|
QTII �, } ,•- .., -a..t� .r -
<br />Tex1r n11 IV-
<br />i
<br />I. - Radii, Ordlnite4� and Deflections. Chord 6-100 ft.
<br />Deg •
<br />kadme
<br />_
<br />At
<br />Ord.
<br />Ten
<br />Diet.'
<br />Def '
<br />Dist-,
<br />IF
<br />1 Ft .
<br />-
<br />}.Deg
<br />]iade�ie
<br />a
<br />Ir3id
<br />Ord
<br />:Taa
<br />,' Drat.
<br />I)ef..
<br />Diet
<br />DeF.
<br />for
<br />1 Ft.
<br />193. 16
<br />I° 51'
<br />2° 171
<br />2° 58'
<br />3° 43`
<br />rol. 15
<br />32
<br />.5333.
<br />to,, 1-
<br />. 26.25
<br />3a lox•--
<br />. 3a 58', -
<br />D'16,
<br />34377
<br />.036
<br />'.145
<br />291
<br />0 0
<br />7°.
<br />119.0
<br />1 528
<br />i6:105
<br />12:21
<br />2.10
<br />t• 20'
<br />17189.
<br />x:073
<br />':109
<br />:291
<br />'.436
<br />.a:592
<br />0:ff
<br />t1�
<br />':M
<br />781.8
<br />1.600
<br />",6.395
<br />-6
<br />1279
<br />2.20
<br />30'
<br />90
<br />11459
<br />:'8594 4
<br />.145.:582
<br />'. 4
<br />:873
<br />1:164
<br />0
<br />0 20
<br />30
<br />.40
<br />764.5
<br />7.17.9
<br />1:627
<br />1:673
<br />.5413;08
<br />0
<br />6:685
<br />13.37
<br />2.25
<br />2.30
<br />50,-6875
<br />5
<br />':182
<br />.727
<br />'3:454
<br />0 20
<br />B ,•'
<br />716.8
<br />1.746
<br />7.6.976
<br />13:95
<br />2.40
<br />1�•F
<br />5729,6
<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: 0
<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 />.7.411
<br />14:82
<br />2.55
<br />20
<br />,4297:3
<br />..::291,1.164
<br />5° 13'-.
<br />`,2.327
<br />0:40
<br />40
<br />'0
<br />105.50
<br />1.892
<br />•7.556
<br />15.11
<br />2.60
<br />30!
<br />3819.8`,.327
<br />103-14
<br />1':300,:2.618
<br />4° Io'
<br />0.45.
<br />6° 57',
<br />_661.7
<br />637.3
<br />1.965
<br />1.846
<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 />5.136
<br />16.27
<br />2.80
<br />°''50'3125.4'..400
<br />1.600
<br />3'.200
<br />0.55-
<br />:30
<br />603.8
<br />2:074
<br />8:281
<br />16.56
<br />2.85
<br />2
<br />2864.9
<br />`.438
<br />1.745
<br />,3:'490
<br />0.60
<br />'` 40
<br />593.4
<br />2.110
<br />5:426
<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 />2.193
<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 />9.150
<br />1S'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 />r9 585
<br />19:16
<br />3.30
<br />1,40,
<br />'2148.8
<br />x.582
<br />2 _327
<br />14:654
<br />0.80.
<br />30.
<br />499.1
<br />2:511
<br />10-.02 -
<br />20:"04
<br />3.45
<br />50
<br />2022.4
<br />':.•:618'2.472
<br />4.945
<br />0.85
<br />12 -
<br />478.3
<br />2:620
<br />10.45'20.01
<br />3.60
<br />8 i ...1910
<br />I'r.655
<br />2.618.
<br />5:235
<br />0.90.
<br />„ •_ „30
<br />459.3
<br />2,730
<br />10.89
<br />21.7.7
<br />3.75
<br />10'
<br />.1809 6
<br />.:6912.763
<br />;5:526
<br />0.95
<br />'13
<br />441.7
<br />2,839
<br />11.32
<br />22:6'4
<br />3.90
<br />,,.20
<br />1719.1
<br />2:908
<br />i. 5'. 817:
<br />1.00,.:.-',30
<br />425.4
<br />2:949
<br />11'.75
<br />23:51
<br />4.05
<br />30",.1637:3
<br />..727
<br />' :764,3.054
<br />6.108
<br />1.05
<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 />.
<br />1' 30"
<br />396.2
<br />3`.16812.62
<br />25.24
<br />4.35
<br />SQ_
<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 />1132:7.
<br />".873
<br />3.490
<br />6.980
<br />1.20:
<br />' 130
<br />370:8
<br />.387;13"'49..26.97
<br />4.65
<br />r 10
<br />1375 4
<br />-:909'
<br />3.635,x7:271
<br />1'.25
<br />16 " -
<br />359.3'
<br />:496.
