The following Tables, originally dedicated to 'the National Association of the Forgers of Iron Work,' England, by James Fo-deN, will be found extremely useful to Smiths, generally, and are accompanied by Practical Examples. - TempletoN.

Diameters And Circumferences Of Circles

Diam.

Circ.

In.

Ft.

In

1

0

31/8

1 1/8

0

0

3 7/8

1 3/8

0

0

4 5/8

1 5/8

0

5

0

5 3/8

1 7/8

0

5 7/8

2

0

2 1/8

0

6 5/8

0

7

2 3/8

0

7 3/8

0

2 5/8

0

8 1/8

0

8 5/8

2 7/8

0

9

3

0

9 3/8

3 1/8

0

0

10 1/8

3 3/8

0

10½

0

10 7/8

3 5/8

0

11 3/8

0

11¾

3 7/8

1

0 1/8

4

1

4 1/8

1

0 7/8

1

4 3/8

1

1 5/8

1

2 1/8

4 5/8

1

1

2 7/8

4 7/8

1

5

1

3 5/8

5 1/8

1

4

1

4 3/8

5 3/8

1

4 7/8

Diam.

Circ.

In.

Ft.

In.

1

5 5/8

1

5 5/8

1

6

5 7/8

1

6 3/8

6

1

6 1/8

1

7 1/8

1

7 5/8

6 3/8

1

8

1

8 3/8

6 5/8

1

1

9 1/8

6 7/8

1

7

1

9 7/8

7 1/8

1

10 3/8

1

10¾

7 3/8

1

11 1/8

1

11½

7 5/8

1

11 7/8

2

7 5/8

2

0 5/8

8

1 1/8

8 1/8

2

2

1 7/8

8 3/8

2

2

2 5/8

8 5/8

2

3

2

3 3/8

8 7/8

2

3 7/8

9

2

9 1/8

2

4 5/8

2

5

9 3/8

2

5 3/8

2

9 5/8

2

6 1/8

2

6 5/8

9 7/8

2

7

Diam.

Circ.

Ft

In.

Ft.

In.

0

10

2

7 3/8

0

10 1/8

2

0

10¼

2

8 1/8

0

l0 3/8

2

0

10½

2

8 7/8

0

10 5/8

2

9 3/8

0

10¾

2

0

10 7/8

2

10 1/8

0

11

2

10½

0

11 1/8

2

10 7/8

0

11¼

2

11¼

0

11 3/8

2

11 5/8

0

11½

3

0

0

11 5/8

3

0

11¾

3

0 7/8

0

11 7/8

3

1

0

3

1 5/8

1

0 1/8

3

2

1

3

2 3/8

1

0 3/8

3

2 7/8

1

3

1

0 5/8

3

3 5/8

1

3

4

1

0 7/8

3

4 3/8

1

1

3

1

1 1/8

3

5 1/8

1

1 ¼

3

5 5/8

1

1 3/8

3

6

1

3

6 3/8

1

1 5/8

3

1

3

7 1/8

1

1 7/8

::

1

2

3

7 7/8

1

2 1/8

3

8 3/8

1

2 ¼

3

Diam.

Circ.

Ft.

In.

Ft.

In.

1

2 1/8

3

9 1/8

1

3

1

2 5/8

3

9 7/8

1

3

10¼

1

2 7/8

3

l0 5/8

1

3

3

11

1

3 1/8

3

11½

1

3

11 7/8

1

3 3/8

4

1

4

0 5/8

1

3 5/8

4

1

1

4

1 3/8

1

3 7/8

4

1 7/8

1

4

4

1

4 1/8

4

2 5/8

1

4

3

1

4 3/8

4

3 3/8

1

4

1

4 5/8

4

4 1/8

1

4

1

4 7/8

4

5

1

5

4

5 3/8

1

5 1/8

4

1

4

6 1/8

1

5 3/8

4

1

4

6 7/8

1

5 5/8

4

7 3/8

1

4

1

5 7/8

4

8 1/8

1

6

4

1

6 1/8

4

8 7/8

1

4

1

6 3/8

4

9 5/8

1

4

10

1

6 5/8

4

10 3/8

1

4

10 7/8

Diam.

Circ.

Ft

In

Ft.

In.

1

6 7/8

4

11¼

1

7

4

11 5/8

1

7 1/8

5

0

1

5

0 3/8

1

7 3/8

5

0 7/8

1

5

1 ¼

1

7 5/8

5

1 5/8

1

5

2

1

7 7/8

5

2 3/8

1

8

5

1

8 1/8

5

3 1/8

1

5

3 5/8

1

8 3/8

5

4

1

5

4 3/8

1

8 5/8

5

1

5

5 1/8

1

8 7/8

5

1

9

5

5 7/8

1

9 1/8

5

6 3/8

1

5

1

9 3/8

5

7 1/8

1

5

1

9 5/8

5

8

1

5

8 3/8

1

9 7/8

5

1

10

5

9

1

10 1/8

5

1

10¼

5

9 7/8

1

10 3/8

5

10¼

1

10½

5

10 5/8

1

10 5/8

5

11

1

10¾

5

11 3/8

1

10 7/8

5

11 3/4

1

11

6

1

11 1/8

6

0 5/8

Diam.

