|
VIII . • - • - _ ;
<br />TADL> IL - Radii, Ordinates and, Deflection& Chord =100 ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord 'Dist,
<br />'Tsn.
<br />' Dcf, .
<br />'Dist
<br />De
<br />ror :
<br />1 Et.
<br />": Deg, _'
<br />Radiaa'.
<br />Mid
<br />Orr;.'
<br />-- Tan ..
<br />Dist:'
<br />Def..-
<br />'Disc '
<br />Def.
<br />for
<br />} r
<br />193.18
<br />t.
<br />t:
<br />t
<br />3° 43'
<br />Ioi : 15
<br />3'i*
<br />t. -
<br />t.
<br />2 25
<br />t.
<br />30_58
<br />Q°10
<br />34377
<br />036
<br />.145
<br />r .291
<br />0 On
<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 />1`:582
<br />010
<br />20'
<br />781.9
<br />1.000
<br />'6395
<br />12-79
<br />2.20
<br />30
<br />.11459
<br />• 109
<br />- .436
<br />'.873
<br />0'15
<br />$0
<br />764.5
<br />1. 6376
<br />'540
<br />13.08
<br />2'2.5
<br />40
<br />804 4
<br />14a•.582
<br />3° 13'
<br />1.104
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6(685
<br />13.37
<br />2.30
<br />50
<br />'6875.5
<br />x..182
<br />".727
<br />1.454
<br />0.25 ",
<br />• 8',
<br />716 8
<br />1-.746
<br />6.976
<br />13.95
<br />2.40
<br />1 '
<br />5729,6
<br />^?218'.
<br />.873
<br />1:745
<br />0.30'
<br />" 20
<br />688.2
<br />E819
<br />7:266
<br />14.53'2.50
<br />.9667
<br />10.'
<br />4911,2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />;30
<br />674.7,1.S55
<br />3° 2Z'
<br />7.411
<br />19.82
<br />2.55
<br />.20
<br />4297.3
<br />-..291
<br />1.164
<br />, 2.327
<br />0.40,.-
<br />'40
<br />661_7,1.892
<br />60°
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819 .8
<br />= .:327
<br />1,309'12.618
<br />0.45.
<br />9.' .
<br />637'.3
<br />1.965
<br />7:54615.69
<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.,o.17,
<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 />603 3.2074
<br />8:281.
<br />16.56
<br />2.85
<br />3 n
<br />2864;9
<br />.430
<br />1.745
<br />>3,.490
<br />0.60
<br />40
<br />593 4
<br />21110
<br />8:426
<br />16.85
<br />2.90
<br />._10
<br />-•2844,6
<br />-.473'1.891
<br />3.'781
<br />0.65:
<br />14,E
<br />573.7`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`2.202
<br />9.150
<br />13.30
<br />3.15
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />;4.363
<br />0.75
<br />11
<br />521 7'2.402
<br />9.585
<br />19.16
<br />3.30
<br />1.40'
<br />'._ 2148.-8'
<br />° .592
<br />2.327
<br />" 4;654
<br />0.80 '
<br />" 1 30
<br />-199,-1
<br />2.511
<br />10:02.20.04
<br />3,45
<br />150.
<br />12022.4
<br />- 619
<br />2.4'(2
<br />?4.945
<br />0.,55;
<br />12
<br />478.32.620
<br />10.'45
<br />20.91
<br />3.60
<br />3
<br />1910.•1
<br />.635
<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 />_69I
<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 />,727,2.90S
<br />,5.817
<br />.1.00'
<br />r, 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'.0.5
<br />14 '
<br />410.3;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 />f 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
<br />'6.689
<br />1.15
<br />15
<br />383..1`-3.277
<br />13.05
<br />26.11
<br />4.50
<br />4. `'
<br />-1432.7.
<br />;873
<br />3.490
<br />6,950'1.20`
<br />30
<br />370:8'3.387
<br />13:49•
<br />26.974.'65
<br />;10.
<br />1375,4
<br />1.909
<br />3.635
<br />;7:271
<br />1.25/
<br />16
<br />359.3.3.496'13.92,
<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'.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
<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`1•.40
<br />18
<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 />8:433
<br />1.45
<br />19
<br />3029
<br />1. 1.5.5
<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 />287.914.374
<br />17.37
<br />34.73
<br />6.00
<br />•10.
