In 400 years, 97 are leap years, and 303 common. The same remark, as in the case of Angular Measure, applies to the mode of subdividing the second of time. COMPARISON OF MEASURES The old ale gallon contained 282 cubic inches. The old wine gallon contained 231 cubic inches. The old Winchester bushel contained 2150 cubic inches. The corn bushel, eight times the above. Hence, with respect to Ale, Wine, and Corn, it will be expedient to possess a TABLE OF FACTORS, For converting old measures into new, and the contrary. N. B. For reducing the prices, these numbers must all be reversed. 1 Chaldron of coals at Newcastle is [By an act of parliament in 1831, coals within 25 miles of the General Post Office, London, must be sold by weight.] . 104809-572 cubic inches 99818-64 cubic inches 53 cwt. 24 Cubic feet of sand, or 18 cubic feet of earth, or 17 cubic feet of clay, make 1 ton. 1 Yard cube of solid gravel or earth contains 18 heaped bushels before digging, and 27 heaped bushels when dug. 27 Heaped bushels make 1 load. FRENCH AND ENGLISH WEIGHTS AND The following is a comparative Table of the Weights and Measures of England and France, which were published by the Royal and Central Society of Agriculture of Paris, in the Annuary for 1829, and founded on a Report, made by Mr. Mathieu, to the Royal Academy of Sciences of France, on the bill passed the 17th of May, 1824, relative to the Weights and Measures termed "Imperial," which are now used in Great Britain. ENGLISH. 1 Inch (1-36th of a yard) 1 Foot (1-3d of a yard) Yard imperial Fathom (2 yards) MEASURES OF LENGTH. Pole, or perch (5 1-2 yards) Furlong (220 yards) Mile (1760 yards) FRENCH. 2.539954 centimetres 1.82876696 metre 201-16437 metres SECTION VI.-Vulgar Fractions. The fractions of which we have already spoken in section the 1st, are usually denominated Vulgar Fractions, to distinguish them from another kind, hereafter to be mentioned, called decimal fractions. A fraction is an expression for a part of a unit, or integer, when it represents a whole of any kind. Thus, if a pound sterling be the unit, then a shilling will be the twentieth part of that unit, and four pence will be four-twelfths of that twentieth part. These represented according to the usual notation of Vulgar Fractions, will be and of respectively. The lower number of a fraction thus represented (denoting the number of parts into which the integer is supposed to be divided) is called the denominator; and the upper figure (which indicates the number of those parts expressed by the fraction) the numerator. Thus, in the fractions,, 7 and 15 are denominators, 5 and 8 numerators. Vulgar fractions are divided into proper, improper, mixed, simple, compound, and complex. Proper fractions have their numerators less than their denominators, as,, &c. Improper fractions have their numerators equal to, or greater than, their denominators, as 4, 12, &c. Mixed fractions, or numbers, are those compounded of whole numbers and fractions, as 7, 123, &c. Simple fractions are expressions for parts of given units, as ,, &c. 4 5 Compound fractions are expressions for the parts of given fractions, as of, of 7, &c. Complex fractions have either one or both terms mixed 52 12 6 5를 numbers as &c. 24' 14' 123' Any number which will divide two or more numbers without remainder is called their common measure. Reduction of Vulgar Fractions. This consists principally in changing them into a more commodious form for the operations of addition, subtraction, &c. Case 1.-To reduce fractions to their lowest terms: Divide the numerator and denominator of a fraction by |