Circ.

Ft.

In.

Ft.

In.

1

11¼

6

1

1

11 3/8

6

l 3/8

1

11½

6

1

11 5/8

6

2 1/8

1

11¾

6

1

11 7/8

6

3

2

0

6

3 3/8

2

0 1/8

6

2

0 ¼

6

4 1/8

2

0 3/8

6

2

6

4 7/8

2

0 5/8

6

2

6

2

0 7/8

6

6 1/8

2

1

6

2

1 1/8

6

6 7/8

2

6

2

1 3/8

6

7 5/8

2

6

8

2

1 5/8

6

2

6

8 7/8

2

1 7/8

6

2

2

6

9 5/8

2

2 1/8

6

10

2

6

10 3/8

2

2 3/8

6

10¾

2

6

11¼

2

2 5/8

6

11 5/8

2

7

0

2

2 7/8

7

0 3/8

2

3

7

2

3 1/8

7

l 1/8

2

7

2

3 3/8

7

2

2

7

2 3/8

2

3 5/8

7

2

7

3 1/8

2

3 7/8

7

2

4

7

3 7/8

2

4 1/8

7

2

7

2

4 3/8

7

5 1/8

2

4 ½

7

2

4 5/8

7

5 7/8

2

7

Diam.

Circ.

Ft.

In. Ft.

in.

2

4 7/8

7

6 5/8

2

5

7

7

2

5 1/8

7

2

7

7 7/8

2

5 3/8

7

2

7

8 5/8

2

5 5/8

7

9

2

7

9 3/8

2

5 7/8

7

2

6

7

10 1/8

2

6 1/8

7

10 5/8

2

7

11

2

6 3/8

7

11 3/8

2

7

11¾

2

6 5/8

8

0 1/8

2

8

2

6 7/8

8

0 7/8

2

7

8

l 3/8

2

7 1/8

8

2

8

2 1/8

2

7 3/8

8

2

8

2 7/8

2

7 5/8

8

2

8

2

7 7/8

8

4 1/8

2

8

8

2

8 1/8

8

4 7/8

2

8

2

8 3/8

8

5 5/8

2

8

6

2

8 5/8

8

2

8

6 7/8

2

8 7/8

8

2

9

8

7 5/8

2

9 1/8

8

8

2

8

8 3/8

2

9 3/8

8

2

8

2

9 5/8

8

9 5/8

2

8

10

2

9 7/8

8

10 3/8

2

10

8

10¾

2

10 1/8

8

11 1/8

2

10¼

8

11½

Diam.

Circ.

Ft

In.

Ft.

In.

2

10 3/8

8

11 7/8

2

10½

9

0 3/8

2

10 5/8

9

0 3/4

2

10¾

9

1 1/8

2

10 7/8

9

2

11

9

1 7/8

2

11 1/8

9

2

11¼

9

2 5/8

2

11 3/8

9

3

2

11½

9

2

11 5/8

9

3 7/8

2

11¾

9

2

11 7/8

9

4 5/8

3

0

9

5

3

0 1/8

9

5 3/8

3

9

5 7/8

3

0 3/8

9

3

9

6 5/8

3

0 5/8

9

7

3

9

7 3/8

3

0 7/8

9

3

1

9

8 1/8

3

1 1/8

9

8 5/8

3

9

9

3

1 3/8

9

9 3/8

3

9

3

1 5/8

9

10 1/8

3

9

10½

3

1 7/8

9

10 7/8

3

2

9

ll 3/8

3

2 1/8

9

11¾

3

10

0 1/8

3

2 3/8

10

3

10

0 7/8

3

2 5/8

10

3

10

1 5/8

3

2 7/8

10

2 1/8

3

3

10

3

3 1/8

10

2 7/8

3

10

3 1/8

3

3 3/8

10

3 5/8

3

10

4

3

3 5/8

10

3

10

4 7/8

3

3 7/8

10

Diam

Circ.

Ft.

In.

Ft.

In.

