|
VIII
<br />TABLM H. - Radii, Ordinates and Deflections. Chord =100 It.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord
<br />Tan.
<br />Ta.
<br />Dist
<br />D el.
<br />Dist
<br />De'
<br />for
<br />1 Ft.
<br />Deg,
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist,
<br />Def.
<br />Dist.
<br />Det.
<br />for
<br />1 Fl.
<br />0"10'
<br />34377.
<br />.036
<br />,145
<br />.231
<br />0:05
<br />71 -
<br />It.
<br />819.0
<br />t,
<br />I. 528
<br />t:
<br />6.105
<br />t .
<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. Goo
<br />6.395
<br />1'2.79.2
<br />20
<br />30
<br />11459.
<br />.109
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5'1.637
<br />4° 40.
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8594.4
<br />.145
<br />.582
<br />1.164
<br />0.20
<br />40
<br />7-17.9
<br />1.673
<br />'6.685
<br />13.37
<br />2.30
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.23
<br />8
<br />710.3
<br />1.746
<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 />2.1-.0
<br />10
<br />4.911.2
<br />.2.55
<br />1.013
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />A0
<br />661.7
<br />1:892
<br />7:65615.11
<br />5° 23'
<br />2. GO
<br />30
<br />3519.8
<br />.327
<br />1.300
<br />2.618
<br />0.45
<br />.. 9 -
<br />637.3
<br />1.965.
<br />7.846.15.69
<br />3° 35'
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1,454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />„8.135
<br />16.27
<br />2.S0
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.53-
<br />"30
<br />603.8
<br />2.074
<br />8.281
<br />1G. 56
<br />2.83
<br />2
<br />2864.9
<br />.430
<br />1.745
<br />3.490
<br />0,60
<br />40
<br />503.4
<br />2:110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3.781
<br />0.65
<br />10 .
<br />573.7
<br />2.183
<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 />18.30
<br />3:1:5
<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
<br />2.511
<br />30.02
<br />20,04
<br />3.45
<br />60
<br />.2022.4
<br />- .618
<br />2.472
<br />4.045
<br />0.85
<br />12 -
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />S
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />4 30.
<br />459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.7.5
<br />10
<br />1309.G
<br />.69t
<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
<br />3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345'-6.689
<br />1.15':
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />4.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />.26.11
<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 />10'.'
<br />359.3
<br />3.496
<br />13.92
<br />27:84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />.7?561'
<br />1'.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 />74852
<br />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 />8.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31`.20
<br />5.40
<br />50
<br />•1185.8
<br />1.055
<br />4.217
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16:51
<br />33101
<br />5.70
<br />4 -
<br />1146.3
<br />1.091
<br />4.362
<br />,8.433
<br />8.724
<br />1.50
<br />_
<br />20
<br />287.9
<br />4.374
<br />17.37'
<br />34.73
<br />6-:00
<br />10
<br />1109.3
<br />1.127
<br />4.507'
<br />9.014
<br />1.55
<br />21
<br />27.1.4
<br />4,594
<br />18.22.
<br />36.44
<br />6.30
<br />20
<br />1074.7.
<br />1.104
<br />4.653
<br />9.305
<br />1.60..
<br />221
<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 />+982.6
<br />1.273
<br />5.088
<br />10-18
<br />t.75,'
<br />25
<br />231.0
<br />5:476
<br />21.£4
<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 />5697
<br />22.50
<br />4.1 99
<br />7.80
<br />10
<br />929,6
<br />1.346
<br />5.379
<br />10.76
<br />1.85.
<br />27
<br />214.2
<br />..918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.11.382
<br />5.524
<br />11.05
<br />1.90 '
<br />28,'
<br />206.7
<br />.139
<br />24.19
<br />48.38
<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 />25.0 4
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5"814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinat•n inches for any cord of length (C) ii e�1ual to .001201
<br />multiplied by.the lyd(Ue ordinate taken from tho above ' 12 Thus, if it
<br />desired to bend a 30 ft, rail to fit a 10 degree curve, its widdle ordinate should
<br />bo .0012X900X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short. Radius Curves.'
<br />Degree
<br />of
<br />. , Radius
<br />r sub chord = sin of,, def. angle
<br />R
<br />Length
<br />of are
<br />Curve
<br />ein.l deLang•
<br />12.5 Ft.
<br />I 15 Ft,
<br />20 Ft.
<br />25 Ft.
<br />for 106 ft.
<br />30°
<br />- 193. IS
<br />r° 51
<br />2°17'
<br />2°58'
<br />3° 43'
<br />10i, t5
<br />32e..
