Diam.

Circ.

Ft

In.

Ft.

In.

6

1

5

4

1

6

1

7

1

7

7

1

8

1

9

1

9 7/8

1

l0 5/8

8

1

11 3/8

2

0 1/8

2

0 7/8

2

1 5/8

9

2

2 3/8

2

3

2

3

2

4

10

2

5

2

6

2

6

2

7

11

2

8 1/8

2

8 7/8

2

9 5/8

2

10 3/8

1

0

2

11 1/8

2

11 7/8

3

0 5/8

3

1 3/8

1

1

3

2

3

2

3

3

3

4

1

2

3

5

3

5

3

6

3

7 1/8

1

3

3

7 7/8

3

8 5/8

3

9 3/8

3

10 1/8

I

4

3

10 7/8

3

11 5/8

4

0

4

1

1

5

4

1

4

2

4

3

4

4

Diam.

Circ.

Ft

In.

Ft.

In.

1

6

4

4

4

5 3/8

4

6 1/8

4

6 7/8

1

7

4

7 5/8

4

8 3/8

4

9 1/8

4

9 7/8

1

8

4

10 5/8

4

11 3/8

5

0

5

0

1

9

5

1

5

2

5

3

5

3

1

10

5

4 3/8

5

5 1/8

5

5 7/8

5

6 5/8

1

11

5

7 3/8

5

8 1/8

5

8 7/8

5

9 5/8

2

0

5

10

5

11

5

11

6

0

2

1

6

1

6

2

6

2

6

3 3/8

2

2

6

4 1/8

6

4 7/8

6

5 5/8

6

6 3/8

2

3

6

7 1/8

6

7 7/8

6

8

6

9

2

4

6

10

6

10

6

11

7

0

2

5

7

1

7

1

7

2 3/8

7

3 1/8

Diam.

Circ.

Ft

. In.

Ft.

In.

2

6

7

3 7/8

7

4 5/8

7

5 3/8

7

6 1/8

2

7

7

6 7/8

7

7

7

8

7

9

2

8

7

9

7

10

7

11

8

0

2

9

8

0 5/8

8

1 3/8

8

2 1/8

8

2 7/8

2

10

8

3 5/8

8

4 3/8

8

5 1/8

8

5

2

11

8

6

8

7

8

8

8

8

3

0

8

9

8

10

8

11

8

11 5/8

3

1

9

0 3/8

9

1 1/8

9

1 7/8

9

2 5/8

3

2

9

3 3/8

9

4 1/8

9

4

9

5

3

3

9

6

9

7

9

7

9

8

3

4

9

9

9

9 7/8

9

10 5/8

9

11 /8

3

5

10

0 1/8

10

0 7/8

10

1 5/8

10

2 3/8

Diam.

Circ.

Ft

In.

Ft.

in.

3

6

10

3

10

3

10

4

10

5

3

7

10

6

10

6

10

7

10

8

3

8

10

8 7/8

10

9 5/8

10

10 3/8

10

11 1/8

3

9

10

11 7/8

0 5/8

1 3/8

2

3

10

2

3

4

5

3

11

5

6

7 1/8

7 7/8

4

0

8 5/8

6 3/8

10 1/8

10 7/8

4

1

11 5/8

12

0

12

1

12

1

4

2

12

2

12

3

12

4

12

4

4

3

12

5

12

6 1/8

12

6 7/8

12

7 5/8

4

4

12

8 3/8

12

9 1/8

12

9 7/8

12

10

4

5

12

11

13

0

13

0

13

1

Diam.

Circ

Ft

. In.

Ft.

In.