<br />13 92-
<br />27:S4
<br />4.80
<br />x- 20 •
<br />1322.5
<br />x.945
<br />3:718
<br />x•7.561
<br />IM
<br />!30
<br />348.5
<br />3.'606
<br />14 35 '
<br />28270
<br />4.95
<br />V- 30--•1273.0
<br />-:t982
<br />3.926
<br />,7.852
<br />1.35
<br />17- ''
<br />338.3
<br />3:716
<br />14.78.:29.56
<br />5.10
<br />'••40-
<br />1228.1
<br />1.018
<br />4:071'
<br />8:143
<br />1.40_
<br />18
<br />319.6
<br />3.935
<br />15.64'.31.20
<br />5.40
<br />x•50::
<br />1185.81.055
<br />4`-217;'
<br />8:433
<br />1'.45 •
<br />'19' .-'
<br />302.9
<br />4."t55.
<br />I6:51".
<br />33,01
<br />5-70
<br />8
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20:
<br />287.9.4.374
<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 />274.4-4.594
<br />18.22
<br />36-44
<br />6.30
<br />20';1074:7
<br />1:164
<br />4:853
<br />9':305
<br />1.60
<br />22 i,
<br />262:0
<br />4-:814
<br />19.08
<br />38:16
<br />6.60
<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 />6.00
<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•,082.6
<br />1`.273
<br />5.088
<br />10.18.
<br />1.75
<br />25' -.
<br />231-0
<br />4:476,21.64
<br />43.25
<br />7.50
<br />6''i.-"-'955:4
<br />1.309
<br />5.234
<br />10.47.
<br />1.80'
<br />26
<br />222:3
<br />8.'697
<br />22:50
<br />44:99
<br />7.80
<br />10 -
<br />'029--6
<br />1'346
<br />5:379
<br />10.76
<br />1.85'
<br />' 27 .
<br />214'. 2
<br />6.918
<br />23 85'
<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 />.139
<br />24.19
<br />48:38
<br />8.40
<br />304881.9
<br />1.418
<br />5.669
<br />11.34
<br />1-95_
<br />29'
<br />199.7,6:360
<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 />90'
<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 (0) is equal to ,0012 C'
<br />maltiplied by the midd�e ,ordinate, taken from the, above table Thue, if it
<br />desired to bends 30 ft. rail to Pita 10 degree curve, Its middle'ordinate ahould
<br />be .0012X900X2:183 or 2.36 inches. J, ,
<br />TABLE III, F Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />t- Radius
<br />50
<br />,y sub chord. sin of def: angle -
<br />R:
<br />- � Length
<br />of arc
<br />Curve
<br />sin. i def. zing.
<br />_ 12 5 Ft.
<br />15 Ft. _
<br />20 Ft.
<br />25_ Ft.
<br />for 100 ft.
<br />30°'
<br />193. 16
<br />I° 51'
<br />2° 171
<br />2° 58'
<br />3° 43`
<br />rol. 15
<br />32
<br />.5333.
<br />to,, 1-
<br />. 26.25
<br />3a lox•--
<br />. 3a 58', -
<br />16i--33
<br />34°
<br />171.01
<br />20 o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161--:80 '
<br />2° 13•
<br />2° ill'
<br />3° 33.
<br />40 26' .
<br />•10066
<br />'.2333
<br />153_58
<br />2° 20'
<br />2°49 r '
<br />3°44 r
<br />4 4 a 0, ...-
<br />;101.85
<br />_
<br />4601
<br />' 146:19
<br />, 2 27
<br />__
<br />-2..57-..
<br />-�
<br />� 3'_55`___ .
<br />'. 4
<br />25
<br />42°
<br />x39,52
<br />2°34`
<br />3° 05
<br />4°.07'
<br />5° 08
<br />402.29
<br />! 44°..
<br />I
<br />:.33147
<br />2. I
<br />° 4 'f'
<br />3``',13'
<br />4° i8'
<br />5a 2' •
<br />2
<br />--102."
<br />03
<br />46°
<br />4x7.97
<br />za 48'
<br />3' 2x1''
<br />4a ?g'
<br />:5°6
<br />__
<br />102.75
<br />•1480 ;
<br />.,.. 122: 92..
<br />20 55' :
<br />30 29'
<br />4° 4°r`
<br />50 50103:00
<br />47
<br />50.
<br />118.31
<br />3 02:
<br />3'38
<br />4 5x
<br />6 04'-'103'24
<br />..3000-
<br />5?°
<br />114�o6
<br />3° 09`• :
<br />3'.461
<br />g° os'
<br />6° 37'
<br />103.54
<br />54°
<br />110, 11
<br />'3*16'
<br />3° 54� •
<br />5° 13'-.
