1. The screw of the Ajax is 16 feet diameter, 17 feet 11 inches pitch, and 3 feet 2 inches length; find the angle and area.

2. The screw of the Arrogant is 15 feet 6 inches diameter, 15 feet pitch, and 2 feet 6 inches length; find the angle and area.

3. The screw of the Blenheim is 16 feet diameter, 20 feet pitch, and 3 feet 4 inches length; find the angle and area.

Section 2.

4. The screw of the Dauntless is 14 feet 8 inches diameter, 18 feet pitch, and 3 feet length; find the angle and area.

5. The screw of the Desperate is 13 feet diameter, 14 feet pitch, and 2 feet 4 inches length; find the angle and area.

6. The screw of the Dwarf is 5 feet 8 inches diameter, 8 feet pitch, and 1 foot length; find the angle and area.

Section 3.

7. The screw of the Encounter is 12 feet diameter, 15 feet pitch, and 2 feet 6 inches length; find the angle and area.

8. The screw of the Fairy is 5 feet 4 inches diameter, 8 feet pitch, and 1 foot length; find the angle and area.

9. The screw of the Greenock is 14 feet diameter, 13 feet pitch, and 2 feet 2 inches length; find the angle and area.

Section 4.

10. The screw of the Hogue is 16 feet diameter, 20 feet pitch, and 3 feet 4 inches length; find the angle and area.

11. The screw of the Minx is 4 feet 6 inches diameter, 5 feet pitch, and 1 foot length; find the angle and area.

12. The screw of the Niger is 12 feet 6 inches diameter, 17 feet pitch, and 2 feet 10 inches length; find the angle and area.

Section 5.

13. The screw of the Phanix is 12 feet diameter, 12 feet 8 inches pitch, and 2 feet 1 inch length; find the angle and area.

14. The screw of the Plumper is 9 feet diameter, 5 feet 7 inches pitch, and 1 foot length; find the angle and area.

15. The screw of the Rattler is 10 feet diameter, 11 feet pitch, and 1 foot 3 inches length; find the angle and area.

Section 6.

16. The screw of the Reynard is 8 feet 9 inches diameter, 8 feet pitch, and 1 foot 4 inches length; find the angle and area. 17. The screw of the Rifleman is 8 feet diameter, 9 feet pitch, and 1 foot 6 inches length; find the angle and area.

18. The screw of the Sharpshooter is 9 feet diameter, 9 feet pitch, and 1 foot 6 inches length; find the angle and area.

Section 7.

19. The screw of the Teazer is 4 feet 6 inches diameter, 5 feet 10 inches pitch, and 1 foot length; find the angle and area.

20. The screw of the Vulcan is 14 feet diameter, 16 feet 6 inches pitch, and 2 feet 9 inches length; find the angle and area. 21. The screw of the Conflict is 13 feet 6 inches diameter, 16 feet 6 inches pitch, and 2 feet 9 inches length; find the angle and area.

PROBLEM 2.

To find the metacentre of a floating body.

Let ADB be a section of a floating body, divided symmetrically by the line O D, Gits centre of gravity, and P the A centre of gravity immersed, corresponding to the waterline A B.

The conditions of stability are, the weight of water displaced is equal to the weight of the floating body, and the

line joining P with G is perpendicular to the water-line A B.

Let Fig. 2 be the water-line section passing through A B, Fig. 1; and V the displacement in cubic ft. Divide the line K L into an even number of equal parts, each equal to (n), at the points a, b, c, &c.; and draw the ordinates a a', bb', cc', &c., perpendicular to the axis K L.

Cube each of the ordinates Kk, a a', bb', &c., and put them in Simpson's Rule and call the result B.

If G is below I, the floating body is stable; but if it is above, then the

L

floating body is unstable. (See Fincham's Outlines of Shipbuilding, page 157.)