|
VIII
<br />TABLE IL - Radii, Ordinates'and Deflections. Chord =100 ft.
<br />Deg.
<br />Radius
<br />Mid,
<br />Ord.
<br />Tan.
<br />Diat,
<br />Def.
<br />Dist.
<br />D°r
<br />1 rt.
<br />Deg.
<br />Radius
<br />. Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Dcf.
<br />Dist.
<br />Dol'
<br />) r t.
<br />193.18
<br />t,
<br />it.
<br />it.
<br />ft.
<br />Iol.r5
<br />32°
<br />it.
<br />t
<br />2° 25'
<br />t.
<br />3° 58'
<br />0'10
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7°
<br />819.0
<br />1.528
<br />.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />.6
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />,109.436
<br />4° ,
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />5591.4
<br />'.145
<br />.582
<br />1.164:
<br />0.20
<br />40
<br />7.17.9
<br />1.673
<br />6.685
<br />t3. 37
<br />2.30
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />71G.8
<br />1.740
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />:218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2.60
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.83
<br />2.1.
<br />20
<br />41-97:3
<br />•.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.592
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.300
<br />2.618
<br />0:45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2.909
<br />0.
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />16.27
<br />2.SO
<br />50
<br />3125.4
<br />-.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />2
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0:60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.591
<br />3.781.0.65
<br />.10
<br />573.7
<br />2.153
<br />8.716
<br />17,43
<br />3.00
<br />20
<br />2155.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />15.30
<br />3. 1.-)
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />'4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />.2148.8
<br />.582
<br />2.327
<br />.4.654
<br />0.80
<br />30
<br />499.1'2.511
<br />10.02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />12
<br />478.3'2.620
<br />10.45
<br />20.91
<br />3.60
<br />8
<br />,1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />10
<br />1909.6
<br />:691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />5,. 817
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30'
<br />1637.3
<br />.764
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1:10
<br />30
<br />396.2-3.168
<br />12.G2
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6."9
<br />1:15
<br />15
<br />383.1,3.277
<br />13.0.5
<br />26:11
<br />4.50
<br />S
<br />1132.7
<br />.873
<br />3.490
<br />6.950
<br />1.20
<br />- 30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />16
<br />3;79.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.56 11.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.926
<br />7.852'1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8x143
<br />1.40
<br />128
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />.1185:8
<br />1.055
<br />4.217
<br />80433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16:51
<br />33.01
<br />5.70
<br />6
<br />1146.3
<br />1.091
<br />4.362
<br />-8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />34f73
<br />6.00
<br />-10-
<br />1109.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />15.22
<br />36'44
<br />6.30
<br />20-
<br />•1074.7
<br />1.164
<br />4.653
<br />0.305
<br />A .G0.•
<br />22
<br />262.0
<br />4.814
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1'.65 -
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />'.9.886
<br />1.70'
<br />24
<br />240.:5
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />50
<br />082.6
<br />1.273
<br />5.088
<br />10.18;
<br />1.75
<br />20
<br />231.0
<br />5.476
<br />2164
<br />43.28
<br />7.50
<br />6
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50 144.99
<br />7.So
<br />10
<br />929.6
<br />1.346
<br />5.37910.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35 146.69
<br />8.10
<br />20
<br />'905.1
<br />1.382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />$.139
<br />24.19 148.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04 150.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00 1
<br />30
<br />193.2
<br />6.583
<br />25.88 151.76
<br />9.00
<br />The middle ordinate in inches for an}• cord of length (C) is equal to .0012 C'
<br />multiplied by the ]riddle ordinate taken from the above table. Thus, if it
<br />iesired to bend n 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2.36 inches.
<br />TABLE111. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />5U
<br />Y, sub chord
<br />=sin of '
<br />R def._ angle
<br />of aLenre
<br />Curve
<br />sin, § def. ang.
<br />12.5 Ft.
<br />15 Ft,
<br />20 Ft.
<br />'25 Ft.
<br />for 100 ft.
<br />30°
<br />193.18
<br />I° 51'
<br />2° 17'
<br />2° 58'3°
<br />43'
<br />Iol.r5
<br />32°
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° 10'
<br />3° 58'
<br />101:33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'3°
<br />21'
<br />4° 12'
<br />loI.48
<br />36°
<br />161.8o
<br />2° 13'
<br />2' 411
<br />3° 33'
<br />4°-26'
<br />1of.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'.
