955.56. 
 
 3. $1-611.30. 6. \\<J . 8. $869.05. 11. $1.523. 
 
 - 
 
 Page 227. 
 
 12. im%- 15. $13,770. n. $14,159.25. 
 
 13. 6758.6. 16. $141. 18. 58,536|f Ibs. 
 
 14. 37,951.2 Ibs. ; $ 128.05. 19. $ 195.07 ; 141.51562 t, 
 
 EXERCISE LXIX. 
 
 Page 228. 
 1. $13.25. 2. $56.25. 3. $1001. 4. 812,266.67; $214.67. 
 
 Page 229. 
 
 5. $12,000. 8. 6.25. 11. $8425. 13. $96. 
 
 6. $1040. 9.8363.75. 12. $97,272. 14. $1840. 
 
 7. $1836. 10. (1)91500; (2) $750; (3) $1125; (4) $1125. 
 
 EXERCISE LXX. 
 
 Page 230. 
 1. $96.79. 2. $962,326.53. 3. $3.866. 4. $15,306.12. 
 
 Page 231. 
 
 5. $6. 7. $204.80. 9. 4032. 11.81240.70. 
 
 6. $17,818.91. 8. $1587.60. 10. 284%. 12. 4869.12. 
 
 13. $1781.80. 
 
 EXERCISE LXXI. 
 
 Page 233. 
 1. $95.94. 2.80.13. 3. 8.46. 
 
ANSWERS. 
 
 37 
 
 4. $183.33. 
 
 5. $327.25. 
 
 6. $1.60. 
 
 7. 12.91. 
 
 8. $13.19. 
 
 9. $7.56. 
 
 10. $3.88. 
 
 11. $51.16. 
 
 12. $62.04. 
 
 Page 234. 
 
 
 13. $37.45. 
 
 22. $487.83. 
 
 14. $68.62. 
 
 23. $323.35. 
 
 15. $9.46. 
 
 24. $6980.12. 
 
 16. $28.18. 
 
 25. $166.98. 
 
 17. $54.27. 
 
 26. $548.22. 
 
 18. $16.69. 
 
 27. $1268.40. 
 
 19. $50.60. 
 
 28. $660.44. 
 
 20. $ 10.29. 
 
 29. $12,474.55. 
 
 21. $483.28. 
 
 30. $11,481.45. 
 
 
 Page 236. 
 
 31.4^%. 
 
 35. 4%, nearly. 39.4%. 43.4%. 
 
 32.41%. 
 
 36. 3f %. 40. 6%, almost. 44. 4 yrs. 
 
 33.4|%. 
 
 37.41%. 41.71%. 45. 2 yrs. 
 
 34. 6%. 
 
 38. 4 T % 4 5-% . 42. 7-ff % . 46. 6 yrs, almo 
 
 
 47. 3 mos. 9 dys. 48. 25 yrs. 
 
 49. 11 yrs. 8 inos. 
 
 50. 3 yrs. 4 mos. 
 
 51. 3 yrs. 9 mos. 
 
 52. 3 mos. 2 dys. 
 
 53. 3 yrs. 5 mos. 
 
 Page 237. 
 
 54. $750. 
 
 55. $336. 
 
 56. $235.29. 
 
 57. $8520. 
 
 58. $411.43. 
 
 59. $1754.39. 
 
 60. $8423.14. 
 
 61. $9723.33. 
 
 62. $4090.91. 
 
 63. $750. 
 
 64. $816.896. 
 
 65. $5982.55. 
 
 Page 238. 
 66. $286.15. 69. $166. 
 
 67. $6050.99. 70. $560. 
 
 68. $19,600. 71. $8432. 
 
 74. 7%, nearly. 
 
 75. 1 mo. 8 dys. 77. $22,222.22. 
 
 76. $524.10. 78. 2 yrs. 10 mos. 3 dys. 
 81. 3 yrs. 4 mos. 24 dys. 82. $4.44. 
 
 72. $8520. 
 
 73. $27.53. 
 
 79. 6ff%, 
 
 80. $47.57. 
 83. 10.20. 
 
38 ARITHMETIC. 
 
 EXERCISE LXXIL 
 Page 241. 
 
 1. May 1/4, 112 dys., $16.33 ; 733.67. 
 
 2. Mar. 4/7, 60 dys., $46.86; $4278.64. 
 
 3. Apr. 6/9, 73 dys., $19.03; $1321.67. 
 
 4. Apr. 19/22, 2 mos. 21 dys., $16.38; $1439.92. 
 
 5. June 2/5, 3 mos. 19 dys., $75.78; $4474.58. 
 
 6. Apr. 4/7, 3 mos. 6 dys., $110.46; $5067.46. 
 
 7. Apr. 1/4, 48 dys, $47.60; $4712.40. 
 
 8. Apr. 14/n, 1 mo. 16 dys, $25.78; $1992.07. 
 
 9. June 25/28, 3 mos. 13 dys, $8.61 ; $660.48. 
 
 10. Mar. 20/23, 35 dys, $48.34; $8991.66. 
 
 11. Feb. 27/Mar. 2, 27 dys, $0.96f ; $214.031 
 
 Page 243. 
 
 12. $865.65. 14. $1207.19. 16. $4558.23. 
 
 13. $1630.64. 15. $4056.80. 17. $1120.26. 
 
 Page 244. 
 
 18. $478.09. 22. $640. 
 
 19. $3059.28 ; $275.34. 23. $512.65 ; $61.52. 
 
 20. $3909.48; $351.85. 24. $596.12; $29.01. 
 
 21. $2348.02; $68.48. 25. $683.31 ; $31.89. 
 
 Page 245. 
 26. $390.31. 
 
 Page 246. 
 27. $162.31. 28. $283.71. 29. $234.13. 
 
ANSWERS. 39 
 
 Page 248. 
 
 30. $1547.73. 31. $391.01. 32. $525.58. 
 
 33. $293.39. 34. $17.61. 
 
 Page 250. 
 
 35. $433.02. 38. $3.52. 41. $303.77. 44. $1441.47. 
 
 36. $703.31. 39. $24.73. 42. $125. 45. $1078.43. 
 
 37. $195.69. 40. $40.62. 43. $1562.50. 
 
 Page 251. 
 46. $220.84. 47. $245.08. 
 
 Page 252. 
 48. $3438.32. 49. $3569.79; $3633.04; $3635.67. 
 
 EXERCISE LXXIII. 
 
 Page 254. 
 
 1. $4395. 4. $4723.50. 7. $4650. 10. 24. 
 
 2. $2450. 5. $1096.871 8. $5200. 11. 971. 
 
 3. $3046.871 6. $11,600. 9. $5000. 
 
 Page 255. 
 
 12. 91|. 15. $329. 18. $754. 21. $857.14. 
 
 13. $1188. 16. $30,000. 19. 3ff %. 22. $271.19. 
 
 14. $270. 17. $9800. 20.9%. 
 
 Page 256. 
 
 23. $366.15. 26. 51%. 29. 6-J f %- 32. $5635. 
 
 24. $390. 27. 5f%. 30. 4 T %%. 33. $4925. 
 25.31^%. 28. 5 T 5 T %. 31. 5-f-%. 34. $5671. 
 
 35. 831. 
 
 Page 257. 
 
 36. 116|. 39. $7291.67. 42. 144. 
 
 37. 1331; 150 ; 166|. 40. 117|. 43. $56. 
 