3

4

10

5 5/8

3

4 1/8

10

6

3

10

6 3/8

3

4 3/8

10

3

10

7 1/8

3

4 5/8

10

7 5/8

3

10

8

3

4 7/8

10

8 3/8

3

5

10

3

5 1/8

10

9 1/8

3

10

3

5 3/8

10

9 7/8

3

10

10 3/8

3

5 5/8

10

10¾

3

10

11 1/8

3

5 7/8

10

11½

3

6

10

11 7/8

3

6 1/8

11

3

11

0 5/8

3

6 3/8

11

1 1/8

3

11

3

6 5/8

11

1 7/8

3

11

3

6 7/8

11

2 5/8

3

7

11

3

3

7 1/8

11

3 3/8

3

11

3 7/8

3

7 3/8

11

3

11

4 5/8

3

7 5/8

11

5

3

11

5 3/8

3

7 7/8

11

3

8

11

6 1/8

3

8 1/8

11

3

11

7

3

8 3/8

11

7 3/8

3

11

3

8 5/8

11

8 1/8

3

11

3

8 7/8

11

8 7/8

3

9

11

3

9 1/8

11

3

11

10 1/8

3

9 3/8

11

10½

Diam

Circ.

Ft

In.

Ft

In.

3

11

10 7/8

3

9 5/8

11

11¼

3

11

11 5/8

3

9 7/8

12

0

3

10

12

3

10 1/8

12

0 7/8

3

10¼

12

3

10 3/8

12

1 5/8

3

10½

12

2

3

10 5/8

12

2 3/8

3

10¾

12

3

10 7/8

12

3

11

12

3 5/8

3

11 1/8

12

4

3

11¼

12

4 3/8

3

11 3/8

12

3

11½

12

5 1/8

3

11 5/8

12

3

11¾

12

6

3

11 7/8

12

6 3/8

4

0

12

4

0 1/8

12

7 1/8

4

12

4

0 3/8

12

7 7/8

4

12

4

0 5/8

12

4

12

9 1/8

4

0 7/8

12

4

1

12

9 7/8

4

1 1/8

12

10¼

4

12

10 5/8

4

1 3/8

12

11

4

12

11½

4

1 5/8

12

11 7/8

4

13

4

1 7/8

13

0 5/8

4

2

13

1

4

2 1/8

13

4

13

1 7/8

4

2 3/8

13

4

13

2 5/8

4

2 5/8

13

3

4

13

3 3/8

4

2 7/8

13

4

3

13

4 1/8

Diam.

Circ.

Ft.

In.

Ft.

In.

4

3 1/8

13

4

3 ¼

13

5

4

3 3/8

13

5 3/8

4

13

4

3 5/8

13

6 1/8

4

13

4

3 7/8

13

6 7/8

4

4

13

4

4 1/8

13

4

13

8 1/8

4

4 3/8

13

4

13

8 7/8

4

4 5/8

13

4

13

9 5/8

4

4 7/8

13

10

4

5

13

10½

4

5 1/8

13

10 7/8

4

13

11¼

4

5 3/8

13

11 5/8

4

14

0

4

5 5/8

14

0 3/8

4

14

0 7/8

4

5 7/8

14

4

6

14

l 5/8

4

6 1/8

14

2

4

14

2 3/8

4

6 3/8

14

4

14

3 1/8

4

6 5/8

14

4

6 ¾

14

4

4

6 7/8

14

4 3/8

4

7

14

4

7 1/8

14

5 1/8

4

14

4

7 3/8

14

5 7/8

4

14

4

7 5/8

14

4

14

7 1/8

4

7 7/8

14

4

8

14

7 7/8

4

8 1/8

14

4

14

8 5/8

4

8 3/8

14

9

4

14

4

8 5/8

14

9 7/8

Diam.

Circ.

Ft

In.

Ft.

in.

4

14

10¼

4

8 7/8

14

10 5/8

4

9

14

11

4

9 1/8

14

11 3/8

4

14

11¾

4

9 3/8

15

0 1/8

4

15

0 5/8

4

9 5/8

15

1

4

15

1 3/8

4

9 7/8

15

4

10

15

2 1/8

4

10 1/8

15

4

10¼

15

2 7/8

4

10 3/8

15

3 3/8

4

10½

15

4

10 5/8

15

4 1/8

4

10¾

15

4 ½

4

10 7/8

15

4 7/8

4

11

15

4

11 1/8

15

5 5/8

4

11¼

15

6 1/8

4

11 3/8

15

4

11½

15

6 7/8

4

11 5/8

15

4

11¾

15

7 5/8

4

11 7/8

15

8

5

0

15

8 3/8

5

0 1/8

15

8 7/8

5

15

5

0 3/8

15

9 5/8

5

15

10

5

0 5/8

15

l0 3/8

5

15

10¾

5

0 7/8

15

11 1/8

5

1

15

11 5/8

5

1 1/8

16

0

5

16

0 3/8

5

1 3/8

16

5

16

1 1/8

5

1 5/8

16

5

1 ¾

16

1 7/8

5

1 7/8

16

2 3/8

5

2

16

5

2 1/8

16

3 1/8

Diam.

