|
:XIII
<br />m
<br />TABLE V111.-NATURAL.TRIGON0METRICAL FUNCTIONS.
<br />Angle
<br />Sine.
<br />Tan.
<br />Cot9.
<br />Cosin.
<br />1
<br />Angle
<br />Sine.
<br />Tana
<br />Cotg.
<br />Covin.
<br />,
<br />-32
<br />.5299
<br />.6249
<br />1.600
<br />.84805
<br />58
<br />30.6225,
<br />.02.04
<br />.7954
<br />1.257
<br />.78251
<br />30
<br />10
<br />.5324
<br />'.6289
<br />1,590
<br />,84650
<br />50
<br />40
<br />,.6248
<br />.8002
<br />1.250
<br />.78079
<br />20
<br />20
<br />.5348
<br />.6330
<br />1.580
<br />,84495
<br />40
<br />50.
<br />.6271
<br />.8050
<br />1.242.
<br />.77897
<br />10
<br />30
<br />.5373
<br />.6371
<br />1.570
<br />.84339
<br />30
<br />,44
<br />.50
<br />.56 .61
<br />.67
<br />.72
<br />.78 .83
<br />40
<br />.5398'
<br />.6412
<br />1.560
<br />.84182
<br />20
<br />39 .
<br />'.620
<br />.8098
<br />1.235
<br />.77715
<br />51
<br />50
<br />.5422
<br />.6453
<br />1.550
<br />.84025
<br />10
<br />10
<br />'.6316
<br />.8146
<br />1.228..77531
<br />.74
<br />SO
<br />.93 L02
<br />1.11
<br />1.20
<br />1.30 1.39
<br />6
<br />.11
<br />20
<br />.6338
<br />.8195
<br />1,220
<br />•.77347
<br />40
<br />83
<br />.5446
<br />.6494
<br />1.540
<br />.83867
<br />57
<br />30
<br />.6361
<br />.8243
<br />1.213
<br />.77162
<br />30
<br />10
<br />.5471
<br />.6536
<br />1.530
<br />.83708.
<br />50
<br />40
<br />.6383
<br />.8292
<br />1.206
<br />.76977
<br />20
<br />20
<br />.5495_
<br />.6577
<br />1.520
<br />.83549
<br />40
<br />50
<br />.6406
<br />.8342
<br />1.199
<br />.76791
<br />10
<br />30
<br />.5519
<br />'6619.
<br />1.51L
<br />.83389
<br />30
<br />1.33
<br />1.50
<br />L67 1.83
<br />2.00
<br />2.17
<br />2.33 2.50
<br />40
<br />.5544
<br />.6661
<br />1.501
<br />.83228
<br />20
<br />40
<br />.6428
<br />.8391
<br />L192
<br />.76604
<br />50
<br />50
<br />.5568
<br />.6703
<br />1.492
<br />;.83066
<br />10
<br />10
<br />`.6450
<br />.8441
<br />L185
<br />•76417
<br />50
<br />2.04 2.24
<br />2.44
<br />2.65
<br />2.85 3.06
<br />12
<br />.22
<br />20
<br />.6472
<br />.8491
<br />1.178
<br />.76229
<br />40
<br />34.
<br />.5592,'.6745
<br />2.22 2.44
<br />1.483
<br />.82904
<br />56
<br />30
<br />.6494.
