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VIII
<br />TA$La H. - Radii, Ordinates and Deflections, Chord _- 100 ft.
<br />Ng .
<br />IMUN
<br />Mid.
<br />Ord.
<br />Tan,
<br />Diet.
<br />Def.
<br />Dist.1kt.
<br />1101-
<br />Deg.
<br />Iladitle
<br />h5d.
<br />Ord,
<br />Tan.
<br />Dist.
<br />Def,
<br />Dist;
<br />Dar'
<br />1 r
<br />..193.18
<br />1' 51'
<br />t.t,
<br />2° 58'
<br />3° 43'
<br />101;15
<br />32°
<br />181.39
<br />t.
<br />t,
<br />t.
<br />3° 58'
<br />0'10'
<br />34377.
<br />,.036
<br />.145
<br />,291
<br />0.055
<br />7'
<br />819,0
<br />1.528
<br />6!106
<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
<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 />764.5
<br />1.637
<br />,6.540'13.08
<br />S° 08
<br />2.25
<br />40.'
<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 />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 />2.40
<br />1
<br />5729'',0
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688,2
<br />1.819
<br />7.266
<br />14.53'2,10
<br />54°
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.85
<br />30
<br />674,7
<br />1.855
<br />7.411
<br />14.82
<br />2.15
<br />20
<br />4297,3
<br />.201
<br />1.164
<br />2.327
<br />0.40
<br />-40
<br />661.7
<br />1.892.
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3810,8
<br />.327
<br />1:309
<br />2.018
<br />0.45
<br />9' ,
<br />637,3
<br />1.065
<br />.7.846
<br />15.69
<br />2:70
<br />40
<br />3137,9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />67.4,6
<br />2.'037
<br />8.136
<br />10.27
<br />2.80
<br />50
<br />3125:4
<br />.400
<br />1.600
<br />3,200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16.562.85
<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 />2.00
<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 />17.43'3.00
<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 />3.15
<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 />10.02
<br />2U'04
<br />3.45
<br />50'
<br />2022A
<br />.618
<br />2.472
<br />4,945
<br />0.85
<br />12 ' "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 />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 />20
<br />1710.1
<br />'.727.
<br />2.908
<br />5,817
<br />1.001
<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 />3.058'12.18
<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
<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 />6,980
<br />1.20
<br />30
<br />370.8
<br />3.387'13.49
<br />26.97
<br />4.65
<br />10
<br />1375.:4
<br />.909
<br />3;635
<br />7,271
<br />1.25
<br />16
<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 />.006
<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 />37
<br />338.3
<br />3.716
<br />14;78
<br />29,56
<br />5.10
<br />40
<br />1228:1
<br />1.018'4.071
<br />8,143
<br />1:40'
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />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;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 />4.607
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594.18.22
<br />36.44
<br />6:30
<br />20
<br />1074'.7
<br />1.164
<br />4.653
<br />9.305
<br />1,60'
<br />22
<br />262.0
<br />4.814
<br />19.08
<br />38.16
<br />13.60
<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 />1011.5.1.237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />340.5
<br />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 />231.0
<br />6.476
<br />21.64"
<br />43.28
<br />7.50
<br />E
<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.S0
<br />10
<br />929.6
<br />1.396
<br />5.379
<br />10.76
<br />1.85•
<br />27
<br />214.2
<br />Z.918
<br />23.35'
<br />46.69
<br />8.10
<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 />881.9
<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 />5.814
<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'n inches for any cord of length (4) is nal to .0012 C'
<br />eair•emoltid to boied nd a 30 fthe .. ail tolfitta 10 dosree curve site middle ordinate bove l shoulif d
<br />be .O012X900X2:183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />Of
<br />- Radius
<br />50
<br />- A eub chord
<br />R in of 's def. angle
<br />Length
<br />of arc
<br />Curve
<br />sin.,idef.ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Et.
<br />25 Ft.
<br />for 100 ft.
<br />30°
<br />..193.18
<br />1' 51'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />101;15
<br />32°
<br />181.39
<br />1° 59'
<br />I0'
<br />2° 25'
<br />3°
<br />3° 58'
<br />101--33 ..
<br />34°
<br />171.01
<br />2° 06'
<br />2°.33'
<br />3° 21'
<br />4° 12'
<br />101.4.8
<br />36°
<br />161, 8o
<br />20 13' "
<br />2° 41"
<br />.3° 33
<br />4° 26'
<br />I,oi .66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />40 40'
<br />101.85
<br />40°
<br />146.19
<br />2° 27'
<br />2° 57�
<br />3° 55'
<br />4° 54'
<br />1o2.o6
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05' .
