C-NRLF 
 
 B 2b2 7MT 
 
LIBRARY 
 
 OF THE 
 
 Jniversity of California. 
 
 Received %yUy^^ • ^^9 9 • 
 
 tccession No.^ y ^"M^ • Cla^s No, 
 
 are now ready. 
 
 In the PRIMER the vowel sounds are presented in an easy 
 and natural manner, being in every case exemplified by real 
 words rather than by arbitrary syllables, and arranged m rhymmg 
 groups. The lessons are composed of sentences woven mto 
 narratives, and hieroglyphic lessons have been introduced for 
 the purpose of making the work of revisal more varied and 
 interesting. 
 
 In the FIRST STANDARD the narrative form has been pre- 
 served throughout, and the lessons, while inciidentally supplying 
 considerable information, are mainly intended to enable the child 
 to overcome the mechanical difficulties of reading. They have 
 therefore been made as light and attractive as possible; many 
 elliptical, and, as a new feature, several alliterative and hiero- 
 glyphic, lessons have been constructed. Easy lessons are also 
 given in Script for the reading and writing of Manuscript. 
 
 In the SECOND STANDARD a variety of interesting matter 
 has been simplified by the syllabification of difficult words and 
 the grouping together of common affixes. A novel feature is 
 the introduction of lessons on the Tenses of Verbs. Useful 
 information is imparted on common objects and animals, with 
 lessons inculcating duty and honour. In Dictation a large pro- 
 portion of the matter is shown in Script ; while the Exercises 
 
Oliver and Boyd's New Code Olass-Books. 
 
 appended to these, direct increased attention to the subjects 
 presented, and furnish plenty of school- work. 
 
 In the THIRD STANDARD, as the child will now have 
 acquired considerable fluency in easy reading, a varied selection 
 has been made from authors that have long been favourites with 
 the young. In the Dictation all the difficulties in spelling 
 monosyllables and easy dissyllables have been anticipated, and 
 the Exercises, which are partly in Script, have been constructed 
 so as to foster the habit of observing words and their distinctions. 
 
 11. GEOGRAPHY. 
 
 Three little works have been prepared by INIr W. Lawsox, 
 F.Il.G.S., St Mark's College, Chelsea; Author of " Geography 
 of the British Empire," etc. 
 
 1. The GEOGRAPHICAL PRIMER will be found adapted to 
 the requirements of Standard IV. The meaning of a Map is 
 clearly explained ; an outline is given of the Chief Divisions of 
 the World ; while the numerous facts have been selected and 
 arranged to suit the age of the pupils. 
 
 2. The GEOGRAPHY OF ENGLAND meets the requirements 
 of Standard V., and is intended to succeed the " Geographical 
 Primer." The style and su!)ject are a little in advance, and 
 there is some attempt to show the dependence of one part of the 
 geography upon another. A Chapter on the principal Railways 
 will be found to meet the increasing desire for information on 
 this subject. 
 
 3. ELEMENTS OF PHYSICAL GEOGRAPHY. This work 
 has been written as a " Specific Subject," with special reference 
 to the New Code. The language and illustrations are simple, and 
 suited to the capacity of pupils of from ten to fourteen years of age. 
 
 III. ARITHMETIC. 
 
 This subject has been undertaken by Mr Alex. Teotter, 
 Teacher of Mathematics, etc., Edinburgh ; Author of " Arith- 
 metic for Advanced Classes," etc. 
 
 Part I. embraces Standards 1 and 2. 
 
 „ II. „ „ 3 and 4. 
 
 Part III. [in preparation) will embrace Standards 5 and 6. 
 
 [Continued at end of Book. 
 
LESSONS 
 
 IN 
 
 ARITHMETIC 
 
 FOR 
 WITH 
 
 TABLES OF MONEY, WEIGHTS, AND MEASURES, 
 
 ACCORDINO TO THE IMPERIAL STANDARDS. 
 
 By JAMES TROTTER, 
 
 LATE OP THE SCOTTISH NAVAL AND MILITARY ACADEMY, 
 
 Author of "A Complete System of Arithmetic," etc. 
 
