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VI11I 6E
<br />TARLM IT - TWH, Ordinates and Deflections, 0hard=100 It.
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist
<br />D
<br />I1 t
<br />Deg.
<br />1{a liva
<br />Mid.
<br />Ord,
<br />Tac
<br />Dist.
<br />Def.
<br />Dist.
<br />Dor
<br />1 Ft.
<br />2° 58'
<br />3° 43'
<br />t.
<br />ft.
<br />ft.
<br />1° 5'
<br />3'
<br />2° 25'
<br />ft.
<br />It.
<br />t
<br />t.
<br />171-01
<br />610'
<br />34377.
<br />.036
<br />.145
<br />.2910
<br />.03
<br />7°
<br />819.0
<br />1,528
<br />B.1D5
<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 />1.600.6.395
<br />2° 27'
<br />42,79
<br />2,29
<br />30
<br />11459.
<br />.109
<br />,436
<br />.873
<br />0.15
<br />30
<br />704.5
<br />1.037
<br />6.54013.08
<br />133.47
<br />2.25
<br />40
<br />859-4,4
<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 />0.25
<br />8
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2,90
<br />1
<br />5720.6
<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,E0
<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 />7.111
<br />14,82
<br />2,55
<br />20
<br />4297.3
<br />.291
<br />1.164'
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />15,11
<br />2.00
<br />30
<br />3819.6
<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 />-3437.9
<br />.364
<br />1,454
<br />2.909
<br />0.50
<br />20
<br />514.6
<br />2.037
<br />8.136'16.27
<br />2,80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8.2.074
<br />8.281
<br />16.56
<br />2.8.5
<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 />i 10
<br />2044.6
<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 />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4'
<br />2.292'
<br />9.t50
<br />18.30
<br />3.1:1
<br />30
<br />2292.0
<br />,545
<br />2,181
<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 />_,4.363
<br />4:654
<br />0,80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50.
<br />�8
<br />2022.4
<br />.618
<br />2.472
<br />4,945
<br />0,85
<br />12
<br />478,3
<br />2.620
<br />10:45
<br />20.9 1
<br />3.60
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30'459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.7:1
<br />10
<br />1809.6
<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 />1 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 />114 -
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />f 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 />1405.0
<br />..836
<br />3.343
<br />6.689
<br />1,15
<br />15'
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />•4
<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 />4.63
<br />-, 10
<br />1375.4
<br />.909
<br />3.035
<br />7.271
<br />1.25
<br />is
<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 />.606
<br />14.35
<br />28.70
<br />4.95
<br />7 '30
<br />1273.6
<br />.982
<br />3.926
<br />- 7.852
<br />1.35
<br />171
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />40-
<br />1228.11,018
<br />4.071
<br />.8.143
<br />1.40
<br />18 .
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />S, 50
<br />1185.8
<br />1.055
<br />4.217
<br />' 8.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16:51
<br />33.01
<br />5.70
<br />5
<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 />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 />27,4 .4
<br />.594.18.22
<br />36.44
<br />6.30
<br />f 20
<br />1074.7
<br />1.164.4,653
<br />9,305
<br />1,60
<br />22
<br />262,0
<br />.814
<br />19.OS
<br />38.16
<br />6.60
<br />30
<br />-.40
<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 .39.87
<br />6.90
<br />1011.5
<br />1.237
<br />4.943
<br />0.886
<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. OAS
<br />WAS
<br />7.75
<br />25
<br />231.0
<br />5.476
<br />21,64
<br />43.28
<br />7.50
<br />955.4
<br />1.309
<br />5.23410.47
<br />1.80
<br />26
<br />222:3
<br />5.697
<br />22.50
<br />44.9D
<br />7.50
<br />a 40
<br />929.6
<br />1.346
<br />5.370
<br />10.76
<br />1.85
<br />27'
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />SAO
<br />20
<br />905.1
<br />1,382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6,139
<br />24.19
<br />48.38
<br />8-40
<br />30
<br />881.0
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.0
<br />1;455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51-7019-00
<br />The middle ordinato in inches for anv cord of longth'(Cl) is equal to 0012 C'
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 10 dogreo curve, ita middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />o f
<br />Curve
<br />Radius
<br />5U
<br />sic. i def. ang.
