652. There are two columns on the same plane, one 70 feet and the other 50 feet high. There is between these a column 5 feet high, the top of which is 100 feet from the summit of the higher, and 80 feet from the summit of the lower. Required the distance between the tops of the two columns.

653. A horse is tied with a rope 38 feet long. If he can reach 2 feet more, how many square rods of land can he graze over? 654. A pond is 25 rods in diameter. How many like this will it take to equal in area one 140 rods in diameter ?

655. Allowing that a horse tied with a halter can reach 3 feet more than the length of the halter, how long a rope must be used to allow a horse to feed over just an acre of ground?

656. What is the difference in the expense of fencing a circular 10-acre lot and one of the same area in a square form, if the fence costs 75 cents a rod?

657. The diameter of a circle is 10 inches; how many inches in the side of the inscribed square?

658. What is the side of the greatest square stick of timber that can be hewn from a log 18 inches in diameter ?

659. A circular field is 600 rods in circumference. What is the side of a square field that contains the same area?

660. What is the diameter of a circular pond that contains 625 times as much area as one 48 rods in diameter ?

661. The area of a triangle is 24 square meters and one side of it is 8 meters; what is the corresponding side of a similar triangle containing 96 square meters?

662. What is the side of a square that contains 361 times as much area as one whose side is 75 feet?

663. What is the side of a square equal in area to a circle 100 meters in diameter?

664. A circular field contains 10 acres; what is the length of its diameter ?

665. What is the area of a circular pond which shall contain 45 times as much area as one 35 rods in diameter ?

666. If a pipe 5 inches in diameter will discharge a certain quantity of water in 16 hours, in what time will a pipe 3 inches in diameter discharge the same quantity?

667. A bushel measure is 18 inches in diameter and 8 inches deep; what are the dimensions of a similar measure that holds half a bushel?

668. If a certain cistern can be emptied by a given pipe in 52 hours, how long will it take a pipe whose diameter is 2 times the diameter of the given pipe to empty it?

669. If a man dig a square cellar that measures 9 feet each way in 3 days, how long will it take him to dig one of the same depth measuring 12 feet each way?

670. What is the side of an equilateral triangle that shall contain 35 times as much area as one whose side is 6 feet?

671. If a pipe 3 centimeters in diameter will empty a cistern in 8 minutes, what is the diameter of a pipe that will empty it in 18 minutes?

672. How many bricks, 8 inches long, 4 inches wide, and 2 inches thick, will be required to build a wall 30 feet long, 8 feet high, and 2 feet thick?

673. How many bricks, whose dimensions are 8 by 4 by 2 inches, will it take to build the walls of a house 50 feet long, 32 feet wide, and 24 feet high, the walls to be 1 foot 6 inches thick, and no allowance made for doors and windows?

674. How many bricks, 8 by 4 by 2 inches, will be required to build a house 36 feet long, 27 feet wide, and 23 feet high, the walls being 1 foot 4 inches thick, the house having 5 doors, each 4 feet wide and 8 feet high, and 30 windows, each 3 feet wide and 6 feet high, no allowance being made for the space occupied by the mortar?

675. A garden whose breadth is 6 rods, and length twice its breadth, has a wall 2 feet thick and 4 feet high around it, outside of the line; what was the cost of this wall at 4 cents a cubic foot?

676. What will be the cost of digging a ditch around the garden above mentioned, within and adjacent to the wall, 3 feet wide, and 2 feet deep, at § of a cent a cubic foot?

677. What would be the cost of walling the garden above mentioned, the central line of the wall to be on the bounding line, the wall to be 2 feet thick and 4 feet high, at 64 cents a cubic foot?

678. How many bricks, each 8 inches long, 4 inches wide, and 2 inches thick, will make a cubical pile 13 feet each way ?

679. How high is a pile of wood which contains 10 cord feet if it is 9 feet long and 4 feet wide?

·680. If a sod 11⁄2 inches thick is taken from the entire surface of a field of one acre, how many cubic yards are taken?

681. Find the solid contents of a cone whose base is 3 feet in diameter and whose altitude is 8 feet.

682. How many cubic decimeters in a globe 5 decimeters in diameter ?

683. How many gallons will a circular cistern hold that is 6 feet in diameter and 10 feet deep?

684. How many quarts of milk will a pail contain whose diameter at the top is 11 inches, at the bottom 9, and whose depth is 8 inches?

685. How many pints does a coffee-pot hold that is 7 in. across the bottom, 4 in. across the top, and 8 in. high?

686. If the diameter of the earth is 7912 miles, how many square miles in its surface?

687. What is the diameter of a globe whose volume is 728 cubic meters?

688. How long is the edge of the greatest cube that can be cut from a 6-inch globe?

689. The weights of 3 stacks of hay of similar form are respectively 3, 5, and 7 tons, and the slant height of the least is 12 feet. Find the slant height of the other two.

690. What are the dimensions of a box similar to, and that will hold 3 times as much as, a box 8 by 6 by 4 inches?

691. If an iron ball 4 inches in diameter weighs 8 pounds, what is the weight of a ball 50 inches in diameter ?

692. If a stack of hay 26 feet high weighs 29 tons, what is the height of a similar stack which weighs 9 tons ?

693. How many bullets of an inch in diameter will be required to make a ball 4 inches in diameter?

694. If a loaf of sugar 10 inches high weighs 8 lb., what is the height of a similar loaf weighing 1 lb. ?

695. Suppose the diameter of the earth is 7912 miles, and that it takes 1404928 bodies like the earth to make one as large as the sun, what is the diameter of the sun?

696. A bin is 15 feet long, 5 feet wide, and 3 feet deep; what is the edge of a cubical box that will hold the same quantity of grain ?

697. If a ball 8 inches in diameter weighs 50 pounds, what is the diameter of a ball that weighs 164 pounds?

698. If a bell 6 inches high, 4 inches in diameter, and † of an inch thick weighs 4 lb., what are the dimensions of a similar bell that weighs 740 lb. ?

699. If a globe of gold 1 inch in diameter is worth $ 100, what is the diameter of a globe worth $3600?

700. A, B, and C own equal shares of a conical stack of hay 20 feet in height. If A takes his from the top, B next, and C last, what is the altitude of the part that each takes?

NOTATION AND NUMERATION.

505. In addition to the table on page 4 the periods above billions are trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions, undecillions, duodecillions, tredecillions, quatuordecillions, quindecillions, sexdecillions, etc.

506. And also, in addition to the table on page 102, the names of the decimal periods below billions are formed by changing the s of the names of the integral periods to ths.

507. The method of numeration, given on pages 4 and 102, is called the French method, and is the one generally used in this country.

508. In the English Method a period consists of six figures, as follows:

ENGLISH NUMERATION table.

509. In the French and English methods the written expressions are the same as far as, and including, hundred millions. But an English billion is a thousand French billions, an English trillion a million French trillions, and

so on.