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y3 41)
<br />z�two$
<br />-
<br />ill
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Dag.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan,
<br />Dist.
<br />lief,
<br />Dist.
<br />Def.
<br />1 or
<br />Deg.
<br />Tia lius
<br />Mid.
<br />Ora,
<br />Tan
<br />. Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />o ,
<br />1 r t.
<br />2° 58'
<br />3° 43'
<br />101.15
<br />320
<br />181-39
<br />1° 59'.;
<br />2° 25'
<br />t.
<br />z, TL -t.
<br />101.33
<br />f L.
<br />171.01
<br />0°•10'
<br />34377.
<br />.036
<br />.145.
<br />.291
<br />0.05
<br />7.
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2'.10
<br />20
<br />17189..
<br />•.073
<br />.291
<br />.582
<br />0.10
<br />20
<br />7S1.$'1.000
<br />146. ig
<br />6.305
<br />12.79
<br />2.20
<br />30,
<br />11459.
<br />.109
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1'.637
<br />6.54013.08
<br />13347
<br />2.25
<br />40.
<br />8594.4
<br />.145
<br />.582
<br />1,164
<br />0.20
<br />40
<br />747A
<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 />.716.8
<br />1.746
<br />,6,976
<br />13;95
<br />2.40
<br />II
<br />6729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />6SS.2
<br />1.819
<br />7.266
<br />14:53
<br />2.;A
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />1o6,5o
<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 />_2,036
<br />2,327
<br />0:40
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />1'5,11
<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 />3437.9
<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 />2.80
<br />50
<br />3125.4
<br />.400
<br />1,600
<br />3.200
<br />0.55
<br />30
<br />003.5
<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 />2.1110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.5
<br />5473
<br />1,891
<br />3.7SI
<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 />0.150
<br />18.30
<br />.3. i'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 />409.1"2.511
<br />10,02
<br />20.04
<br />3.45
<br />80
<br />2022.4
<br />.618
<br />2,472
<br />4.1145
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10,45
<br />20.91
<br />3.60
<br />3
<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 />610
<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 />22.04
<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 />2.940
<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 />.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />..803.199
<br />0
<br />6.398
<br />1.10
<br />30'
<br />396.2.3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<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 />1132.7
<br />'.873
<br />3.490
<br />6.080
<br />1.20
<br />' 30
<br />370.8
<br />3:387
<br />13.49
<br />26.97'4.05
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />Its
<br />359.3
<br />3.406
<br />13.92
<br />27.84
<br />4-80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />,7.501
<br />1.30
<br />30
<br />348.5
<br />-606
<br />14.36
<br />28.70
<br />4.95
<br />/ 30
<br />1273.6
<br />.982
<br />3.926
<br />•7.852
<br />1.35
<br />1.7
<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 />S. 143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />P 50
<br />1185.8
<br />1.055
<br />4.217,
<br />S.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />6
<br />1146.3
<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 />5.014
<br />1,55
<br />21
<br />27.1.4
<br />4.594
<br />18.22
<br />36.,44
<br />6.30
<br />20
<br />'1071.7
<br />1.164
<br />4.653
<br />9,305
<br />1.60
<br />22
<br />262.0,4.814,19.08
<br />35.16
<br />6.60
<br />j30
<br />,1042,1
<br />1.200
<br />4.798
<br />0+.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 />1.75
<br />26
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />0
<br />955,4.1.309
<br />5.234
<br />10.47
<br />1:80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.80
<br />10
<br />029:6'1.346
<br />5'.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.018
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />6.624
<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 />881.9
<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 />859.9
<br />1.465
<br />5.814
<br />11.63
<br />2.00 1
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate in inclies for any cord of length (C) is equal tc3 ..0012 C'
<br />mrltiplied by the middle ordinate taken froln the above table. Thus, if it
<br />desired to bendµ 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 />- R diusr
<br />sin. I def. ang.
<br />l sub chord
<br />R = sin of i def: angle
<br />Length
<br />of are
<br />for 100 ft.