 EDINBURGH: 
 
 OLIVER AND BOYD, TWEEDDALE COURT. 
 
 LONDON : SIMPKIN, MARSHALL. AND CO. 
 
 Price 6d., or 8d. cloth. Advanced Arithmetic, in Continuation of this 
 
 Work, 6d., or 8d. cloth. Also, strongly bound together in 
 
 leather. Is. 3d. Answers to both Works, 6d. each. 
 
 1872. 
 
vt 
 
 T7 
 
 SCHOOL-BOOKS BY JAMES TROTTER, 
 
 LATE OF TUB SCOTTISH NATAL ANI> MILITARY ACADEMY. 
 
 LESSONS in ARITHMETIC for Junior Classes. 6d. 
 A CoMPLBTB System of ARITHMETIC, Theoretical and Practical. 3s. 
 Teotteb's Edition oi MUTTON'S BOOK-KEEPING. 2s. 
 A Complete System of MENSURATION, by Ingram & Trotter. 2*. 
 Ingram and Trotter's EUCLID; containing the Elements of Plan© 
 Geometry and Trigonometry Is. 6d. 
 
 Ingram's Concise System of MATHEMATICS. Revised by Mi 
 Trotter. 4s. 6d. 
 
 Trotter's LOGARITHMS and PRACTICAL MATHEMATICS. 3a. 
 
 Ingram and Tbotteb's Elements of ALGEBRA. 38. 
 
 PRINTED BY OLIVER AND BOYD, EDINBURGH. 
 
ADVERTISEMENT TO THE ENLARGED EDITION. 
 
 The following little Work was originally composed for the 
 use of the Author's Junior Classes. It was afterwards 
 submitted to the public, in the hope that it would be 
 found worthy of an introduction to Public Schools and 
 Academies, and that, from the number and variety of the 
 Exercises, it might prove a useful auxiliary to Governesses 
 and Families. 
 
 This hope having been fully realized, the present Edition 
 has been subjected to a careful revision, and enlarged by 
 the introduction of simple illustrations of the various rules 
 and of a considerable number of Practical Exercises ; at the 
 end of the work also, are given Exercises on that system of 
 Decimal Coinage which, in course of time, is most likely 
 to be adopted in this country. 
 
 These additions have been made by the Author's son, Mr 
 Trotter, Teacher of Mathematics, &c., who has recently pre- 
 pared a Continuation of this Work for Advanced Classes. 
 
MULTIPLICATION TABLE. 
 