Circ.

Ft.

in.

Ft.

In.

5

16

5

2 3/8

16

3 7/8

5

16

5

2 5/8

16

4 5/8

5

2 ¾

16

5 1/8

5

2 7/8

16

5

3

16

5 7/8

5

3 1/8

16

5

16

6 5/8

5

3 3/8

16

7

5

16

7 3/8

5

3 5/8

16

7 7/8

5

16

5

3 7/8

16

8 5/8

5

4

16

9

5

4 1/8

16

9 5/8

5

16

5

4 3/8

16

10 1/8

5

16

10 5/8

5

4 5/8

16

11

5

16

11 3/8

5

4 7/8

16

11¾

5

5

17

0 1/8

5

5 1/8

17

0 5/8

5

17

1

5

5 3/8

17

1 3/8

5

17

5

5 5/8

17

2 1/8

5

5 ¾

17

5

5 7/8

17

2 7/8

5

6

17

5

6 1/8

17

3 5/8

5

17

4 1/8

5

6 3/8

17

5

17

4 7/8

5

6 5/8

17

5

6 ¾

17

5 5/8

5

6 7/8

17

6

5

7

17

6 3/8

5

7 1/8

17

6 7/8

5

17

5

7 3/8

17

7 5/8

5

17

8

5

7 5/8

17

8 3/8

5

17

Diam.

Circ.

Ft

. in.

Ft.

In.

5

7 7/8

17

9 1/8

5

8

17

9 5/8

5

8 1/8

17

10

5

17

10 3/8

5

8 3/8

17

10¾

5

17

11 1/8

5

8 5/8

17

11½

5

17

11 7/8

5

8 7/8

18

0 3/8

5

9

18

5

9 1/8

18

1 1/8

5

18

5

9 3/8

18

1 7/8

5

18

5

9 5/8

18

2 5/8

5

9 ¾

18

3

5

9 7/8

18

5

10

18

3 7/8

5

10 1/8

18

5

10¼

18

4 5/8

5

10 3/8

18

5

5

10 ½

18

5 3/8

5

10 5/8

18

5 7/8

5

10¾

18

5

10 7/8

18

6 5/8

5

11

18

7

5

11 1/8

18

7 3/8

5

11¼

18

5

l1 3/8

18

8 1/8

5

11½

18

5

11 5/8

18

9

5

11¾

18

9 3/8

5

11 7/8

18

6

0

18

10 1/8

6

0 1/8

18

10½

6

18

10 7/8

6

0 3/8

18

11¼

6

18

11¾

6

0 5/8

19

0 1/8

6

19

6

0 7/8

19

0 7/8

6

1

19

6

1 1/8

19

1 5/8

6

19

2

Diam.

Circ.

Ft.

In.

Ft.

In.

6

1 3/8

19

6

19

2 7/8

6

1 5/8

19

6

19

3 5/8

6

1 7/8

19

4

6

2

19

4 3/8

6

2 1/8

19

6

19

6

2 3/8

19

5 5/8

6

19

6

6

2 5/8

19

6 3/8

6

19

6

2 7/8

19

7 1/8

6

3

19

6

3 1/8

19

8

6

19

8 3/8

6

3 3/8

19

6

19

9 1/8

6

3 5/8

19

6

19

9 7/8

6

3 7/8

19

10¼

6

4

19

10¾

6

4 1/8

19

11 1/8

6

19

11½

6

4 3/8

19

11 7/8

6

20

6

4 5/8

20

0 5/8

6

20

1

6

4 7/8

20

6

5

20

1 7/8

6

5 1/8

20

6

20

2 5/8

6

5 3/8

20

3

6

20

3 3/8

6

5 5/8

20

6

5 ¾

20

6

5 7/8

20

4 5/8

6

6

20

5

6

6 1/8

20

5 3/8

6

20

6

6 3/8

20

6 1/8

6

20

6

6 5/8

20

7

6

20

7 3/8

6

6 7/8

20

Diam.

Circ.

Ft

. In.

Ft.