<br />.8541
<br />1.171
<br />.76041
<br />30
<br />10
<br />.5616
<br />.6787
<br />1.473
<br />.82741
<br />50
<br />40
<br />.6517
<br />.8591
<br />1.164
<br />,75851
<br />20
<br />20
<br />.5640
<br />.6830
<br />1.464
<br />:82577
<br />40
<br />50
<br />.6539
<br />.8642
<br />1.157
<br />•75661
<br />10
<br />30
<br />.5664
<br />.6873
<br />1.455
<br />.82413
<br />30
<br />2.22
<br />2.50
<br />2.78 3.06
<br />3.33
<br />3.61
<br />3.89 4.17
<br />40
<br />.5688
<br />.6916
<br />1 446
<br />.82248
<br />20
<br />41
<br />.6561
<br />.8693
<br />1.150
<br />.75471
<br />49
<br />50
<br />.5712
<br />.6959
<br />1.437
<br />.82082
<br />10
<br />10
<br />.6533
<br />.8744
<br />1.144
<br />.75280
<br />50
<br />3.15 3.46
<br />3.76
<br />4.09
<br />4.41 4.72
<br />18
<br />.33
<br />20
<br />A&M
<br />.8796
<br />1.137 '
<br />:75088
<br />40
<br />35
<br />.5736
<br />.7002
<br />1.428
<br />.81915
<br />55
<br />30
<br />.6626
<br />.8847
<br />1.130
<br />.74896
<br />30
<br />10
<br />.5760
<br />.7046
<br />1.419'
<br />:81748
<br />50
<br />40
<br />.66481
<br />.8899
<br />1.124
<br />.74703
<br />20
<br />20
<br />.5783
<br />.7089
<br />1.411
<br />.81580
<br />40
<br />;. 50
<br />.6670'
<br />.8952
<br />1.117
<br />.74509
<br />10
<br />30
<br />:5807
<br />,.7133,
<br />1.402
<br />.81412
<br />30
<br />.
<br />3.50
<br />3.89 4.28
<br />4.67
<br />5.06
<br />5.44 5.83
<br />40
<br />:5831
<br />.7177
<br />1.393
<br />.81242
<br />20
<br />42
<br />.6691
<br />.9004
<br />1.111
<br />.74314
<br />48
<br />50
<br />,5854
<br />.7221
<br />1.385
<br />.81072
<br />10
<br />10
<br />.6713
<br />.9057
<br />1.104
<br />.74120
<br />50
<br />4.26 4.68
<br />5.11
<br />5.54
<br />5.96 6.39
<br />24
<br />.44
<br />20
<br />.6734
<br />.9110'
<br />1.098
<br />.73924
<br />40
<br />36
<br />.5878'
<br />.7265
<br />1.376
<br />.80902
<br />54
<br />30
<br />.6756
<br />.9163
<br />1.091
<br />.73728
<br />30
<br />10
<br />.5901
<br />.7310
<br />1:368
<br />.80730
<br />50
<br />40
<br />.6777
<br />.9217
<br />1.085
<br />.73531
<br />20
<br />20
<br />.5925
<br />.7355
<br />1.360
<br />.80558
<br />40
<br />50
<br />.6799
<br />`.9271
<br />1.079
<br />.73333
<br />10
<br />30.
<br />.5948
<br />.7400
<br />1.351
<br />.80386
<br />30
<br />4.00
<br />4.50
<br />5.00 5.50
<br />6.00
<br />5.50
<br />7,00 7.50
<br />40
<br />.5972 _
<br />:7445
<br />1.343
<br />.80212
<br />20
<br />.43
<br />.6820
<br />.9325
<br />1.072
<br />.73135.
<br />47
<br />50
<br />.5995
<br />.7490
<br />1.335
<br />.80038
<br />10
<br />10
<br />.6841
<br />.9380
<br />1.066
<br />.72937
<br />50
<br />5.37 5.91
<br />6.44
<br />6.98
<br />7.52 8.06
<br />30
<br />.56
<br />20
<br />.,6862
<br />.9435
<br />1.060
<br />.72737
<br />40
<br />37
<br />.6018
<br />.7536
<br />1.327
<br />.79864
<br />53
<br />30
<br />.6884
<br />,9490
<br />1.054
<br />.72537
<br />30
<br />10
<br />.6041
<br />.7581
<br />1.319
<br />.79688
<br />50
<br />40
<br />.6905
<br />..9545
<br />1.048
<br />.72337.
<br />20
<br />20
<br />.6065
<br />.762;
<br />1.311
<br />.79512
<br />40
<br />50
<br />.6926
<br />.9601
<br />1.042
<br />.72136
<br />10
<br />30
<br />.6088
<br />-.7673
<br />1.303
<br />.79335
<br />30
<br />4.89
<br />5.50
<br />6.11 6.72
<br />7, 33
<br />7.94
<br />8.55 9.17
<br />40
<br />.6111
<br />.7720
<br />1.295
<br />.79158
<br />20
<br />44
<br />.6947
<br />.9657
<br />1.036
<br />.71934
<br />46
<br />50
<br />.6134
<br />.7766
<br />1.288
<br />.78980
<br />10
<br />10
<br />.6967
<br />.9713.