 38. 71%. 41. 31%. 
 
 
40 
 
 ARITHMETIC. 
 
 44. $13 decrease. 
 
 45. $8 increase. 
 
 46. $100 increase. 
 
 47. $200 increase. 
 
 Page 258. 
 
 48. $40 increase. 
 
 49. $5 increase. 
 
 50. $20 increase. 
 
 51. $50 increase. 
 
 56. $14.66^. 
 
 57. $5787.46. 
 
 58. $1024.06. 
 
 65. $ 1500 loss. 
 
 66. 31, at 91 
 
 Page 259. 
 
 59. 90|. 
 
 60. 95f (nearly) 
 
 61. 3%, at 63; 
 
 67. $ 180 loss. 
 
 52. $10 decrease. 
 
 53. $40 increase. 
 
 54. &tffe%. 
 
 55. 84. 
 
 62. 
 
 63. 149f 
 , at 67J. 64. 58. 
 
 68. $ 10,000. 
 
 EXERCISE LXXIV. 
 Page 261. 
 
 1. $1102.75. 2.31346.63. 
 
 Page 262. 
 
 3. $1595.20. 6. $946.08. 9. $275.52. 12. $519.31. 
 
 4. $491.38. 7. $716.85. 10. $1262.31. 13. $10,117.62. 
 
 5. $1184.30. 8. $800.52. 11. $1138.81. 
 
 EXERCISE LXXV. 
 Page 263. 
 
 1. $1548.14. 2. $723.90. 3. $2408.01. 
 
 4. 413 4s. 
 
 5. 28. 
 
 6. 821 185. 
 
 Page 264. 
 
 7. $1563.31. 
 
 8. $1945.53. 
 
 9. 7672.5 fr. 
 13. 5026-^- marks. 
 
 10. 14,583.4 fr. 
 
 11. $686.65. 
 
 12. $2838.75. 
 
ANSWERS. 41 
 
 EXERCISE LXXVI. 
 Page 265. 
 
 1. 57f g . 3. $1.02; $0.34. 5. $0.30|f 
 
 2. 139ff Ibs. 4. $0.33f 6. $0.47. 
 
 Page 266. 
 
 7. 1.256. 8. 1.171. 9. 57: 146. 10. 4 : 5. 
 
 41. 1 : 1 : 5 ; 1:1; 1:5; 6 gals. ; 8 gals. ; 12|%. 
 
 Page 267. 
 12. 775ff g lead ; 224 2 V tin. 
 
 Page 268. 
 
 13. 6 mos. 14 dys. 17. 31 dys., July 22. 
 
 14. 57 dys. 18. 46 dys., Aug. 21. 
 
 15. 41 dys. 19. 6 mos. 
 
 16. 94 dys., Aug. 12. 20. 69 dys., Aug. 19. 
 
 * 269. 
 
 21. Aug. 23, 1881 ; $ 749.93. 22. July 23, 1881 ; $ 1934.83. 
 23. May 29, Dr. \ May 30, Or. 
 
 Page 271. 
 
 24. June 17, 1879. 26. Aug. 27, 1880. 
 
 25. Mar. 13, 1883. 27. Dec. 19, 1886. 
 
 Page 272. 
 
 28. $38.06. 29. $153.44. 30. $96.85. 31. $22.43. 
 32. $110.93. 
 
 EXERCISE LXXVII. 
 Page 27(1 
 
 1. 54. 3. 703. 5. 1829. 7. 6879. 9. 7.33. 
 
 2. 89. 4. 142. 6. 354.2. 8. 147. 10. 29.72. 
 
42 ARITHMETIC. 
 
 11. 1.4045. 13. 1.414213. 15. 0.547722. 17. 2.972092. 
 
 12. 0.01446. 14. 2.236067. 16. 1.802775. 18. 0.948683. 
 
 Page 277. 
 
 19. 311.13. 20. 12 ft. 3 in. 21. 8 ft. 11 in. 
 
 22.0.666666; 0.745355; 0.707106; 0.774596; 0.845154; 
 
 0.866025; 0.816496; 0.912871. 
 23. 45; 4.2; 1.42; 23.1; 14.3. 24. 5 ft. 25. 91 in. 
 
 Page 278. 
 26. 60 in. 27. 25 ft, 28. 9 ft. 
 
 EXERCISE LXXVIII. 
 Page 283. 
 
 1. 11. 4. 6.7. 7. 3.91. 10. 4.7117. 
 
 2. 12. 5. 53. 8. 67.31. 11. 25,805. 
 
 3. 2.3. 6. 127. 9. 0.1985. 12. 49.68. 
 
 13. 2,1544; 1.5361; 2.0274. 
 
 14. 1.7099; 0.8220; 1.9660; 0.9085. 
 
 15. 35 sq. ft. 75.84 sq. in. 
 
 EXERCISE LXXIX. 
 Page 285. 
 
 1. 1:16; 1:64. 3. 1 : 2; 1:4. 5. 1:2.154. 
 
 2. 8 : 9261 : 10,648,000. 4. 1 : 2.121. 6. 1 : 0.687. 
 
 Page 286. 
 
 7. 8.299ft. 12. 9: 16; 27:64. 
 
 8. 5040 sq. in. 13. 3.931 in. 
 
 9. 10,648 cu. in. 14. 12 ft. 7.19 in. 
 
 10. 174.1 Ibs.; 6 ft. 4.6 in. 15. 150 rds. 
 
 11. 1 : 0.693. 16. 1:0.63. 
 
ANSWERS. 
 
 43 
 
 EXERCISE LXXX. 
 
 
 
 
 
 
 Page 291. 
 
 
 
 
 
 
 1. 
 
 0.7781. 
 
 9. 
 
 1. 
 
 3980. 
 
 17. 8.3222 - 
 
 -10. 
 
 25. 
 
 
 
 .3222. 
 
 2. 
 
 1.1761. 
 
 10. 
 
 1. 
 
 4771. 
 
 18. 9.5441 - 10. 
 
 26. 
 
 1 
 
 .2040 
 
 
 3. 
 
 1.3222. 
 
 11. 
 
 1. 
 
 6232. 
 
 19. 7.5441 - 
 
 -10. 
 
 27. 
 
 8 
 
 .7481 
 
 -10. 
 
 4. 
 
 1.1461. 
 
 12. 
 
 2. 
 
 6232. 
 
 20. 7.6020 - 10. 
 
 28. 
 
 9 
 
 .7993 
 
 -10. 
 
 5. 
 
 1.5441. 
 
 13. 
 
 1.0791. 
 
 21. 8.6990 - 10. 
 
 29. 
 
 
 
 .2431. 
 
 6. 
 
 0.9542. 
 
 14. 
 
 1. 
 
 7781. 
 
 22. 1.0970. 
 
 
 30. 
 
 2.0212. 
 
 7. 
 
 0.9030. 
 
 15. 
 
 1. 
 
 8751. 
 
 23. 0.0970. 
 
 
 31. 
 
 8.0212 
 
 -10. 
 
 8. 
 
 1.6902. 
 
 16. 
 
 0. 
 
 8751. 
 
 24. 1.5741. 
 
 
 32. 
 
 0.0212. 
 
 EXERCISE LXXXI. 
 
 
 
 
 
 
 Page 292. 
 
 
 
 
 
 
 l. 
 
 0.9030. 
 
