TO MEASURE A PRISM.

RULE.-Find the surface of one end, and multiply that by the length.

What are the contents of a prism, each of its sides being 10 inches, and the length 12 feet? Ans. 3,6.

TO MEASURE A PYRAMID.

RULE. Find the surface of the base, and multiply that by one third of the height.

What are the solid contents of a triangular pyramid, each of its sides being 13, and the height 48?

Ans. 1144.

TO MEASURE A SPHERE, OR GLOBE.

RULE.-Multiply the cube of the diameter by ,5236.

What are the solid contents of a globe, its diameter being

4,5?

Ans. 47,71305.

XXX. Calculation of Speeds.

TO FIND THE SPEED OF ANY GIVEN SHAFT.

RULE.-Begin at the water wheel, and trace out all the driving and driven wheels separately, from the first driver to the last driven on the first end of the given shaft. Multiply the number of teeth in all the driving wheels together, and the product by the revolutions of the water wheel per minute; then multiply all the driven wheels together, and divide the product of the former by the product of the latter; the quotient will express the revolutions per minute of the given shaft.

There is a water wheel which performs 24 revolutions per minute. Connected with this water wheel are 2 driving wheels, and 3 driven wheels; the first driving or water wheel has 90 teeth, the second 54, and the third 48. The first driven wheel has 45, the second 36, and the third 36. How many revolutions per minute has the last driven wheel?

TO FIND THE REVOLUTIONS PER MINUTE OF THE LAST DRIVEN, WHEN BANDS OR BELTS ARE USED.

RULE.-Trace out all the driving and driven pulleys or drums, from the main shaft to the one the revolutions of which are sought. Multiply the diameters of all the driving pulleys or drums together, and the product by the revolutions per minute of the main driving shaft; then multiply the diameters of all the driven pulleys or drums together, and

divide the product of the former by the product of the latter; the quotient will express the revolutions per minute of the last driven shaft, or wheel.

Suppose the diameter of the driving drum on a main shaft to be 18 inches, and driving a changing or speed pulley of 16 inches; on the same shaft with which there is another driving drum of 18 inches, driving a pulley on the end of the cylinder, or frame shaft, of 16 inches diameter. If the speed of the main shaft is 108 revolutions per minute, what is the number of revolutions per minute of the last driven shaft, or wheel?

Speed of main shaft....108 Diam. of 1st driv. pulley. 16 Diam. of drum or shaft ..18 in., 2d do.

864

108

1944

Diam. of 2d driving drum. 18

15552

1944

.16

96

16

256

34992-256-136,6875, the revolu

tions per minute of the last driven shaft.

Ans. 136,6875-13617.

It may be laid down as a general rule, that all these calculations of speeds proceed upon one uniform principle, viz. Separate all the driving wheels or pulleys from the driven; and if wheels, multiply the number of teeth; but if pulleys or drums, multiply the diameters of all the drivers together, and the product by the speed given: then multiply all the driven together, and divide the product of the former by the product of the latter, and the quotient will be the speed sought.

There is a water wheel, the velocity of which is 10 revolutions per minute. To this wheel is attached a driving wheel, containing 200 teeth. This wheel (of 200 teeth) drives a pinion (on the first driven shaft) of 40 teeth, and

on this shaft is a pulley or drum, of 48 inches diameter. This pulley drives, by means of a belt or band, a pulley of 24 inches diameter, which is on the main shaft, or drum. On this shaft there is a pulley of 18 inches diameter. The pulley of 18 in. diameter drives, by means of a belt or band, a pulley of 9 inches diameter. On the same shaft to which the pulley of 9 in. diameter is attached, is a pulley of 20 in. diameter. This pulley drives, by means of a belt or band, a pulley of 2 in. diameter, on a lathe spindle. Required the revolutions per minute of the lathe spindle.

Ans. 2000 revolutions per minute.

MISCELLANEOUS EXAMPLES.

1. At 2 bu. and 6 qts. of ashes per pound, how many bushels of ashes will pay for 11 pounds and 5 oz. of tea? Ans. 24,74609375=24 bu. 23 qts. 7 gills.

2. At 12 yards per cord for wood, how much cloth would be required to pay for 17 cords and 7 cord feet of wood? Ans. 224,21875-2247 yds. 3. At 2 bu. and 12 qts. of wheat per barrel of soap, how many bushels of wheat would be required to pay for 79,26 barrels of soap? Ans. 188,2425-188 bu. 7,84 qts.

4. At one cord and two cord feet of wood per yard of broadcloth, how much wood must be given in exchange for 11 yds.?

Ans. 14,609375=14 cords, 4 cord feet, 14 cubic feet.

5. At 2 yards of cotton cloth per pound of butter, how much cloth would pay for 5 pounds and 3 ounces of butter? Ans. 11,0234375±11 yds. and 6375 of an inch. 6. If a man turn 2 feet and 6 inches of iron in one hour, how much would he turn in 2 hours and 3 minutes?

Multiply 2 h. and 3 m. by 2 ft. and 6 in.

Ans. 5,125=5 feet and 14 inch. 7. What would be the interest on 11 bu. and 11 qts. of potatoes for one year, at I quart of corn per bushel ?

Ans. ,3544921875 of a bushel=11 qts. 2 gills.

8. What would be the interest on 19 pounds and 15 oz. of butter for one year, at 1 pint of peas per pound?

Ans. 3115234375 of a bushel 1 pk. 1 qt. 1 pt. 3 gills.

9. What would be the interest on 9 barrels and 13 galls. of cider for 2 years, 5 m. and 11 days, at 6 qts. of soap per barrel of cider per year? Ans. 1,07902425130208

of a bushel=1 bar. 2 galls. 2 qts.,92 gills.

10. What would be the interest on 39 bu. 31 qts. of corn for 3 years, 7 months, and 17 days, at 13 ounces of cheese per bushel per year? Ans. 117,9008734809027 pounds.

11. A gentleman, being asked how much money he had, replied, If I had as much more as I now have,

as much, as much, as much, and as much, I should then have $1305; what was the amount of money that he had?

Ans. $360.

12. A, B, C, and D spent at a reckoning 105 s.; but being intoxicated, agreed that A should pay of this sum, B, C, and D ; what was each man's bill?

9

13. Divide $2400 between A, B, C, D, E, F, G, and H, giving to A, B, C, D, E, F, G 2%, and H. Ans. A's, $320; B's, $240; C's, $192; D's, $160; E's, $120; F's, $576; G's, $432; H's, $360.

14. Divide $92,15 among four men, giving them in the following proportion :-to A, B, C, D.

Ans. A's, $32,331; B's, $24,25; C's, $19,4; D's, $16,163.

To find the price of any thing by the ton, a ton being the unit. The point will be at the left of hundreds.

Multiply the whole number of pounds by one half the price. Or, divide the number of pounds by 2000, and the quotient will be tons and the decimal parts, which multiply by the whole price.