In

6

7

20

8 1/8

6

7 1/8

20

6

20

8 7/8

6

7 3/8

20

6

20

6

7 5/8

20

10 1/8

6

20

10½

6

7 7/8

20

10 7/8

6

8

20

11¼

6

81/8

20

11 5/8

6

21

0

6

8 3/8

21

6

21

0 7/8

6

8 5/8

21

6

21

1 5/8

6

8 7/8

21

2

6

9

21

2 3/8

6

9 1/8

21

2 7/8

6

21

6

9 3/8

21

3 5/8

6

21

4

6

9 5/8

21

4 3/8

6

21

6

9 7/8

21

5 1/8

6

10

21

6

10 1/8

21

6

6

10¼

21

6 3/8

6

10 3/8

21

6

10½

21

7 1/8

6

10 5/8

21

6

10¾

21

7 7/8

6

10 7/8

21

6

ll

21

6

11 1/8

21

91/8

6

ll¼

21

6

11 3/8

21

9 7/8

6

11½

21

10¼

6

11 5/8

21

10 5/8

6

11¾

21

11

6

11 7/8

21

11½

7

0

21

11 7/8

7

0 1/8

22

7

22

0 5/8

7

0 3/8

22

1

Diam.

Circ.

Ft

. In.

Ft.

In.

7

22

1 3/8

7

0 5/8

22

1 7/8

7

22

7

0 7/8

22

2 5/8

7

1

22

3

7

1 1/8

22

3 3/8

7

22

7

1 3/8

22

4 1/8

7

22

4 ½

7

1 5/8

22

5

7

22

5 3/8

7

1 7/8

22

7

2

22

6 1/8

7

2 1/8

22

7

22

6 7/8

7

2 3/8

22

7

22

7 5/8

7

2 5/8

22

8 1/8

7

22

7

2 7/8

22

8 7/8

7

3

22

7

3 1/8

22

9 5/8

7

22

10

7

3 3/8

22

l0 3/8

7

22

10 7/8

7

3 5/8

22

11¼

7

22

11 5/8

7

3 7/8

23

0

7

4

23

0 3/8

7

4 1/8

23

7

23

1 1/8

7

4 3/8

23

1 5/8

7

23

2

7

4 5/8

23

2 3/8

7

23

7

4 7/8

23

3 1/8

7

5

23

7

5 1/8

23

3 7/8

7

23

4 3/8

7

5 3/8

23

7

23

5 1/8

7

5 5/8

23

7

23

5 7/8

7

5 7/8

23

7

6

23

6 5/8

Diam

Circ.

Ft.

In

Ft.

In.

7

6 1/8

23

7 1/8

7

23

7

6 3/8

23

7 7/8

7

23

7

6 5/8

23

8 5/8

7

23

9

7

6 7/8

23

9 3/8

7

7

23

9 7/8

7

7 1/8

23

10¼

7

23

l05/8

7

7 3/8

23

11

7

23

11 3/8

7

7 5/8

23

11¾

7

24

0 1/8

7

7 7/8

24

0 5/8

7

8

24

1

7

8 1/8

24

1 3/8

7

24

7

8 3/8

24

2 1/8

7

24

7

8 5/8

24

2 7/8

7

24

3 3/8

7

8 7/8

24

7

9

24

4 1/8

7

9 1/8

24

7

24

4 7/8

7

9 3/8

24

7

24

5 5/8

7

9 5/8

24

6 1/8

7

24

7

9 7/8

24

6 7/8

7

10

24

7

10 1/8

24

7 5/8

7

10¼

24

8

7

10 3/8

24

8 3/8

7

10½

24

8 7/8

7

10 5/8

24

7

10¾

24

9 5/8

7

10 7/8

24

10

7

11

24

10 3/8

7

11 1/8

24

10¾

7

11¼

24

11 1/8

7

11 3/8

24

11½

7

11½

25

0

7

11 5/8

25

0 3/8

Diam

Circ.

Ft.

In

Ft.

In.

7

11¾

25

7

11 7/8

25

1 1/8

8

0

25

8

0 1/8

25

1 7/8

8

25

2 3/8

8

0 3/8

25

8

25

3 1/8

8

0 5/8

25

8

25

3 7/8

8

0 7/8

25

8

1

25

4 5/8

8

1 1/8

25

5 1/8

8

25

8

1 3/8

25

5 7/8

8

25

8

1 5/8

25

6 5/8

8

25

7

8

1 7/8

25

7 3/8

8

2

25

7 7/8

8

2 1/8

25

8

25

8 5/8

8

2 3/8

25

9

8

25

9 3/8

8

2 5/8

25

8

25

10 1/8

8

2 7/8

25

10½

8

3

25

11

8

3 1/8

25

11 3/8

8

25

11¾

8

3 3/8

26

0 1/8

8

26

8

3 5/8

26

0 7/8

8

26

1 3/8

8

3 7/8

26

8

4

26

2 1/8

8

4 1/8

26

8

26

2 7/8

8

4 3/8

26

8

26

3 5/8

8

4 5/8

26

4 1/8

8

26

4 ½

8

4 7/8

26

4 7/8

8

5

26

5 ¼

8

5 1/8

26

5 5/8

Diam.

Circ.

F

. In

Ft.