 
 7 
 
 . 0.1003 
 
 13. 0. 
 
 2258. 
 
 19. 2.9579. 
 
 2. 
 
 1.3980. 
 
 
 8 
 
 . 0.3495 
 
 14. 0. 
 
 4660. 
 
 
 
 20. 0. 
 
 6361. 
 
 3. 
 
 3.3804. 
 
 
 9 
 
 . 0.0596 
 
 15. 0. 
 
 2045. 
 
 21. 2.4465. 
 
 4. 
 
 3.8168. 
 
 10 
 
 . 0.1690 
 
 16. 0.2415. 
 
 22. 0.4730. 
 
 5. 
 
 2.5353. 
 
 11 
 
 . 0.1398 
 
 17. 1.1650. 
 
 23. 0.5243. 
 
 6. 
 
 3.4950. 
 
 12 
 
 . 0.0768 
 
 18. 0. 
 
 3904. 
 
 
 
 24. 1. 
 
 3280. 
 
 
 
 
 
 
 
 
 
 
 25. 1. 
 
 1569. 
 
 EXERCISE LXXXIL 
 
 
 
 
 
 
 Page 294. 
 
 
 
 
 
 
 1 
 
 . 9.6020 
 
 -10 
 
 
 11. 
 
 0.1761. 
 
 
 21. 
 
 0.4559. . 
 
 2 
 
 . 9.4559 
 
 -10 
 
 
 12. 
 
 1.1461. 
 
 
 22. 
 
 8.8539 
 
 -10. 
 
 3 
 
 . 9.7781 
 
 -10 
 
 
 13. 
 
 8.2219 - 10 
 
 
 23. 
 
 7. 
 
 6320 
 
 -10. 
 
 4 
 
 . 9.6320 
 
 -10 
 
 
 14. 
 
 7.3980-10 
 
 
 24. 
 
 7.5441 
 
 -10. 
 
 5 
 
 . 9.8539 
 
 -10 
 
 
 15. 
 
 8.1461 - 10 
 
 
 25. 
 
 5. 
 
 1707 
 
 -10. 
 
 6. 0.1461. 
 
 16. 
 
 1.8539. 
 
 
 26. 
 
 4.8293. 
 
 7 
 
 . 0.2219 
 
 
 
 17. 
 
 2.6320. 
 
 
 27. 
 
 5. 
 
 9333. 
 
 
 8 
 
 . 0.3980 
 
 
 
 18. 
 
 6.6320 - 10 
 
 
 28. 
 
 4.1040. 
 
 9 
 
 . 0.3680 
 
 
 
 19. 
 
 1.2219. 
 
 
 29. 
 
 2 
 
 8627 
 
 -10. 
 
 10 
 
 . 0.5441, 
 
 
 
 20. 
 
 9.5441 - 10. 
 
 30. 
 
 7. 
 
 1373. 
 
 
44 
 
 ARITHMETIC. 
 
 EXERCISE LXXXIII. 
 
 Page 299. 
 
 1 
 
 . 1.8451. 
 
 13. 
 
 2.8638. 
 
 25 
 
 . 966. 
 
 37. 
 
 0.6910. 
 
 2 
 
 . 2.0043. 
 
 14. 
 
 7.9428-10. 
 
 26 
 
 . 34,580. 
 
 38. 
 
 48.67. 
 
 3 
 
 . 2.5224. 
 
 15. 
 
 0.9074. 
 
 27 
 
 . 7.162. 
 
 39. 
 
 47.58. 
 
 4 
 
 . 3.5429. 
 
 16. 
 
 0.6991. 
 
 28 
 
 . 0.9982. 
 
 40. 
 
 2.349. 
 
 5 
 
 . 3.2709. 
 
 17. 
 
 9.5762-10. 
 
 29 
 
 . 0.0540. 
 
 41. 
 
 3.721. 
 
 6 
 
 . 3.8386. 
 
 18. 
 
 8.8494-10. 
 
 30 
 
 . 0.3593. 
 
 42. 
 
 61.21. 
 
 7 
 
 . 3.9957. 
 
 19. 
 
 8.5709-10. 
 
 31 
 
 . 0.0001051. 
 
 43. 
 
 0.6137. 
 
 8 
 
 . 3.6424. 
 
 20. 
 
 1.9951. 
 
 32 
 
 . 0.001019. 
 
 44. 
 
 464.9. 
 
 9 
 
 . 3.0457. 
 
 21. 
 
 7974. 
 
 33 
 
 . 416. 
 
 45. 
 
 212.4. 
 
 10 
 
 . 4.7660. 
 
 22. 
 
 16.13. 
 
 34 
 
 . 0.1549. 
 
 46. 
 
 0.8168. 
 
 11 
 
 . 4.8913. 
 
 23. 
 
 2.781. 
 
 35 
 
 . 2.559. 
 
 
 
 12 
 
 . 4.4790. 
 
 24. 
 
 10.21. 
 
 36 
 
 . 165. 
 
 
 
 Page 300. 
 
 47 
 
 . 4.324. 
 
 55. 
 
 129.6. 
 
 63 
 
 . 0.4876. 
 
 71. 
 
 2.351. 
 
 48 
 
 . 0.2783. 
 
 56. 
 
 97.84. 
 
 64 
 
 . 0.006134. 
 
 72. 
 
 1.961. 
 
 49 
 
 . 0.001569. 
 
 57. 
 
 43.8. 
 
 65 
 
 . 17.76. 
 
 73. 
 
 1.97. 
 
 50 
 
 . 3889. 
 
 58. 
 
 5.153. 
 
 66 
 
 . 669.9. 
 
 74. 
 
 0.8834. 
 
 51 
 
 . 0.0006324. 
 
 59. 
 
 0.2061. 
 
 67 
 
 . 29.76. 
 
 75. 
 
 9.683. 
 
 52 
 
 . 0.06523. 
 
 60. 
 
 0.7285. 
 
 68 
 
 . 70.37. 
 
 76. 
 
 13.13. 
 
 53 
 
 . 13.28. 
 
 61. 
 
 0.0005336. 
 
 69 
 
 . 167.1. 
 
 77. 
 
 4.391. 
 
 54 
 
 . 2.684. 
 
 62. 
 
 0.629. 
 
 70 
 
 . 1.838. 
 
 78. 
 
 0.8578. 
 
 Page 301. 
 
 79. 2.534 kg . 
 
 80. 148.5 
 
 sq. 
 
 in. 81. 54.44 
 
 in. 
 
 
 
 
 82. 5.504 
 
 in. 
 
 
 
 
 EXERCISE LXXXIV. 
 
 Page 303. 
 
 1. 
 
 2.3028. 
 
 4 
 
 , 0.268; 
 
 7. 
 
 8.272. 
 
 10. 
 
 1.8117. 
 
 2. 
 
 22.11 ft. 
 
 
 3.732. 
 
 8. 
 
 2.8541. 
 
 11. 
 
 1.186. 
 
 3. 
 
 6.828 + ; 
 
 5 
 
 . 1.3713. 
 
 9. 
 
 9.1231; 
 
 12. 
 
 2.796. 
 
 
 1.17+. 
 
 6, 
 
 , 2.8284. 
 
 
 0.8769. 
 
 
 
ANSWERS. 45 
 
 EXERCISE LXXXV. 
 Page 306. 
 
 
 1 
 
 
 1 
 
 1 
 
 
 1. 
 