<br />1.030
<br />.71732
<br />50
<br />6.48 7.13
<br />7.78
<br />8.42
<br />9.08 9.72
<br />36
<br />.67
<br />20
<br />.6988
<br />.,9770
<br />1.024
<br />.71529
<br />40
<br />38
<br />.6157
<br />.7B 13
<br />1.280
<br />.78801
<br />52
<br />30
<br />.7009
<br />,9827
<br />1.018
<br />.71325
<br />30
<br />10
<br />.6180
<br />.7860
<br />1.272
<br />.78622
<br />50
<br />40
<br />.7030
<br />.9884
<br />1.012
<br />.71121
<br />20
<br />20
<br />.6202
<br />.7907
<br />1.265
<br />.78442
<br />40
<br />50
<br />,7050
<br />.9942
<br />1.006
<br />.70916
<br />10
<br />1.44
<br />2A7
<br />2.89
<br />I
<br />4.33
<br />5.05
<br />5.78
<br />.7071
<br />.1
<br />1,, '
<br />.70711
<br />45
<br />a�
<br />40
<br />Cosin.
<br />Cotg.
<br />Tan.
<br />Sine.
<br />AnglilCosin.
<br />4.44
<br />5.18
<br />Cotg�Tau.Sine.
<br />6.67
<br />Angle
<br />9.63
<br />:XIII
<br />m
<br />TABLE IX. -CALCULATION OF FARTHWORK.
<br />y ,
<br />HEIGHT
<br />cf
<br />1
<br />5
<br />6
<br />7
<br />8
<br />9
<br />10 11
<br />12113
<br />14 15
<br />1
<br />.02.04
<br />.06
<br />.07
<br />.09
<br />,11
<br />.13
<br />.15
<br />.17
<br />.18 .20
<br />.22
<br />.24
<br />.26 .28
<br />2
<br />.04
<br />.07
<br />Al
<br />.15
<br />.18
<br />.22
<br />.26
<br />.30
<br />.33
<br />.37 .41
<br />.44
<br />.48
<br />.52 .56
<br />3
<br />.06
<br />.11
<br />.17
<br />.22
<br />.28
<br />.33
<br />.39
<br />,44
<br />.50
<br />.56 .61
<br />.67
<br />.72
<br />.78 .83
<br />4
<br />.07
<br />.15
<br />.22
<br />.30
<br />.37
<br />.44
<br />.52
<br />.59
<br />.67
<br />.74 .81
<br />.89
<br />.96
<br />1.04 1.11
<br />5
<br />.09
<br />.19
<br />.28
<br />.37
<br />.46
<br />.56
<br />.65
<br />.74
<br />.83
<br />.93 L02
<br />1.11
<br />1.20
<br />1.30 1.39
<br />6
<br />.11
<br />.22
<br />.33
<br />.44
<br />.56
<br />.67
<br />.78
<br />,89
<br />1.00
<br />1.11 1.22
<br />1.33
<br />1.44
<br />1.55 1.67
<br />7
<br />.13
<br />.26
<br />.39
<br />.52
<br />..65
<br />.78
<br />.91
<br />1.04
<br />1.16
<br />1.20 1.42
<br />1.55
<br />1.68
<br />1,81 1.94
<br />8
<br />.15
<br />.30
<br />.44
<br />.59
<br />.74
<br />.89
<br />1.04
<br />1.19
<br />1,33
<br />1.48 1,63
<br />1.76
<br />1.92
<br />2.08 2.22
<br />9
<br />'.17
<br />:33..50
<br />.67
<br />.33
<br />1.00
<br />1.17
<br />1.33
<br />1.50
<br />L67 1.83
<br />2.00
<br />2.17
<br />2.33 2.50
<br />10
<br />.18
<br />.37
<br />.56
<br />.74
<br />..93
<br />1,11
<br />1.30
<br />1.48
<br />1.67
<br />1.85 2.04
<br />2 22
<br />2.41
<br />2.59 2.78
<br />11
<br />.20
<br />.41.61
<br />.82
<br />1.02
<br />L22
<br />1.43
<br />1.63
<br />1.83
<br />2.04 2.24
<br />2.44
<br />2.65
<br />2.85 3.06
<br />12
<br />.22
<br />:44
<br />.67
<br />.89
<br />1.11
<br />1.33
<br />1.56
<br />1.78
<br />2.00