<br />12,5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft,'
<br />30°
<br />193 -IS
<br />1'-51 ,
<br />2° r7'
<br />2° 58'
<br />3° 43'
<br />101.15
<br />320
<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'
<br />3° 2I'
<br />4° 12'
<br />101.48
<br />36°
<br />161.80.
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />4° 26'
<br />iot.66
<br />38°153.58
<br />.0667
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4° 40;
<br />101 8,j
<br />40°
<br />146. ig
<br />2° 27'
<br />2° 57'
<br />3° 55
<br />4° 54'
<br />fo2, o6
<br />42°
<br />139.52
<br />2034�
<br />3° 05
<br />4° 07
<br />S° 08
<br />102.29
<br />44°
<br />13347
<br />2° 41
<br />3° 13
<br />4° 18'
<br />5° 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 />4$0
<br />122.92
<br />2` 55'
<br />3° 29'
<br />4° 40'
<br />S° 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 />174,06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />60 17'
<br />103.54
<br />540
<br />.110.11
<br />-.3° 16'
<br />3° 54'
<br />5° 13'
<br />6° 31'
<br />103.84
<br />56°
<br />1o6,5o
<br />3° 22'
<br />4° 02
<br />5°23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14
<br />3° 29'
<br />4° 10'
<br />S° 34'
<br />6° 57'
<br />10443
<br />6o°
<br />106,00
<br />3° 35'
<br />4° 13'
<br />5° 44'
<br />j 7° 11'
<br />10}"72
<br />Ix
<br />CURVE FORMULAS
<br />T= R tan I I R= T cot. 2 I chord'
<br />_ 5o tan ',,I Chord def. _
<br />T Sin- z D $ = 50. R
<br />Sin. 1, D - 50 Sin. , D No. chords = I
<br />R E= R es. secs f D
<br />Sin j D _ 5o tan 1 l E = T tan j I Tan. def. _ ; chord def.
<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: r. M ultiply the given distance by .01745 (def. for I° for i ft.
<br />sue Table If.), 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 />GEN RAL" DATA
<br />RIGHT ANGLE TRIANGLE:;. Square the altitude, divide by tivlce the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base ioo, Alt. io.1o2=2oo=.5. ioo+.g=ioo.,5 hyp.
<br />Given Hyp. loo, Att. 25.252-200=3.125. 100-3.t25=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 per yard
<br />by 11, and divide by 7..
<br />LEVLLING. 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, ,d2. The` comhined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, d2, d3, etc. are the discrepancies of various
<br />results from the mean, and if Xd2=the sum of the squares of ;these differ-
<br />ences and n=the number of observations, then the probable error of, the
<br />mean= 3dz ,
<br />*0.6745 li(n_1)
<br />SOLAR.-EPHEINIERis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Ketlffel ,4t Esser Co., and furnished upon
<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 />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree
<br />1t
<br />.0167
<br />111
<br />.1833
<br />210
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />5V
<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 />.0833
<br />15
<br />.2500'
<br />25
<br />4167
<br />35
<br />.5633
<br />45
<br />.7500
<br />55
<br />0167
<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 />.9500
<br />8
<br />.1333
<br />18.3000
<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 />AJS33
<br />10
<br />.1667
<br />20
<br />3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TAR1,F
<br />%'-Inches
<br />in Decimals -of a Foot.
<br />1-16 3-32 'rb
<br />3-16
<br />!f
<br />I 5-16
<br />'4
<br />!�
<br />Se %
<br />�a
<br />.0052 .0078 .0106
<br />0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521 I .0623
<br />.0729
<br />F 2 3
<br />4
<br />5
<br />6
<br />i
<br />3
<br />I
<br />9 10
<br />•
<br />11
<br />.0833 .1667 .2560
<br />.3333
<br />.4107
<br />.SUUci
<br />..;7d3a
<br />.6067
<br />.7500 .8333
<br />X1167
<br />r �_v
<br />�1
<br />
|