 Q I 
 
 1 
 
 54- ^ 
 
 1 
 
 O J 
 1 
 
 +1 
 
 1 
 
 1 -1 
 
 9 4- 
 
 1 
 
 3 -J- 
 
 AJ 1 
 1- 
 
 1 
 
 1 
 
 1 
 
 11 
 
 i 1 
 
 3. i, T 4 T> , ft; i T 4 y, H -#A; 2, f, i I, if, f 
 
 4. i i, I, I, A, A, if, ft, ft ; 2, 1, i, , if , i 
 
 VM'Hf Mi TWIT- 
 S' i i. i AV ; 1. i if , tf, iff ; i; f , I; 8, 8i, 8f , 
 
 6- T 7 6A- 10. 1, A tt ft - 
 
 7- 1, i I, A, If, H- 11. 1. i T 8 5, A- 
 
 s. i, i f , tt, *- 12. i, f, if, 
 
 9- i, tt, AV- is- 1, i, i i 
 
 EXERCISE LXXXVI. 
 Tage 308. 
 
 1. 15. 4. 25|. 7. 32, 431. 10. If 
 
 2. 72. 5. 9. 8. 5. 11. 1.1. 
 
 3. 5^-. 6. lOf . 9. 6|. 12. 6. 
 
 EXERCISE LXXXVII. 
 Page 309. 
 
 1. 780. 5. 210. 9. 575. 
 
 2. 74. 6. 765. 10. 209.3 ft,, 788.9 ft. 
 
 3. 88. 7. 1200. 11. 32 mi. 
 
 4. 103J. 8. 507. 12. 5| mi. 
 
46 ARITHMETIC. 
 
 EXERCISE LXXXVIII. 
 
 Page 311. 
 
 1. 4374. 4. |ff. 7. 248.832. 
 
 2.1 5. 2441if. 8. $1464.10. 
 
 3. 22-lf . 6. 7, 14, 28. 9. $ 1338.12 (by logs) ; 
 
 $1338.23 (exact). 
 
 EXERCISE LXXXIX. 
 Page 313. 
 
 1. 728. 5. l|f|f 8. 11,718. 
 
 2. 511. 6. Ifll 9. 4fff 
 
 3. 363. 7. l^ffi 10. $ 7254.40 (iy logs) ; 
 
 4. 98ff. $7253.13 
 
 EXERCISE XC. 
 
 Page 314. 
 
 1.1. 3.f 5.1|. 7.1. 
 
 2.2. 4.1 6. |f 8. f|. l 
 
 EXERCISE XCI. 
 
 The logarithm of a power, obtained by multiplication, is neces- 
 sarily liable to an error in the last place, which may equal half the 
 exponent. A result thus obtained from 4-place logarithms may there- 
 fore be uncertain in the fourth significant digit. 
 
 Page 316. 
 
 1. $82.08. 5. 4.38 yrs. 9.4.1% 
 
 2. $173. 6. 14.29 yrs. 10. $852.80. 
 
 3. 11.8 yrs. 7, 5.95$. 11. $1352; $3656. 
 
 4. 18.9 yrs. 8, 7.6% 12. $1197.50. 
 
ANSWERS. 47 
 
 Page 317. 
 
 13. $1227.80. 15. $2428. 17. $2376. 
 
 14. $4818. 16. $2647. 18. $2418. 
 
 CHAPTER XXV. 
 
 MISCELLANEOUS PROBLEMS. 
 
 Page 318. 
 
 1. 123, 132, 213, 231, 312, 321 ; 1332. 
 
 2. 235, 253, 325, 352, 523, 532; 1,892,000,000,000,000; (by 
 
 logs). 
 3.873, 837, 783, 738, 387, 378; 61,770,000,000,000,000; 
 
 (by logs). 
 
 4.2.093; 2.987; 3.741; 8.984; (by logs). 
 5.0.4309; 13.98; 2.801; 1102.5; (by logs). 
 
 6. 201.1 ; 4.39 ; (by logs). 8. 5268.585 ft, 10. 29.67. 
 
 7. 1533.623 ft. 9. 808.97 ft. 11. 55.31. 
 
 Page 319. 
 
 12. P. 200; C. 101; B. 189. 
 
 13.432 = 54x8; 4 + 3 + 2 9; 3 + 4 + 2-6 + 3. 
 
 14. 196. 15. |ff 19. 7974 dys. 
 
 16- ii rl If, m- 20. 12 ft. 
 
 17.25, 9, 49; 21. 3 mi. 160yds. 
 
 225, 1225, 441, 11025. 22. 38 barges. 
 
 18. 92 ft. 
 
 Page 320. 
 
 23. 458.49 1 ; 13. bu. 29. 146 balls (by logs). 
 
 24. 2803.194 kg . 30. 0.00336 in. 
 
 25. 1.3939 t. 31. 7 dwt. 21 gr. 
 
 26. 1052.09 sq. in. 32. $2250. 
 
 27. 7.407 A. (by logs). 33. 15 cts. per Ib. 
 
 28. 523.6; 4188.8; 1:8. 34. $13.85, $8.85, $4.42^. 
 
48 ARITHMETIC. 
 
 Page 321. 
 
 35. 12,480. 39. 15.2498; 15.25; (by logs). 43. 28 T 4 T . 
 
 36. $15 a year. 40. A gains $5.05. 44. 9 men. 
 
 37. 17^ min. 41. 905 t. 1392 Ibs. 45. SOsq.in. 
 
 38. 12 min. 42. 46.37 sq. in. 
 
 Page 322. 
 
 46. 1367 sq. ft. (by logs). 49. 0.8908 A. (by logs}. 
 
 47. 0.1467 ha (by logs). 50. 224.3 A. (by logs). 
 
 48. 0.2736 ha (by logs). 51. 25.12 sq. rds. (by logs). 
 
 52. 3.946 A. (by logs). 
 
 Page 323. 
 
 53. 0.194167 ha . 55. 866.0254 ft, 57. 61,785 sq. ft. (by logs). 
 
 54. 0.6436 A. 56. 13.2 mm ; 17.62 mm ; 23.36" 
 
 Cmm 
 
 Page 324. 
 
 58. Diagonal, 351.489 ft.; area, 61,785 sq. ft. (by logs). 
 
 59. 314.16 sq. in.; 78.54 sq. ft,; 71.62 sq. in. 
 
 60. 0.2428 ha . 63. 1922.9 sq. in. 
 
 61. 2205.5 sq. ft. (by logs). 64. 50.2656 sq. in. 
 
 62. 9804 sq. ft. (by logs). 65. 523.6 cu. in. 
 
 66. Diam., 5.57 ft.; area, 24.37 sq. ft. (by logs); sphere, 
 
 90.52 cu. ft. (by logs). 
 
 67. Iron, 38.86 kg , 85.66 Ibs.; tin, 8.383 kg , 18.48 Ibs.; lead, 
 
 30.76 kg , 67.83 Ibs.; silver, 0.01233 kg , 0.02717 lb.; (by 
 logs). 
 
 68. 898 balls of a diameter 2.436 in. (by logs). 
 
 Page 325. 
 
 69. 3737.5 Ibs. (by logs). 
 
 70. Weights: 482.24 mg , 482.24 g , 482.24 kg ; surfaces: 
 
 3.1416 qcm , 314.16 qcm , 31,416 qcm . The first, if we take 
 no account of the retardation of the air by friction on 
 the plane. 
 