<br />2.22 2.44
<br />2.67
<br />2.89
<br />3,11 3.33
<br />13
<br />.24
<br />.48
<br />.72
<br />.96
<br />1.20
<br />1.44
<br />1.68
<br />1.92
<br />2.16
<br />2.41 2.65
<br />289
<br />3.13
<br />3.37 _3.61
<br />14
<br />.26
<br />.52
<br />.78
<br />L04
<br />1.30
<br />1.55
<br />1.81
<br />2.08
<br />2.33
<br />2.59 2.85
<br />3.11
<br />3.37
<br />3.63 3.89
<br />16
<br />.28
<br />.56
<br />.83
<br />1.11
<br />1.39
<br />1.67
<br />1.94
<br />2.22
<br />2.50
<br />2.78 3.06
<br />3.33
<br />3.61
<br />3.89 4.17
<br />16
<br />.30
<br />.59
<br />:89
<br />1.18
<br />1.48
<br />1.78
<br />2.07
<br />2.37
<br />2.67
<br />2.96 3,26
<br />3.56
<br />3,85
<br />4.15 4.44
<br />17
<br />.31
<br />.63
<br />.94
<br />.1.26
<br />1.57
<br />1.89
<br />2.20
<br />2,52
<br />2.83
<br />3.15 3.46
<br />3.76
<br />4.09
<br />4.41 4.72
<br />18
<br />.33
<br />.67
<br />1:00
<br />1.33
<br />1.57
<br />2.00
<br />2.33
<br />2.67
<br />3.00
<br />3.33 3.67
<br />4.00
<br />4.33
<br />4.67 5.00
<br />19
<br />1.06
<br />1.41
<br />1.76
<br />2.11
<br />2.46
<br />2,82
<br />3.17.3.52
<br />3.87
<br />4.22
<br />4.57
<br />4.92 5.28
<br />20
<br />.35
<br />.37
<br />,70
<br />'.74
<br />1.11
<br />1.48
<br />1.85
<br />2.22
<br />2.59
<br />2.96
<br />3.33
<br />3.70 4.07
<br />4.44
<br />4.81
<br />5.18 5.56
<br />21
<br />1.17
<br />1,55
<br />1.94
<br />2.33
<br />2.72
<br />3.11
<br />3.50
<br />3.89 4.28
<br />4.67
<br />5.06
<br />5.44 5.83
<br />22
<br />.39
<br />.41
<br />.78
<br />, 81
<br />1.22
<br />1.63
<br />2.04
<br />2.44
<br />2:85
<br />3.26
<br />3.67
<br />4.07 4.48
<br />4.89
<br />5.30
<br />5.70 6.11
<br />28
<br />.43
<br />.85
<br />1.28
<br />1.70
<br />2.13
<br />2.56
<br />2.98
<br />3.41
<br />3.83
<br />4.26 4.68
<br />5.11
<br />5.54
<br />5.96 6.39
<br />24
<br />.44
<br />.89'
<br />1.33
<br />1.78
<br />2.22
<br />2.67
<br />3.11
<br />3:56
<br />4.00
<br />4.44 4.89
<br />5.33
<br />5.78
<br />6.22 6.67
<br />25
<br />.46
<br />.92
<br />1.39
<br />1.85,
<br />2.31
<br />2.78
<br />3.24
<br />3.70
<br />4.17
<br />4,63 5,09
<br />5:56
<br />6.02
<br />6.48 6.94
<br />-26
<br />.48
<br />:96
<br />1.44
<br />1.92
<br />2.41
<br />2.89
<br />3.37
<br />3.85
<br />4.33
<br />4.82 5.30
<br />5.78
<br />6.26
<br />6,74 7.24
<br />27
<br />.50
<br />.1.00
<br />1.50
<br />2.00
<br />2.50
<br />3.00
<br />3.50
<br />4.00
<br />4.50
<br />5.00 5.50
<br />6.00
<br />5.50
<br />7,00 7.50
<br />28
<br />.52
<br />L04
<br />L55
<br />2.07
<br />2.59
<br />3,11
<br />3.63
<br />4.15
<br />4.67
<br />5.18 5.70
<br />6.22
<br />6.74
<br />7.26 7.78
<br />29
<br />.54
<br />L07
<br />1.61
<br />2.15
<br />2.68
<br />3,22
<br />3.76
<br />4.30
<br />4.83
<br />5.37 5.91
<br />6.44
<br />6.98
<br />7.52 8.06
<br />30
<br />.56
<br />1.11