<br />4°. 07'
<br />S° 08
<br />102:29 '
<br />44° ..
<br />133 :47
<br />2° 41'
<br />3° 13'
<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 />r02: 76.
<br />48°
<br />1x2:-92.''
<br />2° 55'•
<br />3° 29'
<br />4° 40'
<br />S'"50'
<br />103:00
<br />50°
<br />118131 ;
<br />3° 02' -
<br />3° 38°
<br />4° 5r'
<br />6° 04'
<br />103.24
<br />52° °
<br />114:06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6°,17'
<br />103.54.
<br />54°
<br />110. 11- '
<br />3° 16'
<br />3° 54'
<br />S° 13'.
<br />6-31 1
<br />103.84
<br />56°
<br />- Io6. 50
<br />3° 22.'
<br />•4° 02'
<br />5° 23'
<br />6° 44'
<br />104-14
<br />58° •
<br />1:.03.44
<br />� 3° 29
<br />4° 10'
<br />5° 34'
<br />6° 57
<br />�. 104-43
<br />60°
<br />loo, 00
<br />3°'35'
<br />4° -18'
<br />5° 44`
<br />' , 7°, I I'.
<br />104.72
<br />Ix
<br />CURVE' FORMULAS
<br />T =.R tan !'1 R= T cot. 1, 1 chord=
<br />4 5o tan s I Chord def.
<br />T Sin.
<br />1' ,; .0 .50- R
<br />R�= - 1
<br />Sin. 12 I3 = 5o Sin. , D No. chords = Y
<br />It F. R ex. sec 8•I ll
<br />Sin. 2 'D 5o tan z 1 E = T tan J.1 Tan. def. = z chord def,
<br />' T ,
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance from tangent to curie, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply the given distance by .01745 (def. for i° for I ft.
<br />7 see'rable 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 />.4 To find deflection for a given angle and distance. Multiply the angle
<br />11 by i01745, and the product by the distance.
<br />GENERAL DATA
<br />'RIGnT ANGLE TRIANGLES.. Square the altitude, divide by twice the ,
<br />base. Add quotient to base fpr hypotenuse.
<br />Given Base loo; Alt. 10.102'.: 200=.5. Inn +,5=100.•5 hyp-
<br />Given Hyp. loo, Alt. 25.252-200=3.1:25, 100-3.125=96:875=13€ise:
<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 />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.674d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, d2. .The ,combined cor-
<br />rection is negative.
<br />' -PROBABLE ERROR. If (11,'42, ds, etc, are the discrepancies of various
<br />results from the mean, and if id2=the sum of the squares of these differ-
<br />ences and n =the number, of observations, then the probable error of the
<br />mean= Ede
<br />t 0.6744 n(n-1)
<br />-SOLAR EPaEMFRis. 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 />TABLE 1', --Inches in Decimals of a Foot.
<br />1-16 3-32 Y, 3-16 I - 16 %". - 3s
<br />.0052 .0078 .010-1 .01St') .0208 .0260 .0313 .0417 .0521 .orl'i .0729
<br />13 '� '4 1 :� u I 7 8 9- IU 11
<br />_.0833 .1667 .2500 .3333 III3167 .:,000 -383:1 .6667 .7500 .3333 .91 til
<br />1+ .0167 11+ .1833 21+ .3500 31+ - .5167 4ll .6833 51+ .8500
<br />2 .0333 12 .21100 22 .3667 32 .5333 42 .7D00 52 .86fii
<br />3 .0500 13 .2167 23 .3833 33 .5500 43 .7167 53 .8833
<br />.. 4 .Of,67 • 14 .2333 24 .4000 34 .•5667 44 .7333 54 .9000
<br />- S :0833 15 '-2.500 25 .4167 35 .5833 45 .7500 55 .9167
<br />6 -1000 16 2667 26 ..4333 36 ,6000 46 .7607 56 .9333
<br />' 7 • 1167 17 2833 27 .4500 37 .6167 47 .7833 ''7 .950Q
<br />8 .1333 18 .3000 28 -.4667 38 .6333 98 .8D00 58 .9661
<br />9 .1500. 19 3167' 29 A833 39 .6500 99 .8167 11 G
<br />t�
<br />9
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.1000
<br />40
<br />.6667
<br />60
<br />.$333
<br />60
<br />1.0000
<br />t�
<br />
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