ANSWERS. 49 
 
 71. End, 78.54 sq. in. ; convex surface, 376.99 sq. in. ; total 
 surface, 534.07 sq. in. ; contents, 4.08 gals. ; (by logs), 
 
 72. 8935 gals, (by logs), 
 
 73. 5.424 in. (by logs). 
 
 74. 552.92 cu. in. 
 
 75. 6.65 in. ; 4.19 in. ; 10.84 cm ; (by togs). 
 
 Page 326. 
 
 76. 31.952 cu. in. 78. 59,259 Y 7 T cu. yds. 80. 15.09 cu. in. 
 
 77. 50.93 bu. 79. 66,966f cu. yds. 81. 2,614,689 cbm . 
 
 Page 327. 
 
 82. 0.14067 1 . 85. 112.07 1 . 88. 178.3 gals. 
 
 83. 98.47 cm radius. 86. 3.302 qts. 89. 22.286 gals. 
 
 84. 1.833 1 . 87. 0.796 pt. ; 2.489 pts.; 3.825 pts. 
 
 90. 0.249 pfc.; 0.963 pt; 2.002 pts. ; (by logs). 
 
 91. 4.596 pks.; 0.531 pk.; 4 pks.; (by logs). 
 
 Page 328. 
 
 92. 10 ft.; 20 ft. 94. 112.8 m ; 564 m ; (by logs.) 
 
 93. 235.5 ; 706.5 ft. ; (by logs). 95. 25. 
 
 96. 261.8 cu. in., a little over 9 pts. 
 
 97. $78.54. 
 
 98. 633 million million million bu. ; 458 hundred thousand 
 
 million yds. ; (by logs). 
 
 99. 8 billion cu. mi. (by logs). 
 
 100. " 2 feet square " means a square 2 ft. on a side ; " 2 square 
 feet," any surface equivalent in area to two squares 
 each 1 ft. on a side. A "foot square" is a square; 
 while a square foot is an equivalent area in any 
 shape. "Half a foot square" is ambiguous. Half 
 "a foot square'' is half a square foot, while "half 
 a foot" square is 6 in. square ; that is, is one-fourth 
 a square foot. 
 
50 ARITHMETIC. 
 
 Page 329. 
 
 101. 25-J- cu. ft. 103. 210.54 hl . 
 
 102. 4.42 qts. 104. 69.115 sq. in. ; 247.401 sq. in. 
 105. 30 ft. ; 100 ft. ; 60 ft. ; 4712.4 sq. ft. 
 
 It is plain that the kid can go 10 ft. beyond each stake on a line 
 joining them, so that her range is 100 ft. long. When she is at the 
 middle of the cord, and draws it taut, imagine a stone midway be- 
 tween the stakes. The stone, the kid, and either stake then make a 
 triangle, right-angled at the stone ; and 50 2 - 40 2 900 = 30 2 , so that 
 the kid is 30 ft. from the stone ; the width of her range is therefore 
 2 x 30 = 60 ft., and its area 4712.4 sq. ft. 
 
 106. 
 
 i 330. 
 
 107. 11 in. ; 13.603 (by logs) ; 117.5 sq. in. (by logs). 
 
 108. 9.784 in. ; 2.446 in. 
 
 The law of \ 452 may be put : The length of pendulums is in- 
 versely as the square of the number of their vibrations in a given 
 time. Therefore, a half-seconds pendulum will be \ x J = } the 
 length of a seconds pendulum ; and a quarter-seconds pendulum, 
 J X J = yV the length. It will be understood that these lengths, 
 39.138, 9.784, 2.446 inches, refer to the theoretical case in which the 
 rod is without weight and all the weight on the end ; or they are the 
 distance apart of two points in a bar of uniform thickness and 
 weight from end to end, at either of which the rod would vibrate at 
 the required rate. 
 
 109. 55.92 cm ; 397.64 cm . 110. 8.17 times. 
 
 111. 1,000,000^. 
 
 Suppose the plunger and piston square: the one would p^ess on a 
 surface of l<i cm , the other on a surface of 10,000<i cm . By driving the 
 plunger in 10 cm , you force 10 ccm of water under the piston. But, as 
 this is spread under 10,000<i cm , you raise the piston thereby only 
 0.001 cm ; that is, only 0.0001 part of the way you move the plunger. 
 Hence, by the principle of virtual velocity (what is lost in time is 
 gained in power), you lift the piston with 10,000 times your force 
 of 100 k s applied. The lifting power, in other words, is 1,000,000^, 
 or 1000*, minus the trifling loss by friction. 
 
ANSWERS. 51 
 
 112. 9,216,000 Ibs. 113. 144,000 Ibs. 
 
 Page 331. 
 
 114. 114 t. ; 6 t. ; 600 t, 115. 56^ t . of 2000 Ibs. 
 
 116. 7.355 m ; 31.869 m per sec. 
 
 As the velocity is in proportion to the time, the velocity in J of a 
 second will be f X (9.806), that is, | X (32.172 ft.) = 24.139 ft. ; in 3J 
 seconds it will have a velocity of 3J X 32.172 = 104.56 ft. per second ; 
 that is, that will be its rate at that instant, but the velocity steadily 
 increases. In the first tenth of a second a stone falls 0.1609 of a foot, 
 but has already acquired a velocity that would carry it 3.217 of a 
 foot in a second. In the next tenth of a second it goes, therefore, by 
 that velocity 0.3217 ft., and, by still falling, 0.1609 more, so that it has 
 gone 0.4826 of a foot ; and its velocity is its old one and 3.217 added, 
 that is, 6.217 feet. In other words, the falling body cannot fall so fast 
 as to lessen its weight ; its weight constantly accelerates its motion. 
 
 117. 0.3876 sec. (by logs). 
 
 118. 198 ra per sec.; 20.19 sec. (by logs). 
 
 119. 651.8 ft. per sec. ; 20.26 sec. (by logs). 
 
 120. 3.81 sec. 332 ' 
 
 The acceleration 32.172 is for a vacuum, 32 ft. is near enough for 
 practical questions ; and 16 ft. for the fall. V210 -^ Vl6 = 3.623 sec. 
 will therefore give the time of falling. To this add -fffo for the 
 sound to come up, and we have the answer 3.811 sec. 
 
 121. 11.428 sec. 122. 747 ft. 123. 133 ft. 
 
 124. 0.04515 sec.; 0.07198 sec.; 0.1428 sec.; 0.17635 sec. 
 
 125. 24 ft. per sec. 
 
 The velocity will be to 32 ft. as V9 is to VB; that is, it will be 
 24 ft. a sec. This law is obtained from experiment. 
 
 126. 40 ft. and 80 ft. per sec. 127. 15 gals, an hour. 
 
 128. GJ gals. 
 
 Page 333. 
 
 129. 3 gals, to area; 3 pts. to friction. 
 
 130. 3f as much ; 15-J as much. 
 
52 ARITHMETIC. 
 
 131. 6135 times the weight of the material. 
 
 Three inches in diameter is 1.5 in. or J ft. radius. Therefore, by 
 the formula, the outer layer of the top will pull out with 
 
 1.227 X | X 200 X 200 = 6135 times the weight of the material. 
 
 132. 5.453 times its weight when on a level with the hand ; 
 
 4.453 times when highest; 6.453 times when lowest. 
 