<br />1.67
<br />2.22
<br />2.78
<br />3,33
<br />3.89
<br />4.44
<br />5.00
<br />5.55 6.11
<br />6.67
<br />7.22
<br />7.78 8.33
<br />31
<br />.57
<br />1.15
<br />1.72
<br />2.30
<br />2.87
<br />3.44
<br />4:02
<br />4.59
<br />5.17
<br />5.74 6.32
<br />6.69
<br />7.46
<br />8.04 8.61
<br />32
<br />.59
<br />1.18
<br />1.78
<br />2.37
<br />2.96
<br />3.56
<br />4:15
<br />4.74
<br />5.33
<br />5.92 6.52
<br />7.11
<br />7.70
<br />8.30 8.89
<br />33
<br />.61
<br />1.22
<br />1.83
<br />2.44
<br />3.05
<br />3.67
<br />4.28
<br />4.89
<br />5.50
<br />6.11 6.72
<br />7, 33
<br />7.94
<br />8.55 9.17
<br />34
<br />.63
<br />1.26
<br />1.89
<br />2.52
<br />3.15
<br />3.78
<br />4.40
<br />5.04
<br />5.67
<br />6.29 6.93.
<br />7.56
<br />8.18
<br />8.81 9,44
<br />35
<br />:65
<br />1.30
<br />1.94
<br />2.59
<br />3.24
<br />3.89
<br />4.53
<br />5.18
<br />5.83
<br />6.48 7.13
<br />7.78
<br />8.42
<br />9.08 9.72
<br />36
<br />.67
<br />1.33
<br />2.00
<br />2.67
<br />3,33
<br />4.00
<br />4.66
<br />5.33
<br />6,00
<br />6.67 7.33
<br />8.00
<br />8.67
<br />9.33 10.00
<br />37
<br />.68
<br />1.37
<br />2.06
<br />2:74
<br />3.42
<br />4,11
<br />4.79
<br />5.48
<br />6.17
<br />6.85 7,54
<br />8.22
<br />8,91
<br />9,59 10.28
<br />38
<br />.70
<br />1.41
<br />2AI
<br />2.82
<br />3,52
<br />4.22
<br />4.92
<br />5.63
<br />6.33
<br />7.03 ,7.74
<br />8,44
<br />9.15
<br />9.85 10.56
<br />39
<br />1.44
<br />2A7
<br />2.89
<br />3.61
<br />4.33
<br />5.05
<br />5.78
<br />6.50
<br />7.22 7.95
<br />8.67
<br />9.39
<br />10.11 10.83
<br />40
<br />.72
<br />.74
<br />1.48
<br />2.22
<br />2.96
<br />3.70
<br />4.44
<br />5.18
<br />5.92
<br />6.67
<br />7,41 3,15
<br />8.89
<br />9.63
<br />10,37 11.11
<br />Table gives cu. yds. in i ft. of a triangle of given width and height. Corrections
<br />for tenths of width are one tenth the values found under each height considering
<br />the widths from 1 to 9 as tenths and similarly the corrections for tenths of height are
<br />one tenth the figures opposite width considering the heights from 1 to 9 as tenths.
<br />Thus if w=16.2 and h=5.3, cu. yds.=1.48+.018 F:089=1.587 cu, yds, or practic-ally 159
<br />cu. yds. per 100 ft. If w exceeds 40 ft., use one half and multiply result by 2, if both
<br />w and h are large use one half of each and multiply result by 4. Any cross-section
<br />may be divided into triangles by the following rule. To the triangle of the sum of
<br />the outside cuts (or Alis) =h, and �6 the roadbed =w, add the triangles formed by
<br />taking the distance out to each break in turn ( =w's) by the difference between the
<br />cuts (or Rile) on each side of it (=h's} always subtracting the outer from the inner.
<br />in
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