ELEMENTARY ARITHMETIC. PART II. CHAPTER I. COMPOUND QUANTITIES.-SECTION I. A CONCRETE quantity is a number used with reference to some particular thing or object; as, 5 shillings, 9 tons, 247 miles. A compound quantity is a concrete quantity expressed in two or more denominations; as, 6 shillings 8 pence; 5 yards 2 feet 7 inches. SECTION II. TABLES OF MONEY, WEIGHTS, AND MEASURES. Money. Accounts are kept in pounds, shillings, pence, and farthings, which are related to each other as follows: 4 farthings make penny. 12 pence 20 shillings But in addition to these, payments are made in the following coins: GOLD.-Half-sovereign (ten shillings). shillings 6 pence); florin (2 shillings); sixpence ; fourpence, or groat; threepence. COPPER.-Halfpenny, or two farthings. The word farthing is a corruption of fourth-ing, and means the fourth of a penny. It is usually written d., the 4 showing that one penny has been divided into four equal parts, the value of each being a farthing; and the 1 showing that one of these equal parts is taken. Two farthings, or one halfpenny, is written d., the 2 showing that one penny has been divided into two equal parts, and the that one of these parts is taken. Three farthings is written d., which shows that a penny has been divided into four equal parts, and that three such parts are taken. Abbreviations.-£ s. d. q., the first letters of the Latin words libra, solidus, denarius, quadrans, are used to denote pound, shilling, penny, and farthing. The long s() was formerly written between shillings and pence, and d., the abbreviation for pence, was omitted. Thus, 35. 8d. was written 3/8. To facilitate rapidity in writing, however, a straight line is now generally used instead of the f; so that 4/9, 17/6, denote 4s. 9d. and 175. 6d. respectively. The following coins are not now in use:GOLD.-Moidore (275.); guinea (21s.); halfguinea (10s. 6d.). SECTION III.-MONEY TABLES. Farthings. The number of pence in any number of farthings may be found by dividing the farthings by 4. Thus, II farthings are 2d., because 11 divided by 4 gives 2 with a remainder 3. The pupil may either learn the above table, or employ the following rule to find the number of pounds in any given number of shillings :-Take the half of all the figures, except the units' figure (which always represents shillings), for the pounds, and if there be a remainder place it before the units' figure for the shillings. Thus 87s. are £4 75.-4 being the half of 8, and 7 being the units' figure ; and 1395. are £6 19s.—the half of 13 being 6 and I over, which latter is placed before the units' figure 9. SECTION IV.-READING EXERCISES IN THE PENCE AND SHILLINGS TABLES, ETC. 9.7 9 5 4 9 8 5947 I 393 6 5 399 8 5 7 10. 3 8 7 9 6 7 5 8 4 9 3 8 8 3 9 11.8 9 5 7 8 6 9 5 3 4 97 6 5 8 12.7 7 5 9 9 5 8 7 4 33 6947 13.9 5 8 7 49 6 3 7 8 9 549 7 14.8 4 9 6 3 5 8 7 9 4 7 6 8 3 9 15. 6 9 7 5 4 8 9 6 7 5 8 9 4 7 6 These exercises should be read from left to right, as follows:-21d., Is. 9d.; 14d., IS. 2d.; 40d., 35. 4d.; 23d., IS. 11d., &c.: or 215., £1 IS.; 40s., £2; 235., £1 35. ; 325., £1 125., &c. The pence and shillings tables may be combined with the multiplication table by multiplying any two successive figures, and giving the number of shillings or pounds in the product. Thus, taking the ninth line, 7 times 9 is 63, 5s. 3d. ; 9 times 5 is 45, 35. 9d.; 5 times 4 is 20, 15. 8d. ; or 7 times 9 is 63, £3 3s.; 9 times 5 is 45, £2 5s.; &c. When the pupil has acquired some proficiency in these exercises, he should name the results only, and not the figures which produce them. Thus, instead of saying 21d. are is. 9d., he should only say 1s. 9d.; and instead of 7 times 9 is 63, 55. 3d., he should think 63, and say 5s. 3d. The preceding table will also supply valuable reading exercises in all of the simple rules, and the pupil who frequently practises them according to the methods here laid down cannot fail to become an expert calculator. 1. Take the columns and add them upwards, then downwards; next add the rows from left to right, and then from right to left. In adding, do not say 6 and 9 are 15; 15 and 7 are 22; 22 and 7 are 29, &c., but only 15, 22, 29, &c. 2. Take the rows and subtract each figure from the following one, increased by 10 if necessary. Thus, the fourth row supplies the following: 5 from 12, 2 from 4, 4 from 13, 3 from 12, &c.; but instead of saying 5 from 12 leaves 7, the pupil should think what number must be added to 5 to make 12, and only say 5 and 7; not even naming the larger number. Next, take the number formed by two figures, and subtract from the following figure, increased by as many tens as may be necessary. Thus, in the fifth row, we get 36 from 45, 65 from 72, 52 from 53, &c.; or as the |