1

6

13

2

13

3

13

3

13

4 3/8

1

7

13

5 1/8

13

5 7/8

13

6 5/8

13

7 3/8

4

8

13

8 1/8

13

8 7/8

13

9 5/8

13

10

4

9

13

11

13

11

14

0

14

1

1

10

14

2

14

2

14

3 3/8

14

4 1/8

4

11

14

4 7/8

14

5 5/8

14

6 3/8

14

7 1/8

5

0

14

7 7/8

14

8

14

9

14

10

5

1

14

10

14

11

15

0

15

1

5

2

15

1 5/8

15

2 3/8

15

3 1/8

15

3 7/8

5

3

15

4 5/8

15

5 3/8

15

6 1/8

15

6 7/8

5

4

15

7

15

8

10

9

15

9

5

5

15

10

15

11

16

0

16

0 5/8

Circumferences For Angled Iron Hoops Angle Inside

Diam.

Circ.

Ft

in.

Ft

In.

6

1

8

1

9 3/8

1

10

1

l1 1/8

7

1

11 7/8

2

0

2

1 5/8

2

2

8

2

3 3/8

2

4

2

5

2

5 7/8

9

2

6

2

7 5/8

2

8

2

9 3/8

10

2

10

2

11

2

11 7/8

3

0

.

11

3

1 5/8

3

2

3

3 3/8

3

4

1

0

3

5

3

5 7/8

3

6

3

7 5/8

1

1

3

8

3

9 3/8

3

10 1/8

3

11

1

2

3

11 7/8

4

0

4

1 5/8

4

2

1

3

4

33/8

4

4 1/8

4

5

4

5 7/8

1

4

4

6

4

7 5/8

4

8

4

9 3/8

1

5

4

10 1/8

4

11

4

11 7/8

5

0

Diam

Circ.

Ft

In

Ft

In.

1

6

5

1 5/8

5

2

5

3

5

4 1/8

1

7

5

5

5

5 7/8

5

6

5

7

1

8

5

8

5

9

5

10 1/8

5

11

1

9

5

11 7/8

6

0

6

1 5/8

6

2

1

10

6

3

6

4 1/8

6

5

6

5 7/8

1

l1

6

6

6

7 5/8

6

8 3/8

6

9

2

0

6

10 1/8

6

11

6

11 7/8

7

0

2

1

7

1 5/8

7

2 3/8

7

3

7

4 1/8

2

2

7

5

7

5 7/8

7

6

7

7

2

3

7

8 3/8

7

9

7

10 1/8

7

11

2

4

7

11

8

0

8

1

8

2 3/8

2

5

8

3

8

4 1/8

8

5

8

5 7/8

Diam

Circ.

Ft.

in

Ft.

In

2

6

8

6

8

7

8

8 3/8

8

9

2

7

8

10 1/8

8

11

8

11 7/8

9

0 5/8

2

8

9

1

9

2 3/8

9

3

9

4 1/8

2

9

9

5

9

5 7/8

9

6 5/8

9

7

2

10

9

8 3/8

9

9

9

10 1/8

9

11

2

11

9

11 7/8

10

0 5/8

10

1

10

2 3/8

3

0

10

3

10

4 1/8

10

5

10

5 7/8

3

1

10

6 5/8

10

7

10

8 3/8

10

9

3

2

10

10 1/8

10

11

10

11

11

0 5/8

3

3

11

1

11

2 3/8

11

3

11

4 1/8

3

4

11

5

11

5

11

6 5/8

11

7

3

5

11

8 3/8

11

9

11

10 1/8

11

10 7/8

Diam

Circ.

Ft

In

Ft.

In

3

6

11

11

12

0 5/8

12

1

12

2 3/8

3

7

12

3

12

4 1/8

12

4 7/8

12

5

3

8

12

6 5/8

12

7

12

8 3/8

12

9

3

9

12

10

12

10 7/8

12

11

13

0 5/8

3

10

13

1

13

2 3/8

13

3

13

4

3

11

13

4 7/8

13

5

13

6 5/8

13

7

4

0

13

8 3/8

13

9

13

10

13

10 7/8

4

1

13

11

14

0 5/8

14

1

14

2 3/8

4

2

14

3 1/8

14

4

14

4 7/8

14

5

4

3

14

6 5/8

14

7 3/8

14

8 3/8

14

9 1/8

4

4

14

10

14

10 7/8

14

l1

15

0 5/8

4

5

15

1

15

2

15

3 1/8

15

4

Diam

Circ.

