Deg.

0'

10'

15'

20'

25'

89

.992546 .992722 .992896

.994522 .994673 .994822

5'
.939693 .940189 .940684 .941176 .941667 .942155 .942642 .943126 .943609 .944089 .944568
71 .945519 .945991 .946462 .946930 .947397 .947861 .948324 .948784 .949243 .949699 .950154
.951057 .951505 .951951 .952396 .952838 .953279 .953717 .954153 .954588
73 .956305 .956729 .957151 .957571 .957990 .958406 .958818 .959232 .959642
74 .961262 .961662 .962059 .962455 .962849 .963241 .963031 .964018 .964404
75 .965926 .966301 .966675 .967046 .967415 .967783 .968148 .968511 .968872 .969231 .969588 .969943
76 .970296 .970647 .970995 .971342 .971687 .972029 .972370 .972708 .973045 .973379 .973712
.974370 .974696 .975020 .975342 .975662 .975980 .976296
.977231
.978148 .978449 .978748 .979046 .979341 .979634
79 .981627 .981904 .982178 .982450 .982721 .982989
80 .984808 .985059 .985309 .985556 .985801 .986045
.986525 .986762 .986996
81 .987688 .987915 .988139 .988362 .988582 .988800 .989016 .989230 .989442 .989651
.990268 .990469 .990669 .990866 .991061 .991254 .991445 .991634 .991820 .992005 .992187
.993069 .993239 .993406 .993572 .993736 .993897 .994056 .994214
.994969 .995113 .995256 .995396 .995535 .995671 .995805 .995937

30'

35'

40'

45'

50'

55'

60'

.996195 .996320 .996444 .996566 .996685 .996802
86 .997564 .997665 .997763 .997859 .997953
87 .998630 .998705 .998778 .998848 .998917
88 .999391 .999441 .999488 .999534 .999577
.999848 .999872 .999894 .999914 .999932

60'

55'

50'

45'

40'

35'

30'

25'

.996917 .997030 .997141 .997250 .997357
.998045 .998135 .998223 .998308 .998392 .998473
.998984 .999048 .999111 .999171 .999229 .999285
.999618 .999657 .999694 .999729 .999762 .999793 .999821
.999948 .999962 .999974 .999983 .999991 .999996
15'

NATURAL CO-SINES.

TABLE V.

TABLES for calculating Cuttings and Embankments 1 chain or 66 feet in length, Slopes 1 to 1, and Breadth 1 foot.

AUXILIARY to Table V.-The Difference in Cube Yards to be added to the Slopes.

TABLE of Offsets for Railway Curves, showing the set off at the end of the first Chain

from the Tangent Point.

TABLE VI.-continued.

297

56

7.071

82

4.829

180

2.200

57

6.947

84

4.714

185

2.141

Note.-This table is used in setting out curves from a tangent; the first offset only is given; the following offsets are easily found by multiplying the first offset by the square of each succeeding chain. As for example: 66.0 x 9 = 594.0÷ 12 = 48.66 feet. See Fig. 2, Plate 31.

TABLE VII.

TABLE showing the first Angle from the Tangent Line, according to the Radius.

Radius
in
chains.

Radius

Angles.

chains.

о

O

0 30 42

6

4 46 49

23

14 44

40

0 42 58

57

0 30 9

4 5 46

24

1 11 37

41

041 55

58

0 29 38

25

1 8 46

42

040 56

59

0 29 8

9

3 11 5

26

1 6 7

43

0 39 58

60

0 28 39

10

2 51 58

27

1 3 40

0 39 4

61

0 28 11

11

2 36 19

28

1 1 23

0 38 12

62

0 27 43

12

2 23 17

29

0 59 16

63

0 27 17

13

2 12 15

30

0 57 18

47

0 36 34

64

0 26 51

14

2 248

31

0 55 27

48

0 35 49

65

0 26 27

15

1 54 37

32

053 43

49

0 35 5

66

0 26 3

16

1 47 27

33

0 52 5

50

0 34 23

67

0 25 39

17

1 41 7

34

0 50 33

51

0 33 42

68

0 25 17

18

1 35 30

35

0 49 7

52

69

0 24 55

19

1 30 29

36

0 47 45

53

0 32 26

70

0 24 33

20

1 25 57

37

0 46 27

54

0 31 50

71

0 24 13

21

1 21 52

38

0 45 14

55

0 31 15

72

0 23 52

(continued)

AUXILIARY to Table V.-The Difference in Cube Yards to be added to the Slopes.

TABLE of Offsets for Railway Curves, showing the set off at the end of the first Chain

from the Tangent Point.