 2 times 
 
 4 times 
 
 6 times 
 
 8 times 
 
 10 times 
 
 12 times 
 
 2 are 4 
 
 2 are 8 
 
 2 are 12 
 
 2arel6 
 
 2 are 20 
 
 2 are 24 
 
 3 ... 6 
 
 3 ... 12 
 
 3 ... 18 
 
 3 ... 24 
 
 3 ... 30 
 
 3 ... 36 
 
 4 ... 8 
 
 4 ... 16 
 
 4 ... 24 
 
 4 ... 32 
 
 4 ... 40 
 
 4 ... 48 
 
 5 ... 10 
 
 5 ... 20 
 
 5 ... 30 
 
 5 ... 40 
 
 5 ... 50 
 
 5 ... 60 
 
 6 ... 12 
 
 6 ... 24 
 
 6 ... 36 
 
 6 ... 48 
 
 6 ... 60 
 
 6 ... 72 
 
 7 ... 14 
 
 7 ... 28 
 
 7 ... 42 
 
 7 ... 56 
 
 7 ... 70 
 
 7 ... 84 
 
 8 ... 16 
 
 8 ... 32 
 
 8 ... 48 
 
 8 ... 64 
 
 8 ... 80 
 
 8 ... 96 
 
 9 ... 18 
 
 9 ... 36 
 
 9 ... 54 
 
 9 ... 72 
 
 9 ... 90 
 
 9 ... 108 
 
 10 ... 20 
 
 10 ... 40 
 
 10 ... 60 
 
 10 ... 80 
 
 10 ... 100 
 
 10 ... 120 
 
 11 ... 22 
 
 11 ... 44 
 
 11 ... 66 
 
 11 ... 88 
 
 11 ... 110 
 
 11 ... 132 
 
 12 ... 24 
 
 12 ... 48 
 
 12 ... 72 
 
 12 ... 96 
 
 12 ... 120 
 
 12 ... 144 
 
 3 times 
 
 5 times 
 
 7 times 
 
 9 times 
 
 11 times 
 
 20 times 
 
 2 are 6 
 
 2 are 10 
 
 2 are 14 
 
 2 are 18 
 
 2 are 22 
 
 2 are 40 
 
 3... 9 
 
 3 ... 15 
 
 3 ... 21 
 
 3... 27 
 
 3 ... 33 
 
 3 ... 60 
 
 4 ... 12 
 
 4 ... 20 
 
 4 ... 28 
 
 4... 36 
 
 4 ... 44 
 
 4 ... 80 
 
 5 ... 15 
 
 5 ... 25 
 
 5 ... 35 
 
 5... 45 
 
 5 ... 55 
 
 5 ... 100 
 
 6 ... 18 
 
 6 ... 30 
 
 6 ... 42 
 
 6... 54 
 
 6 ... 66 
 
 6 ... 120 
 
 7 ... 21 
 
 7 ... 35 
 
 7 ... 49 
 
 7 ... 63 
 
 7 ... 77 
 
 7 ... 140 
 
 8 ... 24 
 
 8 ... 40 
 
 8 ...56 
 
 8... 72 
 
 8 ... 88 
 
 8 ... 160 
 
 9 ... 27 
 
 9 ... 45 
 
 9 ... 63 
 
 9... 81 
 
 9 ... 99 
 
 9 ... 180 
 
 10 ... 30 
 
 10 ... 50 
 
 10 ... 70 
 
 10... 90 
 
 10 ... 110 
 
 10 ... 200 
 
 11 ... 33 
 
 11 ... 55 
 
 11 ... 77 
 
 11... 99 
 
 11 ... 121 
 
 11 ... 220 
 
 12 ... 36 
 
 12 ... 60 
 
 12 ... 84 
 
 12 ...108 
 
 12 ... 132 
 
 12 ... 240 
 
EXPLANATION OF ARITHMETICAL TERMS AND SIGNS. 
 
 Number is either a unit, or consists of a collection of units ; 
 being the name given to our conception of things considered 
 as one or many. 
 
 Abstract numbers. When we consider numbers in their 
 general nature, without referring them to any particular 
 subject, they are then called abstract; as, 3, 7, 10, &c. 
 
 Concrete or applicate numbers. When we consider 
 number not in its general nature, but as applied to certain 
 })articular things, as, two pounds, three pence, &c., it is 
 termed concrete or applicate. 
 
 A WHOLE number cousists of one or more units. 
 
 A FRACTION consists of one or more parts of unity. 
 
 A mixed number consists of a whole number and a 
 fraction. 
 
 A COMPOUND number cousists of several applicate num- 
 bers joined together in one expression ; as, £4, 6s. 8d. 
 
 An even number is that which can be divided into two 
 equal whole numbers. 
 
 An odd number is that which cannot be divided into two 
 equal whole numbers. 
 
 A PRIME number is that which can only be divided by 
 itself and unity, without a remainder; and numbers are 
 said to be prime to each other when no number but unity 
 will divide both without a remainder. 
 
 A SQUARE NUMBER is the product of any number by 
 itself. 
 
 A CUBE NUMBER is the product of a number and its 
 square. 
 
 A COMPOSITE NUMBER is that produced by multiplying two 
 or more numbers together; thus 28 = 4X7 is a composite 
 number, and 4 and 7 are called its component parts. 
 
 An ALIQUOT PART is a number which is contained in a 
 greater an exact number of times ; thus 4 is an aliquot part 
 of 16, but not of 17, as it is contained exactly 4 times in the 
 former, and in the latter 4 times and 1 over. 
 
 An integer is any whole number; as, a pound, a mile, 
 &c., or, 1, 2, 4, 6, 9, &c. 
 