In

8

26

6

8

5 3/8

26

6 3/8

8

26

8

5 5/8

26

8

26

7 5/8

8

5 7/8

26'

8

8

6

26

8 3/8

8

6 1/8

26

8

26

9 1/8

8

6 3/8

26

9 1/2

8

26

10

8

6 5/8

26

10 3/8

8

26

10¾

8

6 7/8

26

11 1/8

8

7

26

11½

8

7 1/8

26

11 7/8

8

27

8

7 3/8

27

8

27

1 1/8

8

7 5/8

27

1 ½

8

27

1 7/8

8

7 7/8

27

8

8

27

2 5/8

8

8 1/8

27

3

8

27

8

8 3/8

27

3 7/8

8

27

8

8 5/8

27

4 5/8

8

27

5

8

8 7/8

27

5 3/8

8

9

27

8

9 1/8

27

8

27

6 5/8

8

9 3/8

27

7

8

27

7 3/8

8

9 5/8

27

8

27

8 1/8

8

9 7/8

27

8

10

27

9

8

10 1/8

27

9 3/8

8

10¼

27

8

10 3/8

27

10 1/8

8

10½

27

10½

8

10 5/8

27

10 7/8

8

10¾

27

11¼

Diam.

Circ.

Ft.

In.

Ft

In.

8

10 7/8

27

11¾

8

11

28

0 1/8

8

11 1/8

28

8

11¼

28

0 7/8

8

11 3/8

28

8

11½

28

1 5/8

8

11 5/8

28

2

8

11¾

28

8

11 7/8

28

2 7/8

9

0

28

9

0 1/8

28

3 5/8

9

28

4

9

0 3/8

28

4 3/8

9

28

9

0 5/8

28

9

28

5 5/8

9

0 7/8

28

6

9

1

28

6 3/8

9

1 1/8

28

9

28

7 1/8

9

1 3/8

28

9

28

8

9

1 5/8

28

8 3/8

9

28

9

1 7/8

28

9 1/8

9

2

28

9

2 1/8

28

9 7/8

9

28

10¼

9

2 3/8

28

10¾

9

28

11 1/8

9

2 5/8

28

11½

9

28

11 7/8

9

2 7/8

29

9

3

29

0 5/8

9

3 1/8

29

1

9

29

9

3 3/8

29

1 7/8

9

29

9

3 5/8

29

2 5/8

9

29

3

9

3 7/8

29

3 3/8

9

4

29

9

4 1/8

29

9

29

4 5/8

Dia.

Circ.

F

I.

Ft.

In.

9

4 3/8

29

5

9

29

5 3/8

9

4 5/8

29

9

4 ¾

29

6 1/8

9

4 7/8

29

9

5

29

7

9

5 1/8

29

7 3/8

9

29

9

5 3/8

29

8 1/8

9

29

9

5 5/8

29

8 7/8

9

29

9

5 7/8

29

9

6

29

10 1/8

9

6 1/8

29

10½

9

29

10 7/8

9

6 3/8

29

11¼

9

29

11 5/8

9

6 5/8

30

0

9

30

9

6 7/8

30

0 7/8

9

7

30

9

7 1/8

30

1 5/8

9

30

2

9

7 3/8

30

2 3/8

9

30

9

7 5/8

30

3 1/8

9

30

3 5/8

9

7 7/8

30

4

9

8

30

4 3/8

9

8 1/8

30

9

30

5 1/8

9

8 3/8

30

9

30

6

9

8 5/8

30

6 3/8

9

30

9

8 7/8

30

7 1/8

9

9

30

9

9 1/8

30

7 7/8

9

30

9

9 3/8

30

8 5/8

9

30

9 1/8

9

9 5/8

30

9

30

9 7/8

9

9 7/8

30

10¼

Diam.

Circ.

Ft.

In.

Ft.

In

9

10

30

10 5/8

9

10 1/8

30

11

9

10¼

30

11 3/8

9

10 3/8

30

11 7/8

9

10½

31

9

10 5/8

31

0 5/8

9

10¾

31

1

9

10 7/8

31

1 3/8

9

11

31

9

11 1/8

31

9

111¼

31

2 5/8

9

11 3/8

31

3

9

11½

31

3 3/8

9

11 5/8

31

9

11¾

31

4 1/8

9

11 7/8

31

10

0

31

4 7/8

10

0 1/8

31

5 3/8

10

31

10

0 3/8

31

6 1/8

10

31

10

0 5/8

31

6 7/8

10

31

10

0 7/8

31

7 5/8

10

1

31

8 1/8

10

1 1/8

31

10

31

8 7/8

10

1 3/8

31

10

31

9 5/8

10

1 5/8

31

10

10

31

10 3/8

10

1 7/8

31

10 7/8

10

2

31

11¼

10

2 1/8

31

11 5/8

10

32

0

10

2 3/8

32

0 3/8

10

32

10

2 5/8

32

1 1/8

10

2 ¾

32

10

2 7/8

32

2

10

3

32

2 3/8

10

3 1/8

32

10

32

3 1/8

10

3 3/8

32

Diam.

