|
VIII
<br />TABim II. ----
<br />i' Defleetions7 Chord` -_100,f t.
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Taa.
<br />Dist,
<br />De[,
<br />Dist.
<br />o r
<br />1 F6
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Ten.
<br />' Dist.
<br />Def.
<br />Diet.
<br />Dor'
<br />7 Ft.
<br />2° 17`
<br />t.
<br />43'
<br />rt.
<br />ft.
<br />181.39
<br />1' $91
<br />It.
<br />fV.
<br />ft.
<br />ft.
<br />34°
<br />0'10'
<br />34377.
<br />036
<br />.145
<br />- .291
<br />0.05
<br />.7°
<br />819.6
<br />1.528
<br />6.105-12.21
<br />3°33'
<br />2.10
<br />20
<br />17189.
<br />.073.291
<br />2° 20'
<br />.582
<br />0.10
<br />.20'
<br />781.8.1.600
<br />400
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />109
<br />.436
<br />' .873
<br />0.15
<br />30
<br />76.1.5
<br />1.037
<br />6.540
<br />13.08
<br />2.23
<br />4D
<br />8594.4
<br />.145
<br />.582
<br />1.164
<br />0.20.
<br />40
<br />747-:9
<br />1.673
<br />6:685
<br />13.37
<br />2.30
<br />5D
<br />.0875.5.-..188
<br />2° 55,
<br />.727
<br />1.454
<br />0.25
<br />S'
<br />50'
<br />1,746
<br />6:976
<br />13.95
<br />2,49
<br />1
<br />5729,G
<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. LO
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />' 2.036
<br />0.3.5
<br />30
<br />674.7:
<br />1.855'
<br />7.411
<br />14.S2
<br />2. 55
<br />i 20,
<br />4297.3,
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.692
<br />7.556
<br />.15.11
<br />2.G0
<br />30,
<br />3,419.8
<br />.,327
<br />1.309
<br />6 2.61
<br />0.45
<br />9-
<br />637.3'1.965
<br />7.846
<br />1,5:G9
<br />2,70
<br />.40
<br />3137.9
<br />.364
<br />1.454
<br />2:909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8,136
<br />16.27
<br />2780
<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 />8.28116.56
<br />2,85
<br />2
<br />2861.9
<br />•.436
<br />1.745
<br />3.4900.60
<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 />1.891
<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 />2.202
<br />9.150
<br />18,30
<br />3.1.5
<br />30
<br />2202,0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />11 .
<br />521.74
<br />2.402
<br />9.585
<br />19,16
<br />3.30
<br />40
<br />-2148.8
<br />.562
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1.
<br />2.511-10,02
<br />20.04
<br />3,4.5
<br />50
<br />2022.4
<br />.613
<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 />9
<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 />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />12
<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 />425.4.2.949
<br />11,75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.704
<br />3.054
<br />6.108
<br />11.05
<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 />.830
<br />3.345
<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 />1432.7
<br />.873
<br />3.490
<br />6.990
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.40
<br />2G.07
<br />4.65
<br />30
<br />1375:4'
<br />.909
<br />3:635
<br />7.271.1.25
<br />16
<br />359.3'3.496
<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 />7.852
<br />1.35
<br />17
<br />338.3'3.716
<br />14.78
<br />29.5G
<br />5.10
<br />-40.
<br />`228.1
<br />I.018
<br />4.071
<br />8.143
<br />1.40
<br />IS
<br />319.6.3.935
<br />15.64
<br />3t.29
<br />5.40
<br />50
<br />" 1185.8
<br />1.055
<br />4.217
<br />5.433
<br />1.45
<br />19'
<br />302:9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />6
<br />1146,.31.091
<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,,:-,1109;'3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />13.22
<br />36.44
<br />6.30
<br />206.
<br />1074.7,
<br />1'. 164
<br />4.653
<br />9.305
<br />1.6U
<br />22
<br />262,0,4314
<br />19.08
<br />38.16,6
<br />G0.
<br />1042.1.1.200
<br />4.798
<br />9.596
<br />1.65'
<br />23:
<br />250, Si
<br />5.035
<br />19.94
<br />30.87
<br />G,9 0
<br />40
<br />1011:5..1.237
<br />4.943
<br />t9.986
<br />1.70
<br />Z4
<br />240'.5,5.255
<br />20:79
<br />41.58
<br />7.20
<br />50,'
<br />'982.6'1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />2311.0
<br />5.476.21.64
<br />43.28
<br />7.50
<br />d
<br />955.4
<br />1.309
<br />5,234
<br />10.47
<br />1.80
<br />Z6
<br />222:3
<br />5:697
<br />22.50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />1.0.76
<br />1.85
<br />Z7
<br />21412.