<br />181.39
<br />r° 59`
<br />2° 25'
<br />3° 10'
<br />3°.58'
<br />101"33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33
<br />3° 2I'
<br />_
<br />.4° 12'
<br />101.4$
<br />36°
<br />161.So•2°
<br />13'<
<br />2° 41'
<br />3° 83
<br />4° 26'
<br />101.66
<br />380 .
<br />153.58.
<br />2° 20,
<br />2° 49
<br />3° 44
<br />4° 40.
<br />ior.8.5.
<br />40'
<br />146.19
<br />2° 27'
<br />2° 57'.
<br />30 55'
<br />4° 54'
<br />102.06
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05.
<br />4° 07'
<br />S° 08
<br />102.29.
<br />44°.:
<br />133.147
<br />20 41'
<br />3° 13
<br />4° 18'
<br />"5° 22'
<br />.102:53
<br />46° -
<br />iz7- 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 />103100
<br />500
<br />118.31
<br />3° 02'
<br />3° 38''
<br />4° 51•'
<br />6° 04'
<br />0 - 24
<br />5z° -
<br />•1 14: 06
<br />3° 09'
<br />3° 4b'
<br />5° oz'
<br />60 r7'
<br />103.'54
<br />54°
<br />11(). it
<br />3° 16'
<br />3° 54'
<br />5° 1.31
<br />6.31 1
<br />103.84
<br />F
<br />560
<br />1o6.5o
<br />3° 22
<br />4° 02,
<br />5° 23'
<br />6° 44'
<br />104. t4
<br />58°°
<br />103.14
<br />3° 29
<br />4° 10'
<br />5° 34'
<br />6° .57`
<br />104.43 '
<br />6o
<br />100.00
<br />3° 35'
<br />4° 18'
<br />S° 44'
<br />:.7° 1•?'
<br />104' 72
<br />Ix
<br />CURVE FORMULAS
<br />F' = EZ' tan 111 R = T cot. 2 1 chord'
<br />T 50. tan 1 Chord def. _
<br />Sin. U
<br />Sin:' 2 U= 5o R Sin. I D i.
<br />No. chords =
<br />Iz E= R ex. sec e I D
<br />2 [1 _ 5o tan z I
<br />Sin. '
<br />�. E = T tan # I Tan. def. = i chord def.
<br />The'square of 'any distance, divided -bv twice the radius, will equal
<br />the distance from•tangent to curve, very nearly.
<br />To find angle fog a given distance and deflection. `
<br />Rule 1. Multiply the given distanceby .01745 (def. for..' for i ft -
<br />see Table II.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the produce by
<br />the given distance:
<br />To -Find deflectionfor a given angle and distance. Multiply tic angle
<br />by .01745i 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 Ioo, Alt. 10.102-200=.5: Ion �'.5=1oo.5 hY1).
<br />Given Hyp. too, Alt. 2.252-200=3.125: 10073.125=96.87=Brise.
<br />Error in first example, .002; in last, .045.
<br />To find Tons of Rail in'one mile of track': multiply weight per yard.
<br />by 11, and divide by 7.'
<br />LFVFLING. The- correction for -curvature and refraction,' -in fci•t
<br />and decimals of feet is equal to 0.574d', where d is the distance in miles.
<br />The correction for curvature alone. is closely, =332.' The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d2, da, etc. are*the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares-vf these differ-
<br />ences and n=tile number of observations, then the probable error of. the
<br />mean d2
<br />-0.6745 11(9-I)
<br />SOLAR EPIMAIERiS. Attention. is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 38x6 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 front observations on the sun and Polaris; stadia nleasurcments;.
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />If
<br />.0167
<br />11'
<br />.1833
<br />211
<br />.3.500
<br />311
<br />:5167
<br />410
<br />.6833
<br />5P
<br />.8500.
<br />2
<br />.0333
<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 />-08:33
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.1.1167
<br />6
<br />.1000
<br />l6
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7G67
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />6L67
<br />47
<br />.7833
<br />57
<br />-.9 X00
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9333
<br />10
<br />.1667
<br />1 20
<br />.333.3
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333 11
<br />60
<br />11.0000
<br />TAB1,1S \'.---Inches in Decimals Of a Foo.. - -
<br />1-16 3-32 3-]6 !' ; i� s� "If
<br />?--
<br />�l8 4 1-16 1t 2 6 _
<br />.0052 .0076 .0104 Ol:i6 .0208 .02'a .0313 .0417 .0621 062.5 0729
<br />3 4 i 6 -r ' 3 9 I 19 ��I I -�
<br />.0633 -1667 .2500 .3333 A1�6T .SUU31 ..7e8a:f _01 _7500 .,83(13 .91,67
<br />,�1
<br />
|