It may be observed, that when a cask is reduced to a cylinder, its contents may be found in cubical inches, and thence its contents in bushels, or any other of the measures of capacity.

The length of the cask is most conveniently taken by callipers; allowing for the thickness of both heads, from 1 to 2 inches, according to the size of the cask. When no callipers can be had, the length of the stave must be taken in a right line, and a proper deduction made for the chimes, with that for the heads. The head diameter is to be taken within the chimes, and from .3 to .6 of an inch must be deducted, on account of the greater thickness of the stave inside the head.

29. How many gallons will a cask contain, the inter or of which measures 34.5 inches in length, 19 inches in diameter at the bung, and 16 inches in diameter at the head; the staves being much curved?

30. How many gallons will a cask contain, the dimensions of which are 43 inches in length, 31.4 inches bung diameter, and 26 inches head diameter; the staves being but little curved ?

31. Find the capacity of a cask measuring 52 inches in length, 33.5 inches bung diameter, 25.3 inches head diameter, and of medium curve between the bung and head.

TONNAGE OF VESSELS.

There are two methods of measuring a vessel practised -one by the ship-carpenter, who builds the vessel at a certain price per ton, and another by the officers of government, who collect the revenue.

CARPENTERS' RULE. For single-decked vessels, multiply together the length of the keel, the breadth at the main beam, and the depth of the hold-all in feet-and divide the product by 95; the quotient is the tonnage. For double-decked vessels, take half the breadth at the beam for the depth of the hold, and work as before.

When a single-decked vessel has its deck bolted at any height above the wale, the carpenter is usually paid for

one-half of this extra height; that is, one-half of the height above the wale is added to the depth below the wale, and this sum is used in the calculation, as the depth of the hold.

GOVERNMENT RULE. "If the vessel be double-decked, take the length thereof from the fore part of the main stem, to the after part of the stern-post, above the upper deck; the breadth thereof at the broadest part above the main wales, half of which breadth shall be accounted the depth of such vessel, and then deduct from the length, three-fifths of the breadth, multiply the remainder by the breadth and the product by the depth, and divide this last product by 95, the quotient whereof shall be deemed the true contents or tonnage of such ship or vessel; and if such ship or vessel be single-decked, take the length and breadth, as above directed, deduct from said length threefifths of the breadth, and take the depth from the under side of the deck plank to the ceiling in the hold, then multiply and divide as aforesaid, and the quotient shall be deemed the tonnage."

32. What is the carpenter's tonnage of a single-decked vessel, the keel of which measures 60 feet, the breadth 20 feet, and the depth 8 feet?

33. What is the carpenter's tonnage of a double-decked 'vessel of 72 feet keel, and 22.5 feet breadth?

34. A merchant agreed with a carpenter to build a single-decked vessel of 58 feet keel, 20 feet breadth at the beam, and 8 feet hold, but afterwards chose to make the hold 10 feet deep, by raising the deck 2 feet above the wale. What tonnage must be paid for?

35. What is the government tonnage of a double-decked vessel, 110.5 feet keel, and 30.6 feet breadth at the beam'

36. What is the government tonnage of a single-decked vessel, which measures 76.4 feet in length, 28.6 feet in breadth, and 12.3 feet in depth?

37. What is the government tonnage of a single-decked vessel, whose length is 66 feet, breadth 20 feet, and depth 9 feet?

XL.

MECHANICAL POWERS.

The MECHANICAL POWERS are certain simple instru ments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually ac counted six in number; viz. the Lever, the Wheel and Aale, the Pulley, the Inclined Plane, the Wedge, and the Screw.

The advantage gained by the use of the mechanical powers, does not consist in any increase of the quantum of force exerted by the moving agent, but, in the concentration of force; that is, in bringing the whole force of power acting through a greater space, into an action within a less space. The principle is illustrated by the consideration, that the quantum of force necessary to raise 1 pound 10 feet, will raise 10 pounds 1 foot.

Weight and Power, when opposed to each other, sig nify the body to be moved and the body that moves it.