Circ.

Ft.

In.

Ft.

In

10

3

32

3 7/8

10

3

32

4 3/8

10

3

32

10

3

32

5 1/8

10

4

32

10

4

32

5 7/8

10

4

32

10

4

32

6 5/8

10

4

32

7

10

4

32

10

4

32

7 7/8

10

4

32

10

5

32

8 5/8

10

5

32

9

10

5

32

9 3/8

10

5

32

9 7/8

10

5

32

10¼

10

5

32

10 5/8

10

5

32

11

10

5

32

11 3/8

10

6

32

11¾

10

6

33

0 1/8

10

6

33

0 5/8

10

6

33

1

10

6

33

1 3/8

10

6

33

10

6

33

2 1/8

10

6

33

10

7

33

2 7/8

10

7

33

3 3/8

10

7

33

10

7

33

4 1/8

10

7

33

10

7

33

4 7/8

10

7

33

10

7

33

5 5/8

10

8

33

6 1/8

10

8

33

10

8

33

6 7/8

10

8

33

10

8

33

7 5/8

10

8

33

8

10

8

33

8 3/8

10

8

33

8 7/8

10

9

33

Diam.

Circ.

Ft.

In

Ft.

In.

10

9 1/8

33

9 5/8

10

33

10

10

9 3/8

33

10 3/8

10

33

10¾

10

9 5/8

33

11 1/8

10

33

11½

10

9 7/8

34

0

10

10

34

0 3/8

10

10 1/8

34

10

10¼

34

1 1/8

10

10 3/8

34

10

10½

34

1 7/8

10

10 5/8

34

2 3/8

10

10¾

34

10

10 7/8

34

3 1/8

10

11

34

10

11 1/8

34

3 7/8

10

11¼

34

10

11 3/8

34

4 5/8

10

11½

34

5

10

11 5/8

34

5 ½

10

11¾

34

5 7/8

10

11 7/8

34

11

0

34

6 5/8

11

0 1/8

34

7

11

34

7 3/8

11

0 3/8

34

11

34

11

0 5/8

34

8 5/8

11

34

9

11

0 7/8

34

9 3/8

11

1

34

11

1 1/8

34

10 1/8

11

34

10½

11

1 3/8

34

11

11

34

l1 3/8

11

1 5/8

34

11¾

11

35

0 1/8

11

1 7/8

35

11

2

35

0 7/8

11

2 1/8

35

11

35

11

2 3/8

35

2 1/8

11

35

11

2 5/8

35

2 7/8

Diam.

Circum.

Ft

In.

Ft.

In.

11

35

11

2 7/8

35

3 5/8

11

3

35

4

11

3 1/8

35

11

35

4 7/8

11

3 3/8

35

11

35

5 5/8

11

3 5/8

35

6

11

35

6 3/8

11

3 7/8

35

11

4

35

11

4 1/8

35

7 5/8

11

35

8

11

4 3/8

35

8 3/8

11

35

11

4 5/8

35

9 1/8

11

35

11

4 7/8

35

10

11

5

35

10 3/8

11

5 1/8

35

10¾

11

35

11 1/8

11

5 3/8

35

11½

11

35

11 7/8

11

5 5/8

36

Diam.

Circum.

Ft.

In.

Ft.

In.

11

36

11

5 7/8

36

1 1/8

11

6

36

11

6 1/8

36

1 7/8

11

36

11

6 3/8

36

2 5/8

11

36

3

11

6 5/8

36

11

36

3 7/8

11

6 7/8

36

11

7

36

4 5/8

11

7 1/8

36

5

11

36

5 3/8

11

7 3/8

36

5 7/8

11

36

11

7 5/8

36

6 5/8

11

36

7

11

7 7/8

36

7 3/8

11

8

36

11

8 1/8

36

8 1/8

11

36

11

8 3/8

36

9

11

36

9 3/8

11

8 5/8

36

Diam.

Circum.

Ft.

In.

Ft.

In.

11

36

10 1/8

11

8 7/8

36

10½

11

9

36

10 7/8

11

9 1/8

36

11¼

11

36

ll¾

11

9 3/8

37

0 1/8

11

37

11

9 5/8

37

0 7/8

11

37

11

9 7/8

37

1 5/8

11

10

37

2

11

10 1/8

37

11

10¼

37

2 7/8

11

10 3/8

37

11

10½

37

3 5/8

11

l0 5/8

37

4

11

10¾

37

4 3/8

11

10 7/8

37

11

11

37

11

11 1/8

37

5 5/8

11

11¼

37

6

11

11 3/8

37

6 3/8

11

11½

37

11

11 5/8

37

7 1/8

Diam.