<br />1.109.,3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4 594
<br />18.22
<br />36.44
<br />6.30
<br />"20
<br />1074.7
<br />1.164
<br />4. 6,53
<br />: 9.303
<br />1.60
<br />22 I
<br />262.014.814
<br />19AS
<br />38.16
<br />6.60
<br />t30 .
<br />-1042.1
<br />1-.200
<br />4.798
<br />? 6:596
<br />1.65 '
<br />23
<br />250.8
<br />5.035
<br />19.144,
<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;5:255
<br />20.79..41'.58
<br />7.20
<br />50
<br />- 982.6
<br />1.273
<br />5.088
<br />10:13:
<br />1.75-
<br />.25
<br />231.0'5.476
<br />21:64.
<br />43.28
<br />7.50
<br />955.4
<br />1.309
<br />5.234
<br />10:47
<br />L.80
<br />26
<br />222.3'5:697
<br />22:50 -44.99.7.80
<br />10
<br />929:6,1.346
<br />5.379
<br />10:76
<br />1.85,
<br />27
<br />214'.2
<br />.918
<br />23.31
<br />46.69
<br />8.10
<br />20
<br />. 905.1
<br />1.382
<br />5.924
<br />11.05
<br />1.90
<br />28 .
<br />206.76.139
<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 />1.455
<br />5.81411.63
<br />2.00
<br />30 L
<br />193.2
<br />6.583
<br />25:88
<br />51.76
<br />9.00
<br />1'he middle ordiIla 0}n inohes for any oord bf length (L') iso nal to 0013 Cs
<br />multiplied by tha uziddio ordinate "taken from the above table, Thus, if it
<br />desired to bendy 30 ft. rail to fit a 10 degree -curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2.36 inches. S ;
<br />TABLI III. :Deflections for Sub Chords for Short Radius'Curves.
<br />Degree
<br />of
<br />Radius]
<br />50 't,R'
<br />}y sub chord - sin of I def. ankle
<br />Length
<br />of arc
<br />Curve '
<br />sin. a def. an 9.
<br />12.5 ,Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />=30°
<br />-181-39
<br />193.18
<br />I° 51':
<br />2° �7,
<br />2° 58,
<br />3° 43'
<br />Ioi : 15
<br />3'i*
<br />.5333
<br />I 59
<br />2 25
<br />3 10
<br />30_58
<br />'101.--33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.45
<br />360
<br />.16i -8o -
<br />'--a°. 13'•:
<br />2°:41..
<br />3° 33'
<br />4° 26' -
<br />1x1.66
<br />38'
<br />153 58
<br />2� 20'.
<br />z° 49'
<br />3° 44'
<br />¢° 4°
<br />.7338
<br />40°
<br />1!45.19,
<br />2°�7,
<br />2° 57'
<br />_
<br />3° 55
<br />-..•._101.89
<br />4° 54,
<br />io2.66
<br />42°
<br />139 52
<br />'° 34,
<br />30 05,
<br />4 07,
<br />5° o8
<br />;02.29 .
<br />_
<br />44°
<br />,. 133.47
<br />P 41'
<br />3° 13'
<br />4° 18'.
<br />5°'2z'
<br />102.53
<br />. 46'
<br />127.97
<br />. 2° 48'
<br />3° 21'
<br />4° 29'
<br />S°• 36' .:
<br />1o2.76
<br />48'
<br />122.92'
<br />2° 55'
<br />3° 29'
<br />4° 40,
<br />5° 50,
<br />103_OC)
<br />50°
<br />-1i8.31.
<br />3' 02`
<br />3°, 38' .
<br />- :4 51'
<br />6° 64,
<br />-Io3.24
<br />52'
<br />'1.14.06`.
<br />3' 09,
<br />3° 46'
<br />5' 02',
<br />6° 1.7'
<br />103.54
<br />.9667
<br />'9 ,
<br />- 1500
<br />3° 54!
<br />5° 13,-
<br />6°.r3i,-
<br />103..84
<br />56°
<br />io6.5o..
<br />3° 2Z'
<br />4` 02': _
<br />5° 23'
<br />6° 44'
<br />104, 14
<br />58°
<br />103. [4:,.
