Equal to, as, 12 inches = 1 foot, or 8×8=16×4. + Plus, or more, signifies addition; as, 4+6+5=15. Minus, or less, signifies subtraction; as, 15-5=10. × Multiplied by, or into, signifies multiplication; as, 8×9=12. Proportion; as, 2:4::8:16; that is, as 2 is to 4 so 18 8 ✓ Prefixed to any number signifies that the square root of that number is required; as, √16=4; that is, 4x4=16. Signifies that the cube root of that number is required; as, 2 added to a number signifies that that number is to be squared; thus, 42, means that 4 is to be multiplied by 4. 3 added to a number signifies that that number is to be cubed; thus, 43, is 4×4X4 64. The power, or number of times The bar signifies that the numbers are to be taken together; Decimal point, signifies when prefixed to a number, that that Signifies difference, and is placed between two quantities when 7 Is put between two quantities to express that the former is greater than the latter; as, a7b, reads a greater than b. Signifies the reverse; as, a Lb, reads a less than b. () Parentheses are used to show that all the figures within them are to be operated upon as if they were only one; thus, p is used to express the ratio of the circumference of a circle to EXPLANATIONS OF THE CHARACTERS USED. IN THE.FOLLOWING TABLES AND CALCULATIONS. Equal to, as, 12 inches = 1 foot, or 8x8 = 16×4. + Plus, or more, signifies addition; as, 4+6+5=15. - - Minus, or less, signifies subtraction; as, 15-5=10. X Multiplied by, or into, signifies multiplication; as, 8×9 = 1%. Divided by, signifies division; as, 72-98. : Is to :: so is : to Proportion; as, 2:4::8:16; that is, as 2 is to 4 so 15 8 Prefixed to any number signifies that the square root of that number is required; as, 16=4; that is, 4x4 = 16. Signifies that the cube root of that number is required; as, 3/644; that is, 4x4x4 = 64. 2 added to a number signifies that that number is to be squared ; thus, 42, means that 4 is to be multiplied by 4. 3 added to a number signifies that that number is to be cubed; thus, 43, is 4X4X4 64. The power, or number of times a number is to be multiplied by itself is shown by the number added; as, 2 3 4 5, &c. The bar signifies that the numbers are to be taken together; as, 8-2+6=12, or 3×5+3=24. Decimal point, signifies when prefixed to a number, that that number has a unit (1) for its denominator; as, .1 is, .155 is 155, &c. 1000' Signifies difference, and is placed between two quantities when it is not evident which of them is the greater. Degrees, minutes, "seconds, "thirds. < Signifies angle. a-, a- 2, a &c., denote inverse powers of a, and are equal 7 Is put between two quantities to express that the former is greater than the latter; as, a7 b, reads a greater than b. Signifies the reverse; as, a Lb, reads a less than b. () Parentheses are used to show that all the figures within them are to be operated upon as if they were only one; thus, (3+2)x5=25. p is used to express the ratio of the circumference of a circle to its diameter 3.1415926, &c. A A'A" A" signifies A, A prime, A second, A third, &c. axd, a.d, or ad, signifies that a is to be multiplied by d. Note. The degrees of temperature used in this work are those of Fahrenheit. er The inch is sometimes divided into 3 barley corns, or 12 lines. A hair's breadth is the 48th of an inch. Gunter's Chain. Ropes and Cables. 6 feet =1 fathom. Geographical and Nautical Measure. 1 degree of a great circle of the earth = 1 knot Log Lines. 69.77 Statute miles. 2046.58 yards. 51.1625 feet, or 51 feet 12+ inches. 1 fathom= 5.11625 feet, or 5 feet 13+ inches. Estimating a mile at 6139 feet, and using a 30" glass. If a 28′ glass is used, and eight divisions, then The line should be about 150 fathoms long, having 10 fathoms between the chip and first knot for stray line. NOTE.-Bowditch gives 6120 feet in a sea mile, which, if taken as the length, will make the divisions 51 feet and 5 1-10 feet. No. 1 is 44 inches in length, and every succeeding number is of an inch. There are 28 divisions, in two series of numbers, viz., from 1 to 13, and 1 to 15. B |