1318. The strain upon a hempen cable being 10 tons, what must be its dimensions that it may bear this safely, and what additional strain will be produced by its own weight if it be 50 fathoms long?

1319. Show that if w be the weight of a unit of length of a bar of uniform section and length 7, the extension X produced by its own weight will be

where m is the modulus of elasticity.

1320. The bearing area of a wire rope of which the circumference is C, being (see Qu. 874), find the dimensions of an iron wire rope which will bear with safety a strain of 10 tons.

1321. Find the length of copper wire rope which it will be just possible to suspend by one end.

1322. What must be the dimensions of a square cast-iron column to support safely, a mass of brick work 12 feet high, one foot thick and six feet long?

1323. It is proposed to substitute sandstone columns for some of granite originally planned, what must be the change in dimensions?

1324. Define the "unit of work," and find the number of units expended in raising a weight of 1 ton of building materials to a height of 40 feet.

1325. Find the time required to raise a block of granite 4 feet long, 3 feet broad, and 2 feet thick, to a height of 20 feet, by two men working at the winch of a traversing crane, the number of units of work by each man per minute thus working being 2600, and the modulus of the machine ·8.

1326. How many gallons of water per minute can be pumped up from the bottom of a shaft 200 fathoms deep by an engine working at a pressure of 15 lbs. to the square inch; the diameter

of the piston being 40 inches, the length of stroke six feet, the number of strokes 10 per minute, and the modulus 65 ?

1327. Supposing the water in the last question to be carried over a wheel of 25 feet diameter which works a pump the water from which also passes over the wheel, find the whole quantity raised, the modulus of the wheel being 55.

1328. A stream of water 10 feet broad and 5 feet deep, flowing at the rate of 37 feet per minute, is conducted over a waterwheel 15 feet in diameter, which works a pump by which the water from the stream is raised to a height of 20 feet; what is the quantity of water raised per hour, the modulus being ·65 ?

1329. Find the horse power of the wheel in question 1328, and compare it with that of the engine in question 1326.

1330. The diameter of the piston of an engine is 30 inches, the mean pressure of the steam is 10.5 lbs. per square inch, the length of the stroke is 12 feet, and the number of strokes per minute is 10; find how many cubic feet of water per hour the engine will raise from a depth of 200 fathoms, the modulus of the engine being 6.

1331. In what time would two locomotives of 100 horse power each, convey a battery of field artillery from Woolwich to Brighton (60 miles), the engines, trucks, and carriages weighing W tons, and the men, guns, horses, and material A tons, supposing a tons to be conveyed in the trucks and carriages at each trip, and the resistances to be 10 lbs. per ton?

1332. The piston of an engine is 3 feet in diameter, the length of stroke 5 feet, the number of strokes per minute 12, the pressure per square inch 15 lbs., and the modulus of the engine is 75; find the quantity of water which can be pumped from a depth of 30 fathoms.

1333. The piston of an engine is 48 in. in diameter; the pressure upon it 15 lbs. per sq. in.: the length of the stroke 5 feet, and the number of strokes 10 per minute; find the horse power of the engine,

1334. If the length of stroke be l, the number of strokes per minute n, and the pressure p; what must be the diameter of the piston in order that the horse power of the engine may be K}

1335. What must be the horse power of an engine which will raise a tilt hammer weighing 1 ton 25 times a minute, the lift being 2 feet?

1336. A locomotive has to move a train of 12 carriages, each weighing, with the passengers, 4 tons, at the rate of 50 miles an hour; what must be its horse power if the resistances be 10 lbs. per ton and the weight of the engine and tender 16 tons?

1337. If the weight of a train be 30 tons and that of the engine and tender 15 tons; find the radius of the driving wheel in order that with a pressure of 15 lbs., pistons of 14 in. diameter, a stroke of 3 feet, and a modulus of 75, the engine may work smoothly, and its full power be available, the resistances being estimated at 10 lbs. per ton.

1338. Find an expression for the diameter of the piston of a locomotive in terms of the radius of the driving wheel, p the pressure per sq. in., 7 the length of stroke, R the total resistance in lbs. and m the modulus.

1339. Show that the length of stroke of a locomotive should be equal to the product of the total resistance, and the radius of the driving wheel, divided by the product of the modulus and the pressure on the piston, and multiplied by π.

1340. A quantity of ballast is to be conveyed in trucks to a distance of 10 miles, by a train of 8 trucks, each weighing 2 tons, and capable of carrying 7 tons of ballast. The engine is of 20 horse power, and weighs with its tender 12 tons; and the resistances are 15lbs. per ton. What quantity of ballast can be delivered in 72 hours, allowing half an hour for discharge and loading at each trip?

1341. How many bushels of coal will be consumed in 24 hours by an engine of 50 horse power, if its duty be 55 millions?

1342. How many bushels of coal will be consumed by an engine of 100 horse power and 70 millions duty, in raising 200000 cubic feet of water from a depth of 150 fathoms ?

1343. An engine of 65 millions duty has to pump water up three separate shafts of 70, 100, and 120 fathoms deep respectively, viz. 10 cubic feet per minute from the first, 20 cubic feet from the second, 50 cubic feet from the third. How many bushels of coal will the engine consume in 12 hours?

1314. If the depths of a number of shafts of a mine be ffff&c. feet, and the number of cubic feet of water pumped from them per minute be u1, w2, w ̧, w, &c. respectively, find the horse power of the engine; and its duty, supposing it to consume B bushels of coal in 24 hours.

1345. Find the number of units of work required to wind up of 4 in. circumference 800 feet long?

a rope

1346. What is the number of units of work required to wind the same rope, supposing it to be laid horizontally on the ground, the coefficient of friction being "70?

1347. Two boxes are worked up and down a shaft 150 feet deep by a connecting rope over a drum. The load each box will contain is 3 cwt. of coal. The engine has a piston of 8 inches diameter, the pressure of steam is 10 lbs., the length of the stroke 3 feet, the number of strokes 20 per minute, and the modulus 52. Find the quantity of coal raised per hour.

1348. Find the quantity of coal raised per hour by the same engine, supposing that only one box be used, that the time occupied in emptying the box added to the time of descent will be equal to the time of ascent of the loaded box, and that no time is lost in unhooking the empty box and hooking the full one at the bottom of the shaft; the rope being 3 inches in circumference and the weight of each box 56 lbs.

1349. Find the number of units of work expended in distributing 5000 tons of ballast equally over a line of railway, sup

posing 18 tons to cover 10 yards length of the line, and the resistances to be 12 lbs. per ton.

1350. Find the number of units of work required to hoist the main-sail of a ship 50 feet by 30 feet to a height of 40 feet, supposing the sail-cloth to weigh 4 lbs. per square yard, and the yard to weigh 5 cwt.

DYNAMICS.

1351. Define the terms "uniform motion," "variable motion," "velocity," "moving force," and "accelerating force."

1352. State the three "laws of motion," and give illustrations of their truth from familiar facts.

1353. State the second law of motion, and mention experimental facts which would lead to its assumption. What is the nature of the final evidence which is considered conclusive as to the truth of this law?

1354. Define "variable velocity;" explain how it is produced by the action of a constant force; state how this connexion is made use of in the dynamical measurement of such a force; and find the numerical representative of the force of gravity, supposing the minute and the yard to be the units of time and space respectively.

1355. Find the unit of space when the accelerating force of gravity is 14, and the unit of time 5 seconds.

1356. Show that, when a body moves under the influence of a constant force ƒ, the space s passed over in the time t will be represented by the formula

1357. An engine starts a train with a pressure which continues uniform for 5 minutes, when it is found that the train