 Minuend is the greater number in Subtraction. 
 
 buBTRAHEND is the Icss number. 
 
4 ARITHMETICAL TERMS AND SIGNS. 
 
 MuLHPLicAND in Multiplication is the number to be 
 multiplied or repeated. 
 
 Multiplier is the number by which we multiply, or 
 which expresses how often the multiplicand is to be repeated. 
 
 Product is the sum or result of the operation in Mul- 
 tiplication. 
 
 Factors. The multiplicand and multiplier are called 
 factors of the product. 
 
 Divisor in Division is the number by which we divide. 
 
 Dividend is the number to be divided. 
 
 Quotient is the number which shows how often 
 
 the divisor is contained in the dividend, or the result of the 
 operation. 
 
 Denomination in applicate numbers is the name of the 
 subject to which the number is applied; as, pounds, shil- 
 lings, yards, miles, &c. 
 
 Numerator is the upper number of a fraction, and shows 
 how many parts of unity are expressed by the fraction. 
 
 Denominator is the under number of a fraction, and 
 shows into how many parts the unit is divided, 
 
 A COMMON measure is any number that will divide two 
 or more numbers without a remainder, and their greatest 
 common measure is the greatest number that will do so 
 thus 2 is a common measure of 12 and 18, and 6 is their 
 greatest common measure. 
 
 A COMMON multiple of two or more numbers is any 
 number that contains each of them an exact number of 
 times, and the least number that will do so is called their 
 least COMMON MULTIPLE ; thus 48 is a common multiple of 
 12, 6, and 4, and 12 is their least common multiple. 
 
 = {equal to) denotes equality; thus 21s. = 1 guinea. 
 
 -f- Cptiis) addition ; thus 6 4-4=10. 
 
 — {minus) subtraction; thus 7 — 3= 4. 
 
 X {multiplied hy) multiplication; thus 4X3 = 12. 
 
 -7- {divided hy) division; thus 18 ~- 6= 3. 
 
 : {is to) : : {as) are signs used in proportion to denote 
 an equality of ratios; thus 4 : 6 : : 8 : 12 denote that the ratio 
 of 8 to 12 is the same as that of 4 to 6, and is read, 4 is to 
 6 as 8 is to 12. 
 
 i represents & farthing ^ or the quarter of any thing. 
 
 i a halfpenny, or the AaZ/of any thing. 
 
 f three farthings, or three quarters of any thing. 
 
AEIIHMETiCAL TABLES. 
 
 ADDITION AND SUBTRACTION TABLE. 
 
 
 1 
 
 2 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 11 
 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 5 
 6 
 
 7 
 8 
 9 
 10 
 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 15 
 
 7 
 8 
 9 
 
 10 
 11 
 l2 
 13 
 14 
 l5 
 16 
 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 
 9 
 
 10 
 11 
 12 
 13 
 
 11 
 15 
 
 15 
 
 17 
 18 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 
 1! 
 19 
 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 2l 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 
 12 13 
 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 !i 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 
 17:18 
 
 19 
 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 59 
 40 
 
 1 
 
 2 
 3 
 4 
 5 
 
 2 
 3 
 4 
 5 
 6 
 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 31 
 32 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 ?1 
 32 
 
 33 
 
 18|19 
 19|20 
 2021 
 21j22 
 2223 
 23:24 
 24 25 
 25^26 
 26 27 
 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 3l 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 6 
 
 7 
 8 
 9 
 
 7 
 8 
 9 
 10 
 
 lOill 
 1112 
 
 12 13 
 
 13 14 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 11 
 12 
 13 
 14 
 15 
 16 
 
 11 
 
 18 
 
 19 
 20 
 21 
 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 
 13 
 14 
 15 
 16 
 I7 
 18 
 19 
 20 
 21 
 22 
 23 
 
 14 
 l5 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 
 27 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 
 28 
 29 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 
 Note. Before commencing Arithmetic it is absolutely neces- 
 sary that the pupil should commit to memory that part of the 
 preceding table which is cut off by a double line. The remaining 
 part should likewise be learned as soon as possible. The same 
 remark applies to the Multiplication and Division Table on the 
 next page, as well as to all the tables which follow. Indeed the 
 earlier that a child begins to learn the Arithmetical Tables, the 
 more lasting will the impression be upon the mind, and his pro- 
 gress in Arithmetic afterwards will be easy and unobstructed. 
 