<br />3° 44
<br />4°,40'
<br />101.8,;
<br />40°
<br />146. 19.
<br />2° 27' .
<br />2° 57'
<br />3° 5J'
<br />4° ,
<br />I0z.06
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />5° 06
<br />102.2(9
<br />44°
<br />133-47
<br />2° 41'
<br />3° 13'
<br />4° IS'
<br />S° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 48' '
<br />3° 21'
<br />4°.29'
<br />5°-36'
<br />102.76
<br />48°
<br />122.92
<br />2° 55'
<br />3°. 29'
<br />4° 40'
<br />5° 50'
<br />-103.00
<br />50°
<br />118.31
<br />3° 02
<br />3° 38'
<br />4°, 51'
<br />6° 04''
<br />103.24
<br />52°
<br />114,o6
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103. ;54
<br />54°
<br />110.11
<br />3° 16'
<br />3°54
<br />5° 13'
<br />6° 31'
<br />Ici3.. 84
<br />50
<br />1o6.5o
<br />3°22'
<br />4° 02'
<br />5° 23'6°
<br />44'
<br />104.14
<br />580
<br />103.14
<br />3' 29'
<br />4°•10,
<br />5°34'
<br />6° 57'
<br />104.43
<br />60°
<br />100. o0
<br />3°35'
<br />4°18'
<br />5°44'
<br />7°•I1' I
<br />10+.72
<br />rX
<br />CURVE FORMULAS
<br />T= R tan a. 1 R= '1' cot. z 1 chord'
<br />T ._ 5o tan.} I Chord def.._
<br />Sit]. ; ll 50 R
<br />It
<br />Sin 12 D _ 50 Sin. § D No. chordsl-
<br />Az E = R ex. sec
<br />Sin, z D = S0 tan I L = 9' tan I 1 Tan. def. = z chord def.
<br />T ,
<br />The square of any distance, divided by twice. the radius, will. equal
<br />the distance from tangent to curve, very nearly,
<br />'To find angle for a given distance'and deflection.
<br />Rrdr 1. Multiply the given distance by .01745 (def. for i' for I ft.
<br />see Table 11.), and divide given deflection by the product.
<br />Rule 2. -Multiply given deflection by 57.3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. iblultiply the angle
<br />by .01745, and,the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES." Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 16.10x-200=.5. 100+.5=[00.,5 liyp.
<br />Given Hyp. ioo, Alt. 25.25'=200-3.125: 100-3.125=96.875=Base.
<br />Error in first example, .002; in last,'.045:
<br />To find Tons of Rail in one mile of track: multiply weight ]xr yard
<br />by 11, and divide by 7. "•
<br />LEVELING. The correction for curvature and refraction, in -feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance i6-ruilcs.
<br />The correction for curvature alone is closely;, ;d'. T.he .combined cor-,
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d2, d,, etc. are the -discrepancies of varioils
<br />results from the mean, and if 2d'=the sum of the squares of these.differ-
<br />ences and n=the n6mber of observations, then the probable error of the
<br />mean= vdz '
<br />=1--0.674i
<br />SOLAR EP11ENfER1S. Attention is called to the Solar F.,phemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished inion
<br />request. This handy booklet, 3;x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; directions. and tables for determining the meridian and the
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnet ic'declination; arithmetic constants, etc.
<br />TA13LF IV.-D'linutes in Decimals of a Degree. "
<br />t/
<br />.0167.
<br />11'
<br />.1833
<br />211
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.0.333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42'
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0500
<br />.13
<br />.2167'
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />.53
<br />.8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />:5
<br />.0833
<br />15
<br />.2500
<br />. 25
<br />.4167
<br />35
<br />.5533
<br />45
<br />.7-500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16,2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />•7833.
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />33
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.150019
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9533
<br />10
<br />.1667 1
<br />1 20
<br />1 .3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1-0000
<br />TAR1.1t 1`. --Inches in Decimals of a Door.
<br />1-16 3-3'2 }'g 3-16 J,i 5-16 '•e ss a� ;ti
<br />0052 (.0048 I .0104 0156 I .0208 I .0260 I .0313 I .0417 .0521 .062.5 .0720
<br />1 3 I.1 1 :i 1 �i i 3 I 9 10 77
<br />.0833 .1667 .2500 .3:433 .4167 SOOo SS3a 6667 7500 1 .8333._ .9167
<br />
|