 As this circle is vertical, the weight of the stone acts alternately 
 
 with and against the centrifugal force ; so that, on a level with the 
 
 hand, it pulls (by the formula) with 5.453 times its weight ; but at 
 
 the highest point with 4.453, and at the lowest with 6.453 times. 
 
 Page 334. 
 
 133. With 0.0752 of its weight. 
 
 30 mi. per hour is 44 ft. per sec. A circumference of 800 ft. radius 
 measures 5026.55 ft., nearly. The force is therefore 1.227 X 800 x 
 (5 02 e s s) 2 = 0.0752 of its weight. 
 
 134. 21.735 times its weight, 135. 186.116 times its weight. 
 
 Page 335. 
 
 136. 1 lb. ; 1 lb. 
 
 18 in. = I yd., and } yd. of chain = J lb. weight. Therefore, i lb. 
 and 1 lb. are the answers. 
 
 137. 100 yds. 
 
 The horizontal tension is 25 Ibs., which represents 100 yds. of rope. 
 Hence, radius = 100 yds. 
 
 138. 71f yds. 
 
 The weight of the rope being |fg | of what it was, it takes only 
 f of 100 yds. = 71f yds. 
 
 139. 2145 Ibs. 
 
 1980 ft. = 660 yds., and 3} x 660 = 2145 Ibs. tension. Ans. 
 
 140. ! (19.5x11.5) -28.031 ft. 
 
 Half-chain = 15.5 ft., sag = 4 ft. ; sum of half-chain and sag = 19.5, 
 diff. = 11.5. Therefore, by Prop. II., radius = 1(19.5 x 11.5) = 28.031. 
 
ANSWERS. 53 
 
 141. UL x 28.031 16.27 Ibs. ; by III, log -J- span = log 
 
 19.5 + log 11.5 + log (1.2900 - 1.0607) + colog 4 + 
 0.0612 ; whence span = 29.58 ; batter *= 1.808. 
 
 The chain weighs Jf Ib. to a ft., and the tension is therefore 
 }f (28.031) = 16.27 Ibs. By Prop. III., log 1 span = log 19.5 + log 11.5 
 + log(1.2900 ~ 1.0607) + colog 4 + 0.0612. Whence span = 29.58 ft. 
 By Prop. IV., batter = iff! - 1.808. 
 
 142. Eadius, 91.75" 1 ; tension, 91. 75 kg ; span, 30.85 m ; batter, 
 
 5.92; depression at 10 cm from ends, 1.689 cm . 
 
 Half-chain = 15. 5 m , sag = 1.3 m ; therefore, by Prop. II., radius = 
 16.8 X 14.2 4- 2.6 = 91.75 m , and (by Prop. I.) tension = 91.75 k . By 
 Prop. III., log i span = log 16.8 + log 14.2 + log (1.2253 - 1.1523) 
 + colog 1.3 + 0.0612. Whence span = 30.85 m . By Prop. IV., bat- 
 ter = 9 ^~ = 5.92. 10 cm now becomes hypotenuse to a right tri- 
 angle whose legs are in the proportion 1 : 5.92 ; and the square of 
 10 = 100 is to be divided in the proportion I 2 : 5.92 2 = 1 : 35.05. The 
 smaller of these parts, 2.773, is the square of 1.665 cm , the depres- 
 sion required. The advantage of logs is here especially manifest. 
 Log _L2_ = 2 - log 35.05 = 0.4553 ; one-half of which is 0.2277, 
 which is log 1.689. 
 
 143. Suppose the sag 26. 5 m : it gives, by III., half-span 
 
 40.05 ; suppose the sag 26. 6 m , it gives half-span 
 39.95, whence sag is 26.55, as nearly as four-place 
 logs can get it. Batter, 0.676; tension, 97 Ibs. or 
 44* 
 
 Page 336. 
 
 144. By position and Prop. III., sag = 22.55 m , and tension 
 
 - 111.3 Ibs. 
 
 145. By position and Prop. III. ,120.95 ft.; 109.96ft.; 102.6ft. 
 
 146. 1750 gr. ; (1728 H- 4) x 16 - 6912, and sp. gr. = 6.912. 
 
 147. 3.578 in.; 6.253 in. 
 
 148. 66.45 Ibs. ; 7.673 in. 
 
 149. 515.67 Ibs.; 15.19 in. 
 
54 ARITHMETIC. 
 
 150. 7.312 in. 
 
 2 gals, are 462 cu. in. Therefore, -f^ x 462 = 42 sq. in. is the area 
 of the end of the cylinder. As log diarn. 2 + log 0.7854 = log 42, we 
 have 2 log diam. = log 42 - log 0.7854, or log diain. - J (1.6232 + 
 0.1049) = 0.8640, and diameter = 7.3117 inches. 
 
 151. 8.084 in. 153. 6.2832 cm . 154. 48 ft. 
 
 152. 20.6 cm . 155. 530.7 times. 
 
 Page 337. 
 
 156. 4.22 times its weight. 
 
 The carriage going at 10 mi., the top of the wheel goes at 20 mi., 
 or 29 J ft. per second. The radius of the curve is 6J ft., the total cir- 
 cumference of which would be 12| x 3.1416 =39.7936 ft. The force, 
 therefore, is 
 
 1.227 X 61 x (l^lljj) 2 = 4.224 times its weight. 
 
 157. In going one rnile the wheel turns 530.7 times. There- 
 
 fore the point travels 3J- X 4 X 530.7 = 6722.2 ft. 
 
 158. 2.776 1 . 
 
 A square shaft to enclose the neck would contain 6 x 6 x 7.5 = 
 270 ccm ; one to enclose the body would contain 13 x 13 x 15.3 = 
 2585. 7 ccm . A square frustum would have its bases 6 x 6 < i cm and 
 13 X IS** 6 , and the square root of their product would be 6 x 13*i cm . 
 Add the three and multiply by i of 7.2 cm , gives 679.2 ccm . The 
 three solids added make 3534. 9 ccm , which, multiplied by 0.7854, to 
 reduce it from square to round form, gives 2776. 3 ccm = 2.776 for 
 the contents. 
 
 159. 1.25 1 . 
 
 Proceed as in 158. The cylinder holds 1.6 2 X 8 x 0.7854 ccm . The 
 frustum Y(17.5 2 + 1.6 2 + 17.5 x 1.6) X 0.7854 ccm ; and the sum of the 
 two is 1.25 1 . 
 
 160. 2.4845 1 . 161. 33,072.6 qcm ; 25.7967 kg . 
 162. Cap. 7.607 1 ; weight, 68.71 kg . 
 
 The cavity is 32 - 2 x 3.8 = 24.4 cm in diameter; and 3 times 
 log 24.3 + log 0.5236 gives log of contents in cubic centimeters, that is, 
 7.607 1 . The exterior size is 32 3 x 0.5236 ccm ; subtracting cavity, and 
 multiplying by 7.2. gives 68.71 k s as the weight. 
 
163. 673.6 qcm . 
 
 ANSWERS. 55 
 
 Page 338. 
 
 On every side imagine a multitude of straight lines going straight 
 up the shade. The space between any two would be measured by 
 the product of its length, 13.4 cm , and its average breadth, or breadth 
 in the middle. But these middle breadths constitute a circumference 
 round the shade, with a diameter J(25 + 7). Therefore the curved 
 surface is 13.4 X 16 x 3.1416 - 673.6<i cm . 
 