ARITHMETICAL TABLES. 
 
 X) 
 
 ^ 
 
 s 
 
 § 
 
 o 
 
 o 
 
 CO 
 
 o 
 
 t 
 
 o 
 
 CT) 
 
 "^ 
 
 00 
 00 
 
 ■o" 
 
 CO 
 
 o 
 
 00 
 
 co" 
 
 CO 
 
 t 
 
 CO 
 
 o 
 
 t 
 
 o" 
 o" 
 
 CO 
 
 t 
 
 o 
 CO 
 
 CO 
 
 05 
 
 00 
 
 cO~ 
 
 t 
 1 
 
 co" 
 
 o 
 
 CO 
 
 00 
 
 CO 
 CO 
 
 CO 
 
 C5 
 
 t 
 
 oo" 
 
 CO 
 CO" 
 
 CO 
 
 CO 
 
 i 
 
 o 
 
 00 
 
 CO 
 
 
 CO 
 
 CO 
 
 CO 
 
 i 
 
 8 
 
 § 
 
 
 CO 
 CO 
 
 cr> 
 
 CO 
 
 CO 
 (N 
 
 CO 
 o 
 
 CO 
 
 oc 
 
 (N 
 
 00 
 §! 
 
 CO 
 
 c^ 
 
 C<l 
 c^ 
 
 00 
 CD 
 
 CO 
 
 1 
 
 CO 
 
 OS 
 00 
 
 l> 
 
 o 
 
 CO 
 CO 
 
 CO" 
 CO 
 
 CO 
 
 kO 
 
 t 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 05 
 
 t 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 i 
 
 o 
 
 00 
 CO 
 
 2 
 
 
 CO 
 
 lO 
 CO 
 
 CO 
 
 CO 
 
 CO 
 o 
 CO 
 
 00 
 
 o 
 
 CO 
 
 OC' 
 QO 
 
 cT 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 CO 
 CO 
 
 CO 
 CO 
 
 l> 
 
 CO 
 
 t 
 
 CO 
 
 CO 
 
 t 
 
 CO 
 
 00 
 
 l> 
 
 CO 
 
 "<# 
 
 CO 
 
 
 Ci 
 Co" 
 
 o 
 
 00 
 Oi 
 
 Ci 
 
 CO 
 
 CO 
 oo" 
 
 CO 
 
 t 
 
 co~ 
 
 o 
 
 05 
 X; 
 
 £L 
 
 CO 
 
 CO 
 
 To 
 
 1 
 
 CO 
 
 CD 
 
 00 
 00 
 
 CO 
 o 
 CO 
 
 to 
 CO 
 
 -^ 
 
 
 o 
 'f 
 
 CO 
 
 CO 
 CO 
 
 CO 
 
 CO 
 o 
 
 CO 
 
 
 CO 
 CO 
 
 FT 
 
 o 
 
 -^ 
 
 CO 
 
 o 
 
 CO 
 
 05 
 tH 
 
 t 
 
 CO 
 
 
 
 s 
 
 
 — ( 
 
 o 
 
 X) 
 
 
 CO 
 
 ^ 
 
 ^ 
 -* 
 
 s 
 
 CO 
 
 00 
 
 s 
 
 -ob- 
 
 o 
 
 o 
 CO 
 
 CO 
 
 CO 
 
 
 CD 
 
 00 
 CO 
 
 o 
 
 00 
 
 CO 
 
 05 
 
 cd" 
 
 00 
 
 o" 
 
 co" 
 
 t 
 
 CD 
 CO 
 
 2 
 
 00 
 
 co~ 
 
 CO 
 
 t 
 
 To 
 
 CO 
 
 00 
 
 ?^ 
 
 05 
 
 o 
 
 05 
 
 !>■ 
 
 CO 
 
 xO 
 
 co" 
 
