6. What is the cube root of 729? of 1,728? of 3,375? of 8,000? of 10,000? of 12,000? of 15,625? of 27,000? of 30,000? of 45,000? of 60,000?

Answers. 9; 12; 15; 20; 21.52; 22.89; 25; 30; 31.06; 35.6 39.16.

7. There are 2,150 cubic inches in a bushel; required the side of a cube that will contain 1 bushel.

Ans. 12.88 inches nearly.

8. There are 282 cubic inches in an ale gallon; what is the side of a cube that will hold an ale gallon?

The surveyor's chain is composed of 100 links, and

60 geographical, or 69 statute miles The mean length of a degree on the 69.01745 miles.

A French mile is

A Scotch mile is

An Irish mile is

A Russian mile is

Pavers' and painters' work is computed in square yards.

3. Solid or Cubic Measure.

1728 solid inches make

27 solid feet

1 solid foot.

1 solid yard.

161⁄2 solid feet make a perch of brick or stone.

4. Table of Capacities.

231 cubic inches make 1 wine gallon.

1 ton.

1 cord foot.

1 cord.

7276.5 solid inches make a wine barrel of 31 gallons. 282 solid inches make 1 ale gallon.

10152 solid inches make 1 barrel of ale of 36 gallons. 277.274 cubic inches make an English imperial gallon, it being nearly one-fifth larger than the wine, and one-sixtieth smaller than the ale gallon.

268.8 solid inches make 1 gallon, dry measure.

2150.42 cubic inches make 1 bushel.

277 cubic inches make an English imperial gallon, dry

measure.

2218.2 solid inches make an English imperial bushel. 2553.6 solid inches make a coal bushel in Vermont. 2688 solid inches make a coal bushel in New York.

14553 cubic inches make a hogshead of wine. 31020 solid inches make a hogshead of ale of 110 gallons. 15228 cubic inches make an ale hogshead of 54 gallons. 1 ounce Troy weight equals 1.097143 ounce avoirdupois. 7000 grains Troy weight make 1 pound avoirdupois. 144 pounds avoirdupois make 175 pounds Troy weight. Plumbers' work is rated at so much a pound, or by the hun

dred.

13. MENSURATION.

Four methods of raising a perpendicular.

1. Take two inches between the legs of a pair of dividers, or compasses; then place one foot of the dividers on the end of

the line upon which you wish to erect the perpendicular, and strike an arc of a circle equal to, or greater than one-fourth of the circumference of the circle of which it is a part, and cutting the line on which the perpendicular is to be raised; then take two inches and thirteen-sixteenths of an inch between the legs of the dividers, and, placing one foot on the line where it is cut by the arc of the circle, strike the arc with the other leg, and the point where the two arcs cut each other will be perpendicular to the end of the line: consequently, draw the perpendicular from the end of the line through this point, and the thing is done. Thus

1.

Perpendicular.

2. Place one foot of the dividers on the end of the line, and strike a circular arc cutting the line; then with the same space between the dividers, place one foot on the line at the point where it is cut by the arc, and set off double the space between the dividers on the said arc; then place one foot of the dividers on the point in the arc to which the dividers reached the first step, and strike a circular arc over the point; then place one foot of the dividers on the point to which the dividers reached the second step, and strike a circular arc cutting the former, and the point where the arcs cut each other will be per

pendicular to the end of the line. In the same manner a perpendicular may be drawn from any point in the line. Thus

3. Place one foot of the dividers on the end of the line, and the other at a, (some point between the line and the perpendicular;) then strike a circular arc cutting the line, and through the centre of the circle, of which the said arc is a part, draw a right line from the point where the arc cuts the given line, and extend it until it meets the said arc on the opposite side of the diameter; and the point where the right line meets the arc will be perpendicular to the end of the given line: consequently, draw the perpendicular through this point, and the thing is done.

4. Draw a right line and lay off, or set off, 5 equal spaces on this line; then, having taken 3 of these between the legs of the dividers, place one foot on the end of the line and strike a circular arc; then, having taken the 5 spaces between the legs of the dividers, place one foot on the 4th space from the end of the line, and strike an arc cutting the former, and the point where the two arcs cut each other will be perpendicular to the end of the line. Thus