<br />.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />005,1
<br />1.382
<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 />587.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.716-160
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9.1.455
<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 ordinate in inches for any coal of length (G) is equal to .0012C,
<br />multiplied by the middle ordinate taken Froin the above table. '.lThns, if it
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its 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 />of
<br />Curve
<br />Radius
<br />50
<br />M sub chord
<br />]t = sin of i def. angle
<br />len th
<br />Le -of arc
<br />for 100 ft.
<br />sin. i; def. ang.
<br />12,5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1.51 1
<br />2° 17`
<br />2° 58'3'
<br />43'
<br />:lot -15
<br />32°
<br />181.39
<br />1' $91
<br />2°25.
<br />310' .
<br />3'58,
<br />101.33
<br />34°
<br />171.01
<br />2° o6'
<br />20 13'
<br />3° 21'.
<br />-4° 12'
<br />10148
<br />360
<br />16i,8o
<br />2° 13'-
<br />2°,41'
<br />3°33'
<br />4° 26'
<br />1oi.66
<br />38°
<br />153.58.
<br />2° 20'
<br />2° 49'
<br />3' 44
<br />4° 40'
<br />101.85
<br />400
<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'S°
<br />08
<br />102.29
<br />44°
<br />133.47
<br />20 41'
<br />3° 13
<br />4° 18'
<br />S° 22'
<br />t02.53
<br />460
<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° 29'4°
<br />40'
<br />5° 50'
<br />103.00
<br />50'
<br />r 18.31
<br />3° 02,
<br />3° 38,
<br />4° ,5,,
<br />6' 04'
<br />103.24
<br />52°
<br />614.o6
<br />3° 09'
<br />3o 46'
<br />5° O2'
<br />6° 17'
<br />103•.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° 54'
<br />5° 13' .
<br />60 31'
<br />103-84
<br />56°
<br />106.50
<br />3° 22'
<br />4° 02'
<br />.5 23'
<br />6° 44'
<br />10.1. 14 -
<br />580
<br />103:14
<br />3°29
<br />4' Io`
<br />5° 34'
<br />6° 57'
<br />104-43
<br />60°
<br />100,00.t.
<br />3' 35`
<br />4° 18'
<br />50 44'
<br />7' 11'
<br />104.72
<br />EX
<br />CURVE FORMULAS 7 S r 9
<br />T =.R tan � I i7'- = cot. R = T 1 I chords
<br />T '50 tan i a f z j 2' 5D Chord def. _
<br />Sin. s IJ p _ R
<br />Sin. 1j 2 fa R Sin. j D No. chords = I
<br />R E- R ex. secs 1 D
<br />Sin. a D = S0 tan I
<br />1' E = T tan I I Tan. def. _ ;chord des.
<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 />Rule I. Multiply the given distance by .01745 (def. for 1° 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. Multiply the angle
<br />by .01745; and the product by the distance.t7.9o`'
<br />GENERAL DATA p-�
<br />RIGHT-ANGLE TRIANGLES. Square the altitude, divulenby twice the
<br />base. Add quotient to base for hypotenuse. ed 0
<br />Given mase too, Alt. ro.ro2-2oo=.5- too+.5=loo-.5 hyp•
<br />Given Hyp. loo, Alt. 25.252-200=3.125. 100-3.125=96.875=Base..
<br />Error in first example, .002; in last, .045• -
<br />To finis Tons of Rail in one mile of track: multiply weight per yard
<br />by I i, and divide by 7.
<br />LEVELIFC. The correction for curvature and refraction, in 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,d'. The combined cor-
<br />rection is negative.
<br />. FROKARLE ERROR. If di, d2, da, etc, are the discrepancies of various
<br />results from the mean, and if zd2=the sum of the squ red of these differ-
<br />ences and n=the number of observations, then the pF6W11e error of the_
<br />mean = 212 /3 yl - iCL+ e-7
<br />-0.6745
<br />_
<br />n(n-1) sz 2�r ��tD� �40 5. 7.q`S
<br />,tea ar,
<br />SOLAR EPHEMER1s. 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 from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. --Minutes in Decimals of a Degree.
<br />It
<br />.0167
<br />ll'
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />41'
<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 />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 />-0000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.41.67
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />,7667
<br />56
<br />.!1:333
<br />7
<br />.1I67
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />-6107
<br />47
<br />.7833
<br />57
<br />.911100
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48.8000
<br />58
<br />0667
<br />9
<br />.1500
<br />19
<br />.3167.
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />•.8107
<br />59
<br />X9833
<br />70
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6657
<br />50
<br />.8333
<br />60
<br />1-0000
<br />TARLE -'.--inches in I)ecimals of a hoot.
<br />1-16 3-32 z 3-16 !•a i 5-16 ?� r'
<br />-0052 I .0078 .0104 .0156 .0208 I .0260 I .0313 I .0417 .0521O6?•50729
<br />1 1 3 4 I 6 7 3 9_ 10 11
<br />0833 .1667 .2500 .3333 .4167 .5000 :,833 6667 .7500 1 .8333 .9167
<br />
|