 164. 368.61 1 ; 2.26195<r 
 
 The volume of the half-cylinder - J (0.8 2 X 0.7854 X 1.2). That of 
 the half dome is J (0.8 3 x 0.5236), and the sum of the two - 368. 61 1 . 
 The area of the floor is J (0.8 2 X 0.7854); of the wall, J X 0.8 x 3.1416 x 
 1.2 ; and of the roof, } X 4 x 0.8 2 x 0.7854 ; the sum being 2.26195i m . 
 
 165. 9.8855". 
 
 The cylinder is 3.4 m x 0.8 2 X 0.7854. The two caps would make a 
 sphere, O.S 3 x 0.5236. Half the sum is 9.8855 hl . 
 
 166. 21.04 mi. 167. 23. 6G mi. 
 
 168. 67.8 mi. 
 
 The sailors' offing is V52.5 miles toward the coast, and V40,250 
 miles from Aconcagua ; therefore, 200.6 - 140 = 60.6 from the coast, 
 sind the ship is 60.6 -f 7.25 = 67.85 miles from land. 
 
 169. 28.5 mi. 
 
 Page 339. 
 
 170. 21,110 A. (ly logs). 174. 12.85 km . 
 
 171. 229 mi. ; 93.5 mi. ; 41.8 mi. 175. 1950 m . 
 
 172. 1429 ft. ; 5714 ft. ; 12,860 ft. 176. 8475 ft. 
 
 173. 122.5 km ; 173.2 km . 177. 53.88 mi. 
 
 Page 340. 
 
 178. 2.5946 km ; 87.1667 km . 181. 2.79 mi. 
 
 179. 16 h. 3.2 min. 182. 14.16 sec. 
 
 180. 30.63 km . 183. 0.67 sec. ; 7.07 sec. 
 
56 ARITHMETIC. 
 
 184. 6.93 ; 7.13 sec. sound ; 8.02; 9.G8 sec., balls; (by logs). 
 The wind at li mi. an hour goes 1G.1 ft. a second, which must be 
 added to the velocity of the sound for one gunner, and subtracted for 
 the other. 
 
 185. 7.18 sec. 
 
 Page 341. 
 186. $34.125. 187. 22 Y 2 min. 
 
 188. 126,233.8 gals. 
 
 As the canal slopes only on its sides, not at its ends, the capacity 
 is the same as if its top and bottom were each 7J yds. 
 50 x 7.5 x f - 50 x 12.5 = 625 cu. yds. 
 
 189. A, 70.5; B, 45.5 Ibs. 
 
 190. 51f min. 
 
 The man rows 4 mi. an hour for 1.2 hours ; that is, rows 4.8 mi., 
 but only makes 4 mi. Therefore, the current bears him down 0.8 mi. 
 in 1.2 hours, or flows at f mi. per hour. When he rows with it he 
 will therefore go 4| mi. per hour, and row 4 mi. in f hour = 51f min. 
 
 191. 40.8 ft. 193. 852.G4 sq. in. 
 
 192. 12 T 9 Q- carats; 15 carats. 194. 8.12 in. 
 
 Page 342. 
 
 195. 203,996 shot, 
 
 The cylinder would hold 785.398 cu. in. Reduce 0.3927 cu. ft. to 
 inches by multiplying by 1728, and subtract from 785.398. The 
 remainder is what is lacking ; and this divided by O.I 3 X 0.5236, that 
 is, by 0.0005236, will give the number of shot. 
 
 196. 2.353 in. 
 
 -fa of 231 is 3.85 cu. in., the capacity of a glass. 2.5 x 2.5 x 0.785 \ 
 will be the area of the top. Divide the capacity by the top area, 
 and the quotient is J the depth. 
 
 197. 1 min. 9.58 sec. 
 
 The train is 72 sec. in passing from one signal to the other. 
 When it reaches the second signal, the sound of the first signal is 
 therefore 72 X 1090.2 2640 ahead of it ; and this distance, divided 
 by 1090.2, is 72 sec. - 2.422= 69.578 sec., the required interval. 
 
ANSWERS. 57 
 
 198. 20.71 ; 29.29 yds. 
 
 The square of one distance is twice the square of the second; the 
 distances must therefore be in the proportion 1 : V2, or 1 : 1.4142 and 
 2.4142 : 50 = 1 : smaller distance. 
 
 199.5.366ft.; Ifff; (by logs). 
 
 The cubical cistern holds 04 cu. ft., and requires 5 x 16 = 80 sq. ft. 
 of lead to line it. 
 
 The round cistern will require 16 x 0.7854 sq. ft. on the bottom. 
 Subtract this from 80 sq. ft., and divide by 4 X 3.1416, and you have 
 the permitted depth. Multiply this by the area of the bottom for 
 the capacity. 
 
 200. $12.60. 202. 96f nights. 
 
 201. 192.2 mi. 203. 22.015 in. 
 
 Page 343. 
 
 204. 1 long ton ; 2400 Ibs. 205. 9 ft. ; 7 ft. 206. 8 oz. 
 
 207. 6 Ibs. 
 
 The substance being in the left pan, requires 9 Ibs. in the right to 
 balance it. But 4 Ibs. in the left pan required the substance in the 
 right. That is, 4 Ibs. is to the substance as the substance was to 
 9 Ibs. ; and, by the rule of three, 4x9 = true weight squared. Hence 
 the substance weighs 6 Ibs. 
 
 208. 181.82 Ibs. 209. 17.68 k ^. 
 
 Page 344. 
 
 210. Less than 144 Ibs. 212. 88f % 0; 11.1% H. 
 
 211. Less than 0.754 in. 213. 28f %. 
 
 214. 24.32%. 
 Page 345. 
 
 215. 48%. 219. 23.46 oz. 223. 831 grs. 
 
 216. 18|f %. 220. 52^% ; 12%. 224. 960 m *. 
 
 217. 4 T 2 % % . 221. 40% . 225. 40K 
 
 218. 187.6 oz. 222. 7.83 Ibs. 226. ll,052.6 g . 
 227. 6530.6*. 228. 18.37% water; 81.63% sulphuric acid. 
 229. 2722| mg . 230. Fe 2 8 . 231. S0 2 . 
 
58 ARITHMETIC, 
 
 Page ;*. lii. 
 
 233. C 5 H 8 ; ll|f%. 
 
 234. 00. 
 
 The numbers actually formed are those from 10 to 99 ; 90 in all. 
 To show how many can be formed, consider that each digit may be 
 followed by itself or by either of the other 9, giving 100 sequences 
 of 2 figures ; but 10 of these begin with naught, and are to be reject- 
 ed, leaving 90. 
 
 235. 45. 
 
 As 10 is even and 99 odd, one-half the 90, viz., 45, is odd. 
 
 236. 648. 
 
 The digit in the thousands' place must be either 1, 2, or 3. Either 
 of these may be followed in the hundreds' place by either of the 6 
 given digits, making 18 different hundreds. Each of these may be 
 followed in the tens' place by either of the 6, giving 108 different 
 tens ; each of which may have G digits, giving G48 numbers if you 
 include the 1000. 
 
 237. 55. 
 