THE LEVER.

A lever is any inflexible bar, which serves to raise weights, while it is supported at a point, which is the centre of its motion, by a

fulcrum or prop. There are several kinds of lever used in mechanics; the more common kind, however, is that which is shown above.

As the distance between the weight and fulcrum is to the distance between the power and fulcrum, so is the power to the weight.

It must be observed, that, in the above proportion, anu in all the succeeding proportions of weight and power, the power intended is only sufficient to balance the weight. If the weight is to be raised, sufficient power must be

added to overcome friction; then any further addition of power will produce motion; and the comparative velocity of the weight and power, will depend on the comparative length of the two arms, of the lever. It is a universal principle in mechanics, that the ratio of the power to the weight is equal to the ratio of the velocity of the weight to the velocity of the power

1. If a man weighing 160 pounds rest on the end of a lever 10 feet long, what weight will he balance on the other end, the fulcrum being 1 foot from the weight?

In this example, the distance between the weight and fulcrum being 1 foot, that between the power and fulcrum is 10--19 ft. Then 1 ft. : 9 ft. 160 lb. : A

2. Suppose a weight of 1440 pounds is to be raised. with a lever 10 feet long, the fulcrum being fixed 1 foot from the weight; what power must be applied to the other end of the lever, to effect a balance?

(9ft.: 1ft.1440lb. : A)

3. If a weight of 1440 pounds be placed 1 foot from the fulcrum; at what distance from the fulcrum must a power of 160 pounds be placed, to balance the weight? (160lb. 1440 lb. 1 ft.

A)

4. At what distance from a weight of 1440 pounds must the fulcrum be placed, so that a power of 160 pounds, applied 9 feet from the fulcrum, will effect a balance?

(1440lb. 160 lb. 9 ft. A)

:

5. If one arm of a lever be 44 feet, and the other 5 feet, what power must be applied to the longer arm, to balance a weight of 500 pounds on the shorter arm?

6. Suppose a lever 6 feet long, with one end applied to a rock, which weighs 1000 pounds, and resting on a fulcrum 1 foot from the rock; what power must be applied to the other end, to balance the rock?

7. Suppose a bar 12 feet long to have 60 pounds attached to one end, and 30 pounds to the other, at what distance from each end must a fulcrum be placed, to produce a balance?

8. If A and B carry a weight of 250 pounds, suspended upon a pole between them, 5 feet from A, and 3 feet from B, how many pounds does each carry?

THE WHEEL AND AXLE.

The wheel and axle are here represented, with the weight attached to the circumference of the axle, and the power applied to the circumference of the wheel. The principle of the lever is obvious in the wheel and axlethe axis or common centre being the fulcrum, the circumference of the wheel being the power end of the lever, and the circumference of the axle, the end applied to the weight. Hence, the radius of the axle is to the radius of the wheel, as the power is to the weight: or, by a statement more frequently convenientAs the diameter of the axle is to the diameter of the wheel, so is the power to the weight.

9. A mechanic would make a windlass in such manner, that 1 pound applied to the wheel, shall be equal to 10 pounds suspended from the axle. Now, supposing the axle to be six inches in diameter, what must be the diameter of the wheel?

10. Suppose the diameter of a wheel to be 8 feet, what must be the diameter of the axle, that I pound on the wheel shall balance 15 pounds on the axle ?

11. Suppose the diameter of an axle to be 4 inches, and that of the wheel 3 feet; what power at the wheel will balance 28 pounds at the axle ?

12. If the diameter of a wheel be 7 feet, and that of the axle 8 inches, what weight at the axle will balance 40 pounds at the wheel?

13. There are two wheels; one of which is 6 feet in hameter, with an axle of 9 inches diameter; and the other Is 4 feet in diameter, with an axle of 7 inches diameter. Suppose the power cord of the smaller wheel to be coiled upon the axle of the larger; what weight on the axle of the smaller wheel would be balanced 100 at the power cord of the larger wheel?