 CO 
 
 o 
 o 
 
 CO 
 
 t 
 
 CO 
 
 CO 
 
 o 
 
 C5 
 
 X 
 
 
 
 CO 
 CO 
 
 
 00 
 00 
 
 C5 
 
 o 
 
 CO 
 
 2 
 
 CO 
 
 
 CO 
 
 
 00 
 CO 
 
 
 CD 
 
 CO 
 
 CO 
 
 CO 
 
 2 
 
 00 
 
 o 
 
 CO 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 g 
 
 1 
 
 o 
 
 § 
 
 ^ 
 
 o 
 
 
 00 
 CO 
 
 o 
 
 o 
 00 
 
 05 
 05 
 
 00 
 00 
 
 t>. 
 
 GO 
 
 CO 
 05 
 
 X 
 
 o 
 
 05 
 
 00 
 05 
 
 CO 
 
 t 
 
 o 
 
 CO 
 CO 
 
 CO 
 
 
 00 
 
 CO 
 
 CO 
 
 
 § 
 
 2 
 
 
 
 CO 
 
 o 
 
 00 
 
 GO 
 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 00 
 
 
 o 
 
 CD 
 
 CO 
 CO 
 
 CO 
 
 s 
 
 00 
 
 o 
 
 05 
 
 CO 
 05 
 
 CO 
 
 o 
 
 GO 
 
 o 
 
 kO 
 05 
 
 s 
 
 CO 
 
 
 
 o 
 CO 
 
 CD 
 
 g 
 
 
 g 
 
 00 
 
 o 
 
 05 
 
 c 
 o 
 
 to 
 
 
 TO 
 
 00 
 
 OS 
 
 CO 
 
 CO 
 
 c 
 
 ^ 
 
 00 
 CO 
 
 s^ 
 
 CO 
 
 o 
 -^ 
 
 o 
 
 CO 
 
 CO 
 CO 
 
 00 
 
 -^ 
 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 ^ 
 
 CO 
 
 00 
 
 GO 
 
 CO 
 
 
 CO 
 kO 
 
 o 
 
 CO 
 
 CO 
 
 
 kO 
 
 00 
 
 CO 
 
 CO 
 
 
 ^ 
 
 
 to 
 
 CO 
 
 00 
 
 o 
 
 CO 
 
 CO 
 
 
 CO 
 00 
 
 00 
 tH 
 
 05 
 
 o 
 
 CO 
 CO 
 
 CO 
 
 CO 
 
 CO 
 CO 
 
 CO 
 
 
 o 
 CO 
 
 CO 
 
 CO 
 
 CO 
 
 *>* 
 
 CO 
 
 T— ( 
 
 CO 
 CO 
 
 ^ 
 
 o 
 
 CO 
 
 
 00 
 00 
 
 05 
 
 o 
 CO 
 
 '"' 
 
 
 (M 
 
 CO 
 
 Tt< 
 
 lO 
 
 CD 
 
 r> 
 
 00 
 
 CJ5 
 
 o 
 
 ^ 
 
 CO 
 
 CO 
 
 05 
 
 o 
 
 CO 
 
 
 Note. In using the preceding table for a Division one, we 
 take the numbers in the left-hand column out of the numbers in 
 the same horizontal line, and the number of times each is con- 
 tained will be found either in the top or bottom line. 
 
ARITHMETICAL TABLES. 
 
 STERLING MONEY. 
 
 4 farthings qi's. =■ 1 penny d. 
 12 pence =: 1 shilling 5. 
 
 5 shillings =. 1 crown cr. 
 
 20sMm„gs ={Lrrefg^''£ 
 21 shillings = 1 guinea G. 
 
 TROY WEIGHT. 
 24 grains ^r.= 1 penny weiglit (fitf^ 
 20 dwt. = 1 ounce oz. 
 
 12 ounces = 1 pound lb. 
 
 Gold, Silver, and Jewels, are weighed 
 by Troy Weight. 
 