Ft.

In

. Ft.

In.

4

6

15

4 7/8

15

5

15

6 5/8

15

7

4

7

15

8

15

9 1/8

15

10

15

10 7/8

4

8

16

11

16

0 5/8

16

1

16

2

4

9

16

3 1/8

16

4

16

4 7/8

16

5

4

10

16

6 5/8

16

7 3/8

16

8

16

9 1/8

4

11

16

10

16

10 7/8

16

11

17

0 5/8

5

0

17

1

17

2

17

3 1/8

17

4

5

1

17

4 7/8

17

5

17

6

17

7 3/8

5

2

17

8

17

9 1/8

17

10

17

10 7/8

5

3

17

11

18

0

18

1 3/8

18

2

5

4

18

3 1/8

18

4

18

4 7/8

18

5

5

5

18

6

18

7 3/8

18

8

18

9 1/8

Observations on Table containing the Circumferences foR Angled Iron Hoops. - Angle Outside.

As this Table will be useful to those smiths who chiefly work angled iron, it will be necessary to remark, that the observation made on Tables relating to the Diameters and Circumferences of Circles, respecting adding the thickness of the iron to the diameter, must be attended to in this, with this difference, - the breadth of the angle must be added to the diameter.

Example. - Suppose a hoop is wanted to be made of 2 inch angled iron, whose diameter inside must be 12 inches. Here the 2 inches must be added to the 12 inches, which raises the number to 1 foot 2 inches. Looking into the Table, I find the circumference, or length of iron requisite for the hoop, is 3 feet 6 inches.

Observations on Table containing the Circumferences for Angled Iron Hoops. - Angle Inside.

The observations respecting this Table are the reverse to those on the preceding one, - viz. the breadth of the angle must be taken from the diameter, - for this reason, that the diameter is taken from outside to outside of the ring.

Suppose a ring is to be made of angled iron, whose diameter outside is to be 12 inches, the breadth of the angle 2 inches; then, by taking 2 inches from 12 inches, we have left 9 inches. Looking into the Table in the column of diameters, I find in the circumference column, opposite 9 inches, 2 feet 8 inches, which is the length of iron necessary for the ring.

It has been already observed, that between angled and plain iron a considerable difference exists with regard to the proportion of the circumference to the diameter: this is owing to the angle or flange on one side of the bar, and when the iron is formed into a hoop: it contracts more or less, as the angle or flange may be inside or outside of the hoop. From repeated ex periments on this subject, I have ascertained that the proportions of the diameters to the circumferences are as follows:-For the angle inside as 1: 34248, and for the angle outside the hoop, as 1: 2.9312:: Diam: Circ'f.

Problem -To find the circumference of an ellipse, or an oval hoop or ring.

Rule. - Add the length of the two axes together, and multiply the sum by 1.5708 for the circumference; or as it may be used in the Table of Circumferences, take half the sum of the axes as a diameter, with the breadth of the iron added, and enter the Table of Circumferences where it will be found.

Ex. - Required the circumference of an elliptical hoop, whose axes are 18 and 13 inches, the thickness of the iron being 2 inches.

18 + 13 = 31 2 = 15 + 2 = 18 inches the diameter.

Entering into the Table of Diameter with 18 inches, the circumference will be found to be 4 feet 9 inches.

In constructing elliptical hoops of angled iron, with the angle outside, reference must be made to the Tables for hoops of angled iron; the operation will be similar to the above example. But in hoops where the angle is inside, the thickness of the iron must be taken from half the sum of the axes.

Note. - It must be observed, that in the examples given in the Observations on Table relating to the Diameters and Circumferences of Circles, and also on hoops formed of angled iron, that those circumferences are nothing more than the ends of the iron meeting together; therefore, every smith must allow for the thickening of the ends of the metal previous to scarving the same in order to weld it