17. Any prime number greater than 3, divided by 6, will leave a remainder of 1 or 5: that is, every number greater than 3, is one of the forms 6n + 1, or 6n

1.

18. The number of prime numbers is infinite.

19. A square number cannot terminate with an odd number of cyphers.

20. If a square number terminate with 4, the last figure but one will be an even number.

21. If a square number terminate with 5, it will terminate with 25. 22. No square number can terminate with two equal digits, except two cyphers, or two fours.

23. No number whose last digit is 2, 3, 7, or 8, is a square number. 24. If a cube number be divisible by 7, it is also divisible by the cube of 7.

25. The difference between any integral cube and its root is always divisible by 6.

26. Neither the sum nor the difference of two cubes can be a cube.

27. A cube number may end with any of the natural numbers. 28. All the powers of any number that end with 6, will terminate with 6 so with the numeral 5.

TABLE

Of the first Nine Powers of the first Nine Numbers.

749 343 2401 16807117649 823543 5764801 40353607 4096 32768 262144 2097152 16777216 134217728 981 729 6561 | 59049 531441 4782969 43046721 387420489

8 64 612

Imperial gallons in a litre

Lbs. per square inch in 1 kilogramme per square

millimetre.

Cwts. ditto, ditto.

Volume of a sphere whose diameter is 1

Arc of 1° to rad. 1

Are of 1' to rad. 1

Arc of 1" to rad. 1

Degrees in an arc whose length is 1
Grains in 1 oz. avoirdupois

2.20548

0.3435031

0.2200967

1422

Grains in a cubic inch of distilled water, Bar. 30 in., Th. 62°

Cubic inches in an ounce of water

Cubic inches in the imperial gallon.
Feet in a geographical mile

Feet in a statute mile

Log. of ditto

Log. of ditto

Length of seconds' pendulum in inches

Cubic inches in 1 cwt. of cast iron

252.458

1.73298

277.276

6075.6

3.7835892

5280

3.7226339

39.19084

430.25

To find the weight in lbs. of 1 foot of common rope, multiply the square of its circumference

in inches by

Ditto for a cable

*044

to '046

*027

TABLE

Surface of Boilers' Tubes of Different Lengths and Diameters.

RECIPES FOR MAKING DIFFERENT
KINDS OF GLASS.

1. Bottle Glass.-1. Dry glauber salts, 11 pounds; soaper salts, 12 pounds; half a bushel of waste soap ashes; sand, 56 pounds; glass skimmings, 22 pounds; green broken glass, 1 cwt.; basalt, 25 pounds. This mixture affords a dark green glass.

2. Yellow or white sand, 100 parts; kelp, 30 to 40; lixiviated wood ashes, from 160 to 170 parts; fresh wood ashes, 30 to 40 parts; potter's clay, 80 to 100 parts; cullet, or broken glass, 100. Îf basalt be used, the proportion of kelp may be diminished.

2. Green Window, or Broad Glass.-Dry glauber salts, 11 pounds; soaper salts, 10 pounds; half a bushel of lixiviated soap waste; 50 pounds of sand; 22 pounds of glass pot skimmings; 1 cwt. of broken green glass.

3. Crown Glass.-300 parts of fine sand; 200 of good soda ash 33 of lime; from 250 to 300 of broken glass; 60 of white sand; 30 of purified potash; 15 of saltpetre; (1 of borax;) 1⁄2 of arsenious acid.

4. Nearly White Table Glass.--1. 20 pounds of potashes; 11 pounds of dry glauber salts; 16 of soaper salt; 55 of sand; 140 of cullet of the same kind.

2. 100 parts of sand; 235 of kelp; 60 of wood ashes; 1 of manganese; 100 of broken glass.

5. White Table Glass.-1. 40 pounds of potashes; 11 of chalk; 76 of sand; of manganese; 95 of white cullet.

2. 50 of purified potashes; 100 of sand; 20 of chalk, and 2 of saltpetre.

6. Crystal Glass.-1. 60 parts of purified potashes; 120 of sand; 24 of chalk; 2 of saltpetre; 2 of arsenious acid; of manga

nese.

16

2. Purified pearlashes, 70 parts; white sand, 120; saltpetre, 10; of arsenious acid; of manganese.

3. 67 of sand: 23 of purified pearlashes; 10 of sifted slaked lime; of manganese; 5 to 8 of red lead.

4. 120 of white sand; 50 of red lead; 40 of purified pearlash; 20 of saltpetre;

of manganese.

5. 120 of white sand; 40 of pearlash purified; 35 of red lead; 13 of saltpetre; of manganese.

1 2

6. 30 of the finest sand; 20 of red lead; 8 of pearlash purified; 2 of saltpetre; a little arsenious acid and manganese.

7. 100 of sand; 45 of red lead; 35 of purified pearlashes; of manganese; of arsenious acid.

1

5

7. Plate Glass-1. Very white sand, 300 parts; dry purified soda, 100 parts; carbonate of lime, 43 parts; manganese, 1; cullet, 300. 2. Finest sand, 720 parts; purified soda, 450; quicklime, 80; saltpetre, 25; cullet, 425.

A little borax has also been prescribed; much of it communicates an exfoliating property to glass.