<br />6°.31'
<br />163,84
<br />56°
<br />105.50
<br />3° 22'
<br />:4' 02'
<br />S°;23�
<br />6° 44'
<br />?04.14
<br />58°
<br />103-14
<br />3° 29'
<br />4° Io'
<br />5° 34'
<br />6° 57',
<br />164.43
<br />60°
<br />100.00
<br />3° 35':
<br />4°'18
<br />5° 44'
<br />7° 11'-,
<br />104.72
<br />li
<br />-CURVE FORMULAS
<br />T R tan, z I
<br />o-tan.R=T cot, i i Cchards
<br />I - o .
<br />D .- 50 R
<br />'Sin. ; D. - •50 ., R - Sin. D I,
<br />No. chords
<br />.= E '= R ex. sec ; I D
<br />Sm. :b : ,SOa 11 z'I
<br />E-1= T•tan }`I Tan. def. =.j chord'def.
<br />The sgliare of any distance, divided by twice'the radius, will equal
<br />'.the distance from tangent to curve, very nearly.:. "
<br />7 To find angle for given distance and'defiectiun.
<br />"--Rule I `: 14fultiply.the given distance by .0[745 (def, for I°`for I ft:
<br />'see Table I L),• and divide given.,deAecfioit by the.product.
<br />Rule 2'. Multiply given.deflection by 57.3, and'divide the product by
<br />the' givcrr•distance - y'
<br />TO -find deflection for aigrveK angle and distance._ Multipiyahe angle.
<br />by.:oi74.5 '"and the product by the distance ,: . ' -
<br />GENERAL' DATA
<br />RiGiii Axcl E TRIANGLES.. Square the altitude; divide by twice the
<br />base.'___Add ".quotient to base for hypotenuse. .
<br />r. Given Base 100 -Alt. ro io' : Zoo'=:5. too+.5,100.5 hyp.
<br />iGiven Elyp._too, Alt. 2gsg==zoo. 3-125. 100 3.125=96.875 .Base.'
<br />Error infirstexample, .002,; in last;'.045.- ,
<br />To find .Tons of Rail it one'mile of .track: multiply weight perryard
<br />'by it; and divide by, 7.
<br />LEv>11141;.' The:c6rrectiori,for'curvature;and-_refraction; in feet
<br />and,decimals'of feet is'equA to O',574dl, where .d is the distance in miles.
<br />'I he correction tor'• curvature . alone' is', closely, ' M! -The combined cor-
<br />rection is negative
<br />Pli(i AeLE,ERROR "If d1; 'd2,-d,,'etc."ar& fie discrepancies. of various
<br />results from the mean, and'if,Zd?-the'surh of the squares of these differ-
<br />°ences and n=the n 1inber-of observations, then the probable error of the
<br />-0.6745q(n,-1) r
<br />SOLAR, EP11EMH1Us: Attention •is'call''Ed to thee -Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co:, and' furnished upon
<br />request,This handy booklet, 31x6 in., .has about 190 pages of data very
<br />useful'to the:Surveyor; such "-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 />inagnetic',declination'; arithmetic constants, etc.
<br />'TABLE IV. -Minutes in Decimals of a Dezree.
<br />•1r
<br />":0167
<br />1V
<br />.1833
<br />211
<br />-.3500
<br />•311
<br />.0167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.033312
<br />S'a
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333.
<br />42-
<br />.7000
<br />52
<br />•53
<br />.8667
<br />3
<br />.0500
<br />. 13
<br />.2167
<br />23
<br />.3833
<br />33
<br />,5500
<br />43
<br />-7167
<br />7
<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 />5833
<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 />.0333'
<br />7
<br />-.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />:6167
<br />47
<br />-7833
<br />57
<br />9300
<br />8
<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 />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />19
<br />.1667
<br />20
<br />.3333
<br />__
<br />.30
<br />.5000
<br />'40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />'
<br />:F.%ri1.E V.
<br />Inches in.Decirnal5 of a.loot.
<br />1-16
<br />3-32
<br />Y
<br />3-16,
<br />14
<br />5-16
<br />i2
<br />S'a
<br />'s
<br />.0052.1
<br />.0078
<br />.0104,
<br />.M56
<br />_
<br />.0208 I
<br />.0260
<br />,0313
<br />.0417
<br />.0521
<br />-0625
<br />.0729
<br />1
<br />3
<br />4
<br />5
<br />6
<br />I
<br />7
<br />8
<br />9
<br />10
<br />11\
<br />.0833
<br />.1667
<br />-2500
<br />.3333'
<br />III
<br />.4167
<br />x000
<br />.:7833
<br />.6667
<br />.7,500
<br />.8333'
<br />.9167
<br />
|