At the polar regions ice is perpetually observed at the surface of the earth. PROPERTIES OF NUMBERS. ↑ A Prime Number is that which can only be measured by 1 or 2 & Composite Number is that which can be measured for divided without a remainder by some number greater than unity. $ A Perfect Finder is that which is equal to the sum of all its Hivisors, or stiglot parts: thus & = { - } - { * If an ad number divides an even number, it will also divide the half of it. 5. if the last digit of any number be divisible by 2. the whole number is divisible by 2 5. If the two lass digits be divisible by 4, the whole number is divisible by 1. f the raree last figits be fivisible by 3, the whole number is divisible by 8. 27 a number terminate with 3, it is divisible by 3; and if it terminate with 9, it is divisible by either 20 or 5. 9. If the sum of the digits constituting any number be divisible by 3 or 4 the whole is divisible by 3 or 90 and if also the last digit is even, the whole number is divisible by X 206 I the sum of the digits of any number be livisible by 6, and the right and digit by the whole is disible by 5. 2. If the sum of the 1st, 3d, 5th, de, digits of any number be equal to that of the 2d, 4th, 5th, de, that number is divisible by It Thus $27943 contains 1= 1980 times exactiv. 15. if a square number be either multipiled or divided by a square, the product or quotient is a spars; and conversely, if a square number be other multipled or divided by a number that is not a square, the product or quotient is on a squire, 18. The product arising from two different prime numbers cannot be a square number. 14. The product of no two different numbers, prime to each other that is, I being the common measure) can make a square, unless each of those numbers be a square. 15. The square root of an integral number, that is not a complete square, can neither be expressed by aut neger ær by any rational fraction; so with de qube root of an integer 16. Every prime number greater than two, is made up of 4 times some number 1-1; that is, of one of the forms Lor divided by 6, will leave a 17. Any prime number greater than 3, der greater than 3, is one remainder of 1 or 5: that is, every of the forms 6n + 1, or 6n — 1. of prime numbers is infinite. Jis ber 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. et qui ima donna, egya 25. The difference between any integral cube and its root is always divisible by 6. Ch 26 Neither the sum nor the difference of two cubes can be a cube. ole27. 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. jk, gå pigil dava Of the first Nine Powers of the first Nine Numbers. 5 25 125 625 3125 1562578125 390625 1953125 864 512 YHE 46656 279936 1679616 10077696 40353607 4096 32768 262144 2097152 16777216 134217728 9 81 729 6561 59049 531441 4782969 43046721 387420489 Imperial gallons in a litre Lbs. per square inch in 1 kilogramme per square millimetre. Cwts ditto, ditto 0.024711 2.20548 0.3435031 0.2200967 1422 12.7 0 5235988 0.017453293 Grains in a cubic inch of distilled water, Bar. 30 7000 252.458 1-73298 277-276 6075.6 397.60 English oak To find the weight in lbs. of 1 foot of common in inches by Ditto for a cable TABLE ⚫044 to 046 *027 Surface of Boilers' Tubes of Different Lengths and Diameters. RECIPES FOR MAKING DIFFERENT 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. If 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; (I of borax;) of arsenious acid. 1 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; 13 of manganese; 100 of broken glass. 5. White Table Glass.1. 40 pounds of potashes; 11 of chalk; 78 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. 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. 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. 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. ིན་ A little borax has also been prescribed; much of it communicates an exfoliating property to glass. |