<br />Sub chord - sin of z dei. angle
<br />R
<br />Length
<br />of arc
<br />for 100 it,
<br />12.5 . Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193- IS
<br />I°
<br />511
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />101.15 ,
<br />32°
<br />:81.39
<br />1° 5'
<br />3'
<br />2° 25'
<br />l0'
<br />3° 58'
<br />1 o .33
<br />34°
<br />171-01
<br />2° 06'
<br />2' 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />O
<br />36
<br />161.8o
<br />°
<br />2 13'
<br />2' 41/
<br />3' 33/
<br />4O 26'
<br />fo1.66
<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 />30 55'
<br />4° 54'
<br />102.o6
<br />42°
<br />139.52
<br />2 34`
<br />3° 05'
<br />4° 07'
<br />5' 08
<br />IO2.29 .
<br />44°
<br />133.47
<br />2' 41
<br />3° 113
<br />4° 18'
<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 />30-29'
<br />4° 4a'
<br />S° 50'
<br />103.00
<br />50 .
<br />tI8.31.,
<br />3° 02`
<br />3' 38
<br />4° 5t'
<br />6' 04'
<br />103.24
<br />52°
<br />,114. c6
<br />3° 09'
<br />3' 46'
<br />5° 02'
<br />60 17'
<br />103.:84
<br />540
<br />110.11
<br />3° 16'
<br />30 54'
<br />50 13'
<br />6° 31'
<br />103.84
<br />560
<br />106.50
<br />3. 22'
<br />4' 02'
<br />15 23'
<br />6' 44'
<br />104.14
<br />58
<br />103--14
<br />3 29
<br />4 10
<br />5 34
<br />6 ,1r
<br />104.43
<br />600
<br />100.00
<br />3° 3`5'
<br />4° i8'
<br />5044
<br />j 7° 'C
<br />1 104.72
<br />nc
<br />i -CURVE FORMULAS
<br />T=Rtan I
<br />= cot. b0 -' chord'
<br />a
<br />50 tan � R T I ' I Chard def. =
<br />D R = lz .
<br />' Sin. ; .D - 5o Sin. D No. chords = I
<br />R E = R ex. sec f IJ
<br />Sin. ; D = 50 tan z I E = T tan 4 1 Tan. def. _ chord def.
<br />I .
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance from tangent to curve, very pearly.
<br />Te find angle fora given distance and deflection.
<br />Rule 1. 'Multiply the given 'distance by .01745 (def. for 1° for..
<br />ft:
<br />see Table I1.), 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, Multiply 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 too, Alt. 10.102 - 200=.5. 100+.5=100.5 hyp.
<br />Given Hyp. 100, Alt. 25.252-200=3.125- 100.-3,125=96.875=11ase.
<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 t 1, and divide by 7,
<br />LF.VELIffiG. The correction for curvature and refraction, is feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, ad'. The combined cor-
<br />rection is negative. -
<br />PROBABLE ERROR. If dt, d2, dx, etc. are the discrepancies of various
<br />results from the mean, and'if Ede=the sum of,the squares,of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= Yd I.
<br />-0.6745 n(n-1)
<br />SOLAR EPI1E1t1ERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Xeuffel & Esser Co., and furnished upon
<br />request,. Jhis handy booklet, M gk(i 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 />magnetic declination; arithmetic constants, etc.
<br />TABLE 1V. -Minutes in Decimals of a Degree.
<br />1f
<br />.0167
<br />]If
<br />.1833
<br />211
<br />.3500
<br />31'
<br />5167
<br />411
<br />.6833
<br />51,
<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 />.3667
<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 />.1833
<br />45
<br />.75,00
<br />55
<br />(1167
<br />6
<br />.1000
<br />16
<br />.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 />.9.500
<br />8
<br />.1333
<br />18.3000
<br />28
<br />'.4607
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />X1067
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />!9833
<br />10
<br />.I667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6607
<br />50
<br />.83333
<br />60
<br />1.0000
<br />rARLE.. V.,- Inches in Decimals of a hoot.
<br />1-16 3-32 3p 1 3431 !-4 5-16 3% " 5' " ;s
<br />.0052 .0078 .0103 .0156 I .0208 .0260 .0313 I .0317 .0521 f .063:5 .0719
<br />1 3 4 iJl :� 6 7 'S 9 4 l0 t 1
<br />0833 .1667 .2500 .3:333 .4167 .5000 .583:1 .6607 .751Y0 .8333 blti7
<br />
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