Circum

Ft.

In.

Ft.

In

11

11¾

37

11

1l 7/8

37

7 7/8

12

0

37

8 3/8

12

0 1/8

37

12

37

9 1/8

12

0 3/8

37

12

37

9 7/8

12

0 5/8

37

10¼

12

37

10 5/8

12

0 7/8

37

11 1/8

12

1

37

11½

12

1 1/8

37

11¾

12

38

12

1 3/8

38

0 5/8

12

38

1

12

1 5/8

38

1 3/8

12

38

1 7/8

12

1 7/8

38

12

2

38

2 5/8

12

2 1/8

38

3

12

38

3 3/8

12

2 3/8

38

12

38

4 1/8

12

2 5/8

38

4 5/8

If a Hoop of larger diameter than 12 feet is required, double some number.

Observations on Tables relating to the Diameters and Circumferences of Circles.

I do not intend to enter into any labored argument to prove the general utility of these Tables, as their simplicity and clearness are sufficient to stamp their value to the artist and mechanic. It will be clearly perceived, on inspection, that the Table commences with as small a diameter as is generally used in hoops and rings, viz. one inch, and increases by the regular gradation of one-eighth of an inch, to upwards of twelve feet; and in the column marked Circumference, against each Diameter stand the respective circumferences: hence all that is necessary on inspecting these Tables is to enter into them with any proposed diameter or circumference, and an answer to the inquiry is immediately obtained.

Example.- Required the circumference of a circle, the diameter being 8 feet 7 7-8 inches?

In the column of circumferences, opposite the given diameter, stands 27 feet 2¼ inches, the circumference required.

But it will be necessary to observe, that in the formation of hoops and rings a contraction of the metal takes place. Now, the just allowance for this contraction is the exact thickness of the metal, which must be added to the diameter.

Ex. - In making a hoop whose diameter inside is 6 feet 9 1-8 inches, the thickness of the iron being ½ inch, this ½ inch must be added to the given diameter, which will make it 6 feet 9 5-8 inches; this will allow 1 5-8 inch for the contraction in bending in a hoop of the above diameter, giving the circumference or length of iron required for the hoop, 21 feet 4 3-8 inches.

The foregoing example appertains to the formation of hoops or iron bent on the flat; but in the formation of rings or iron bent on the edge, the same rule must also be followed, only taking care to add the breadth instead of the thickness. As for example:

To make a ring whose inside diameter is 8 feet 2¼ inches, the breadth of the iron being 2½ inches; by adding the 2½ inches to the given diameter, will increase it to 8 feet 4¾ inches; opposite to this diameter in the column of circumferences stands 26 feel 4½ inches, being the length of iron necessary for the ring.

The foregoing observations relate more particularly to plain hoops and rings; but as respects the hoops that are on the wheels of railway carriages, a difference must be observed, which is as follows: These hoops having a flange projecting on the one edge of the surface, it will be necessary, in addition to the thickness of the metal, to add two-thirds of the thickness of the flange to the diameter, as the flange side would contract considerably more than the plain surface; this is supposing the tires are in a straight form, but, in general, they come from the iron-works in a curved state. In the latter case, it will be only necessary to add the thickness of the bare metal, as the aforesaid portion of the thickness of the flange is allowed for in the curve. It has been found that the curve may be exactly obtained, by using four times the circumference of the hoop as a radius.

If the tire has not been previously curved, it may easily be done in the operation of bending; the smith must pay particular attention to this, or he will have his hoop bent in an angle.

But the practical utility of this Table is not confined to smiths alone; to the millwright it will be found equally useful and expeditious, as on a bare inspection of the Table he may ascertain the diameter of any wheel tha may be required to be made, the pitch and number of teeth being given.

Ex.-Suppose a wheel were ordered to be made to contain sixty teeth, the pitch of the teeth to be 3 7:8 inches, the dimensions of the wheel may be ascertained simply as follows:

Multiply the pitch of the tooth by the number of teeth the wheel is to contain, and the product will be the circumference of the wheel: thus with one-half of this number as a radius, the circumference of the wheel will be described.

3 7/8 inches pitch of the tooth.

Diameters And Circumferences Of Circles 59

However, by inspecting the column marked Circumference, I find the nearest number to this is 19 feet 4 3-8 inches, which is the eighth of an inch less than the true circumference; but if this 1.8 were divided into 60 equal parts, it would not make the difference of a single hair's-breadth in the size of each tooth; so that it is sufficiently near for any practical purpose. The diameter answering to this circumference is 6 feet 2 inches; consequently.