<br />3°.29'
<br />4° Io'
<br />S° 34
<br />b°,5i'
<br />104 .43.
<br />60°
<br />too.o6
<br />3° 35'
<br />4° 18''
<br />5° 44'
<br />7' I1'
<br />104 -J2
<br />Lk
<br />CURVE FORMULAS
<br />T R tan '1 1 , R = T cot. .I chord' -
<br />1 59•tan- z -i. Chord def. 1;
<br />so - -- -
<br />Sin. `s D 50 Sin.^; D No. chords I
<br />R-- E = R' ex. sec I
<br />SIn:'D 5 h ' Li- T tan'} I Tan. dei. � chord def,
<br />'The isqljare of any distance, divided by twice the radius, wil1.2equal
<br />the disfance'from-tangent to curve, very nearly.
<br />'To find angle for a given distance and deflection. "
<br />R61e' i:. Multiply the given distance' by .01745 (def. for I" 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 product by
<br />the given dis'tance.' -' � ,
<br />To'find deflection far a given angle and distance. Multiply the angle
<br />hy., iii745, and the product by the' -distance.
<br />GENERAL DATA
<br />IG4T,ANGLE TRIANGI.SS. Square the altitude, divide by twice the
<br />base: -
<br />.,Add quotient to base for hypotenuse. ,
<br />"Given Base•ioo; Alt. 10.10? -200=.5. 100+-5=100.5 hyl).
<br />Given Kyp'loo,•Alt. 25.252: 200=3.125. Ioo-3.125=96.875=Base..
<br />Error in first example; .002; in last, -.045.'
<br />"To•fiInd"Tons of'Rail in'one mile of track: multiply weight per yard
<br />by 1.1, a id divide_bY.7•
<br />LEVELING. The: correction for curvature and refraction,, in feet
<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, 3d2. The combined car -
<br />rection is, negattve:. ` '"
<br />`-PROHABLH ERROR: If di, d1 de,. etc. are the discrepancies of various
<br />"results from the mean; and,if-2id'=the s -6m of the squares of these differ-
<br />.ences and .n=ihe.nllinhei of observations, then the probable error of the
<br />;leanIdr
<br />�
<br />V'�the
<br />Ok45SOLAR EmEb1ERIS. Attention is .called to the Solar Ephemeris for
<br />current year ,published by Keuffel & Esser Co., and furnished upon
<br />request. "This handy46oklet, 38x6 in:,' has about 190 pages of data very
<br />useful -to the Surveyor;'such as the'adjustntents of transits, levels and solar
<br />attachments; directions' and fables', for determining the meridian and the
<br />latitude from observations of .the sull and=Polaris; stadia measurements;
<br />magnetic decliliation; arithmetic constants, etc.
<br />IVL-�Minutes in Decimals of a Degree.
<br />�t
<br />E�
<br />1,
<br />'1l
<br />.0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />-_5167
<br />411
<br />.6833
<br />W
<br />.8500
<br />� -
<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 />.7338
<br />54
<br />.9000
<br />.8333
<br />70833
<br />15_
<br />.2500
<br />_25
<br />.4107
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9107
<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 />s'
<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 />29
<br />.4833
<br />39
<br />.6.500
<br />49
<br />.8167.
<br />54
<br />.9833
<br />_
<br />40'
<br />.1667
<br />20
<br />.3167
<br />1 .3333 11
<br />30
<br />.5000 11
<br />40
<br />1 .6667 11
<br />50
<br />.8333 j,
<br />60
<br />1.0000
<br />TAn1,r -V.-Inches
<br />in Dec lmais ora root•
<br />.
<br />1-16
<br />3-32
<br />Is
<br />3-16
<br />%
<br />5-16
<br />� -
<br />'/z
<br />%
<br />71'
<br />0052 ,�
<br />.0078
<br />.0104
<br />.0156
<br />.0208.
<br />.0260.
<br />.0313
<br />.0417
<br />.0521
<br />.0625 .I
<br />,0729
<br />4
<br />5
<br />1
<br />6
<br />7
<br />1
<br />8
<br />9
<br />10it
<br />II
<br />833
<br />.1, 667
<br />.2500
<br />.3333.
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.0167
<br />
|