 By a dominoe is meant two numbers, side by side. Double-blank 
 is 00. The next pieces introducing 1 are 01, 11 ; those introduc- 
 ing 2 are 02, 12, 22. Every number introduced requires new 
 pieces exceeding by one the number introduced. Thus, as we have 
 seen that to go to double-2 requires 6; to go to double-3 will re- 
 quire 6 + 4 = 10 pieces ; double-4, 10 + 5 = 15 pieces. The ordinary 
 set is 15 + 6 + 7 = 28 pieces ; and for double-9's we should require 
 28 + 8 + 9 + 10 = 55 pieces. 
 
 238. 31. 
 
 With a single piece, 5 amounts ; with 2 pieces, 4 + 3 + 2 + 1 = 10 
 amounts ; with 3 pieces, 10 amounts ; with 4 pieces, 5 amounts ; with 
 all 5 at once, 1 amount ; with the 5 in their various combinations, 
 therefore, 5 + 10 + 10 + 5 + 1=31 amounts. 
 
MATHEMATICS. 
 
 WENTWORTH'S SERIES. 
 
 HHHE United States Bureau of Education, in Circular of Infer- 
 
 " mation, No. 3, 1890, says, on the subject of mathematical 
 text-books, "If we were called upon to name the writer whose 
 books have met with more wide-spread circulation during the past 
 decennium that those of any other author, we should answer, 
 \Ventworth. ... In point of scientific rigor, Wentworth's books 
 are superior to the popular works of preceding decades." 
 
 These two points indicate the two leading characteristics of 
 these remarkable books. They combine mathematica. scholarship 
 with all the elements of school-room popularity. The author's 
 aim was to be helpful. He has made a study of his subjects with 
 the psychology and probable capacity of the students constantly in 
 mind. His books enable the average student not merely to learn 
 something, but to master the study, and at the same time they 
 give the brighter ones a plenty to exercise their faculties upon. 
 
 There is no attempt to make a parade of learning. On the other 
 hand, there is no absolution from solid work. Everything is made 
 simple, practical, direct, and thorough. Mental energy is econo- 
 mized. The teacher has to use his strength only in the necessary 
 work of teaching, and the pupil his only in the necessary work of 
 acquiring. 
 
 To learn by doing, and to learn one step thoroughly before the 
 next is attempted, are the chief elements of the method, and yet 
 no books give pupil or teacher less of the tread-mill feeling. The 
 consciousness of mastery constantly cheers and invigorates the 
 student, while the teacher has the satisfaction of wielding an in- 
 strument fitted to the hand. 
 
 All will recognize in these characteristics the marks of ideal 
 text-books. No one will claim that any series could be suited to 
 every particular case. The merit of Wentworth's is that it suits 
 in all but now and then a peculiar one. The books are found 
 everywhere in the United States, and here and there all around 
 the world. The testimony of use may be summed up in one word, 
 Satisfaction. What more can one desire than to be satisfied? 
 
 08 
 
70 
 
 MATHEMATICS. 
 
 Wentworth's School Algebra. 
 
 By G. A. WENTWORTH, Professor of Mathematics in Phillips Exeter 
 Academy. Half morocco, v -- 362 pages. Mailing price, 31.25; for 
 introduction, $1.12. Answers in pamphlet form, free, on teachers' 
 orders. 
 
 TN" this book the author has availed himself of his own expe- 
 rience in writing and teaching the elements of Algebra, and of 
 the experience of hundreds of others. Where improvement was 
 possible, it has been made. 
 
 The School Algebra is offered as exactly right for the usual high 
 school and academic courses. It gives a thorough and practical 
 treatment of the principles of Algebra up to and including the 
 binomial theorem, and is strictly in line throughout with the 
 author's College Algebra. For college preparation it is particu- 
 larly well suited. 
 
 The problems in this book are nearly all new, either original or 
 selected from recent examination papers, and are graded with the 
 utmost care. They are sufficient in number to illustrate and fix 
 all the principles, and interesting and varied enough to hold the 
 student's attention through the book. The passage from Arith- 
 metic to Algebra is made easy, and the advantages of using letters 
 clearly pointed out. The treatment of fractions has been further 
 simplified. Radicals precede quadratics. There is at the end a 
 carefully made collection of miscellaneous examples, covering 
 nearly every principle of Algebra. This, with the author's College 
 Algebra, makes a complete and consistent course. 
 
 OPINIONS OP TEACHERS WHO ARE USING IT. 
 
 I. H. Mauser, Prin. 3IcEwensville 
 Academy, McEwensville, Pa. : After 
 a thorough test in the class-room 1 
 can only say that I know of nothing 
 better. It is just the work to arouse 
 the enthusiasm and to bring out the 
 thought power of the student. It is 
 admirably arranged and carefully 
 graded, and imparts such a knowl- 
 edge of elementary algebra, in so 
 attractive a way, as no other work 
 does. Too much cannot be claimed 
 for it. 
 
 Florence A. Stowell and Mary S. 
 
 Cohoon, Teachers in High School, 
 Binghamton, N. Y. : We are using 
 it in the first year's work in our 
 High School. We consider it ex- 
 cellent in scope and arrangement of 
 topics, and better adapted to our 
 requirements than any other algebra 
 we have used or inspected. 
 
 A. J. Volland, Principal of High 
 School, Racine, Wis. : My opinion of 
 Wentworth's School Algebra may be 
 drawn from the fact that the book 
 is now in use in this school, and is 
 uivinp; satisfaction. 
 
8Q MATHEMATICS. 
 
 Wentworth & Hill's Exercises in Algebra. 
 
 I. Exercise Manual. 12mo. Boards. 232 pages. Mailing Price, 40 
 cents; Introduction Price, 35 cents. II. Examination Manual. 12mo. 
 Boards. 159 pages. Mailing Price, 40 cents; Introduction Price, 33 
 cents. Both in one volume, 70 cents. Answers to both parts together, 
 25 cents. 
 
 HpHE first part (Exercise Manual) contains about 4500 problems 
 "* classified and arranged according to the usual order of texk 
 books in Algebra; and the second part (Examination Manual) 
 contains nearly 300 examination-papers, progressive in charac- 
 ter, and well adapted to cultivate skill and rapidity in solving 
 problems. 
 
 British Mail: All engaged in the 
 practical woik of education will 
 appreciate these Manuals, as they 
 are calculated to save the master 
 
 much precious time and labor, and 
 to give his students the benefit of 
 progressive and carefully thought* 
 
 out exercises. 
 
 Wentworth & Hill's Exercises in Geometry. 
 
 12mo. Cloth. 255 pages. Mailing Price, 80 cents ; Introduction Price 
 70 cents. 
 
 rpHE exercises consist of a great number of easy problems foi 
 beginners, and enough harder ones for more advanced pupils. 
 The problems of each section are carefully graded, and some of the 
 more difficult sections can be omitted without destroying the unity 
 of the work. The book can be used in connection with any text- 
 book on Geometry as soon as the geometrical processes of reason- 
 ing are well understood. 
 
 select propositions from it to supple 
 ment every stage of our work. 
 
 Amelia W. Platter, High School, 
 Indianapolis, Ind. : I find the sub- 
 ject so carefully graded, that I can 
 
 Analytic Geometry. 
 
 By G. A. WENTWORTH. fievised edition. 12mo. Half morocco, xii + 
 301 pages. Mailing Price, $1.35; for introduction, $1.25. 
 
 rpHE aim of this work is to present the elementary parts of the 
 
 subject in the best form for class-room use. 
 
 The connection between a locus and its equation is made per- 
 fectly clear in the opening chapter. 
 
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