4 inches long, the average breadth 18 inches, and the average thickness 15 inches?

389. To find the content of round timber,

RULE. Find one fourth of the mean girth, and square it, and multiply it by the length.

OBS. An allowance must be made for the thickness of the bark No rough timber under 6 inches in diameter is measured in this way. This rule, though generally used, gives the content too small.

EXAMPLES.

6. What is the content of a tree 24 feet long, and its mean girth 8 feet?

7. What is the content of a tree 30 feet long, and its mean girth 5 feet, 8 inches?

GAUGING.

SECTION XLIV.

390. GAUGING is the process of finding the content of vessels of all kinds.

391. The dimensions, in gauging, are taken on the inside of the vessel.

392. RULE. Add together the squares of the head, the bung, and twice the middle diameter. This sum, multiplied by the length, and also by .000566, gives the content in wine gallons; multiplied by .0004642, gives the content in beer gallons; by .000487, in dry gallons.

OBS. 1. This is the most accurate method of finding the contents in casks.

OBS. 2. The middle diameter may be found by measuring the

What is the rule for finding the content of round timber? What is gauging? What is the rule for gauging?

circumference of the cask half the distance between the bung and the head, and dividing it by 3.1416, and then subtracting twice the thickness of the staves.

OBS. 3. A diagonal rod is sometimes used for finding the content of casks, but it does not give the contents so accurately as the preceding rule.

1. What is the content, in wine gallons, of a cask whose length is 40 inches, the bung diameter 34 inches, the head 27, and the middle diameter 32 inches?

(342+272+642)×40.0005667=135.577.

EXAMPLES.

2. What is the content of a cask, in wine gallons, measuring 48 inches in length, the head diameter 34, the middle 36, and bung 40 inches?

3. What is the content of a cask, in wine gallons, measuring 50 inches in length, the bung diameter 36 inches, the middle 34, and the head 32?

4. What is the content of a cask, in wine gallons, measuring 50 inches in length, the bung diameter 40 inches, the middle 36, and the head 34?

TONNAGE OF VESSELS.

SECTION XLV.

393. THE following rule is adopted by ship carpenters, who build vessels at a certain price per ton:

RULE. Multiply the length of the keel, breadth at the main beam, and depth of the hold together, and divide their continued product by 95, and the quotient will be the tonnage.

In double-decked vessels, one half of the breadth is taken as the depth.

What is the carpenters' rule for finding the tonnage of vessels ?

GOVERNMENT RULE. If the vessel be double-decked, take the length from the fore part of the main stem to the after part of the main post, above the upper deck, the breadth at the broadest part above the main wales, half of which breadth shall be accounted the depth of such vessel, and deduct from the length of the breadth, and multiply the remainder by the breadth, and the product by the depth, and divide this last product by 95. The quotient will be the govern

ment tonnage.

If the vessel be single-decked, multiply the length and breadth, as before taken, by the depth, taken from the under side of the deck to the ceiling in the hold.

EXAMPLES.

1. What is the tonnage of a single-decked vessel, by the carpenters' rule, whose keel is 75 feet, the breadth 24 feet, and the depth 8 feet?

2. What is the tonnage of a double-decked vessel, by the carpenters' rule, whose keel is 80 feet, and breadth 27 feet?

3. What is the tonnage of a single-decked vessel, by the government rule, which measures in length 84 feet, in breadth 32 feet, and in depth 12.5 feet?

4. What is the tonnage of a double-decked vessel, by the government rule, which measures at the keel 120 feet, and 36 feet breadth at the beam?

MECHANICAL POWERS.

SECTION XLVI.

394. THERE are six mechanical powers, viz., the lever, the wheel and axle, the pulley, the inclined plane, the screw, and the wedge.

What is the government rule for finding the tonnage of vessels ? How many mechanical powers are there? What are they?

395. The lever is a bar, supposed to be inflexible, movable upon a fulcrum.

396. To find what weight can be raised by a given power,

RULE. The power is to the weight as the distance from the fulcrum to the weight is to the distance from the power to the fulcrum.

1. If the power be 150 pounds, the long arm 8 feet, and the short arm 2 feet, what weight can be raised?

OBS. The distance from the power to the fulcrum is called the long arm, the distance from the fulcrum to the weight, the short arm.

2. If the arms of a lever are 15 feet and 3 feet, and the weight 600 pounds, what is the power?

397. If the lever rest on two fulcrums, the whole length is to the short arm as the whole weight is to the weight on the short arm; or the long arm is to the short arm as the weight supported by the short arm is to the weight supported by the long arm.

EXAMPLES.

3. If A and B carry a weight of 300 pounds suspended upon a pole 9 feet long, and there is 5 feet between the weight and A, and 4 feet between the weight and B, how many pounds does each carry?

4. If A and B carry 150 pounds upon a lever 8 feet long, where must the weight be placed, that A may carry of it?

398. The principle of the wheel and axle is the same as that of the lever; the long arm of the lever

What is the lever? What is the rule for finding what weight can be raised by a given power? What is the principle of the wheel and

corresponding to half the diameter of the wheel, and the short arm to half the diameter of the axle.

EXAMPLES.

5. If the diameter of a wheel be 4 feet, and that of the axle 6 inches, what weight will 160 pounds raise ? 6. What weight will 300 pounds raise, if the diameter of a wheel be 10 feet, and that of the axle 2 feet?

399. In movable pulleys, the power is to the weight as 1 is to twice the number of pulleys.

EXAMPLES.

7. What weight can 300 pounds raise, with 3 movable pulleys?

8. What power can raise 2 tons, with 10 movable · pulleys?

OBS. In the preceding examples no allowance is made for friction. In all practical applications, this allowance must be made.

400. On an inclined plane, the length of the plane is to its perpendicular height as the weight is to the power.

EXAMPLES.

9. An inclined plane is 30 feet long, its perpendicular height is 6 feet. What power will draw up a weight of 500 pounds?

10. What power will draw a train of cars weighing 50,000 pounds up an inclined plane, which rises 10 feet in 60 rods?

401. The principle of the screw is the same as that of an inclined plane. The power is to the weight as the distance between two threads of the screw is to the circumference of a circle described by the power.

What is the proportion of the power, in movable pulleys, to the weight? What is the rule for the inclined plane? What for the screw?