-Sign of subtraction, signifying _minus_ or less; thus, 4-3 = 1. × Sign of multiplication, signifying multiplied by or into; thus, 4 × 3 = 12. ÷ Sign of division, signifying divided by; thus, 4 ÷ 2 = 2. {} () [] Brackets, denoting that the quantities between them are to be treated as one quantity; thus, 5 {3(4 + 2)-6(3-2)} = 5 (18-6) = 60. Letters are used to shorten or simplify a formula. Supposing we wish to express length × breadth × depth, we may put the initial letters only, thus, _l_ × _b_ × _d_, or, as is usual when algebraical symbols are employed, leave out the sign × between the factors, and write the formula _lbd_. When division is to be expressed in simple form, the divisor is written under the dividend; thus (_x_ + _y_) ÷ _z_ = (_x_ + _y_) ________ _z_ ° ’ ” are signs used to express certain angles in degrees, minutes, and seconds; thus 25 degrees 4 minutes 21 seconds would be expressed 25° 4’ 21”. √ This sign is called the radical sign, and placed before a quantity indicates that some root of it is to be taken, and a small figure placed over the sign, called the exponent of the root, shows what root is to be extracted. Thus ²√ _a_ or √ _a_ means the square root of _a_ ∛ _a_ ” cube ” ∜ _a_ ” fourth ” ρ This sign is used to denote the force of gravity at any given latitude. π The Greek letter pi is invariably used to denote 3·14159, that is, the ratio borne by the diameter of a circle to its circumference. When the figure 2 is affixed to any number, as diameter² or 12², the number is to be squared, as 12 × 12 = 144, the square; and with ³ affixed, the number is to be cubed--_i.e._, multiplied twice by itself, as 6³ = 6 × 6 × 6 = 316, the cube of 6. =ENGLISH WEIGHTS AND MEASURES.= MEASURES OF LENGTH. 12 lines = 1 inch. | 8 furlongs } 12 inches = 1 foot. | 1760 yards } = 1 statute mile. 3 feet = 1 yard. | 5280 feet } 6 feet = 1 fathom. | 6086 feet = 1 naut. mile. 16½ feet = 1 pole. | 7·92 inches = 1 link. 220 yards = 1 furlong. | 100 links } 66 feet } = 1 chain. 22 yards } SQUARE MEASURE.