 APOTHECARIES' WEIGHT.* 
 20 grains gr. = 1 scruple ^ 
 3 scruples = 1 dram ^ 
 
 8 drams = 1 ounce 5 
 
 12 ounces = 1 pound lb. 
 
 Used only for medical prescriptions. 
 
 AVOIRDUPOIS WEIGHT. 
 16 drams cZr.^i 1 ounce oz. 
 
 16 ounces = 1 pound lb. 
 
 28 pounds = 1 quarter qr. 
 
 4 quarters = 1 hundred wt. cvA. 
 20 hund wt.= 1 ton T. 
 
 112 lbs. = 1 cwt. 
 
 7000 grains = 1 lb. avoird. 
 
 14 lb. = 1 stone 
 
 This table is used for all articles, except 
 Gold, Silver, and Jewels. 
 
 LINEAL MEASURE. 
 
 12 lines li. 
 
 12 inches 
 
 3 feet 
 5i yards 
 
 40 poles 
 
 8 furlongs 
 
 reO yards 
 
 = 1 inch 171. 
 
 = 1 foot ft. 
 
 =. 1 yard i/d. 
 
 = 1 pole po. 
 = 1 furlong fur. 
 
 = 1 mile ml. 
 = 1 mile 
 
 2 yds. or 6 feet = 1 fathom 
 2 i feet = a military pace 
 
 4 inches = 1 hand 
 
 1 1 foot = 1 cubit 
 
 22" yds. or 66 ft. = 1 chain; and as 
 the chain contains 100 links, 
 each link is = 7*92 inches, 
 and 80 chains = 1 mile. 
 
 CLOTH MEASURE. 
 
 2} inches = 1 nail nl. 
 
 4 nails = 1 quarter qr. 
 
 4 quarters = 1 yard yd. 
 
 8 quarters = 1 Flemish ell Fl. e. 
 
 5 quarters = 1 English ell En. «. 
 
 6 quarters =: 1 French ell Fr. e. 
 37 inches = 1 Scotch ell Sc. e. 
 
 GEOGRAPHICAL MEASURE. 
 6076 feet nearly = 1 geo. mile 
 3 miles = 1 league le. 
 
 20 leagues = 1 degree dpg. or" 
 360 degrees =. the earth's cir- 
 cumference 
 
 SQUARE, OR LAND MEASURE. 
 
 144 square inches = 1 square foot 
 9 sq. feet = 1 square yard 
 
 30 J sq. yards ^ 1 pole or perck 
 40 perches = 1 rood ro. 
 4 roods =1 acre ac. 
 
 640 acres = 1 sq. mile 
 
 36 sq. yards = 1 rood of building 
 100 sq. feet =1 square of flooring 
 
 10 sq. chains, or ) ^ 
 
 100,000 sq. links | — -^ acie 
 
 CUBIC, OR SOLID MEASURE. 
 1728 cubic inches = 1 cubic foot 
 27 cubic feet = 1 cubic yard 
 
 40 cubic feet of) 
 
 rough, or 50 of V= 1 load lo. 
 
 hewn timber J 
 42 cubic feet = 1 ton shipping 
 
 6 cubic feet = 1 barrel bulk 
 
 MEASURE OF CAPACITY. 
 2 pints pt. = 1 quart qt. 
 
 4 quarts = 1 gallon 
 
 2 gallons = 1 peck 
 
 4 pecks = 1 bushel 
 
 8 bushels = 1 quarter 
 
 pk. 
 bu. 
 qr. 
 
 ANGULAR MEASURE. 
 60 seconds " =1 minute ' 
 60 minutes = 1 degree ** 
 
 30 degrees = 1 sign 5. 
 
 12 signs = 1 circle cira. 
 
 • In the British Pharmacopoeia (1864), the 
 whue the lb. avoir, of 7000 grains, and the oz. 1 
 
 . Troy of 4f10 prains has been abolished, 
 »oir. of 437^ grains, have been adopted. 
 
ARITHMETICAL TABLES. 
 
 APOTHECARIES' 
 FLUID MEASURE * 
 
 60 minims min. = 1 drachm Jl. drm. 
 
 8 drachms = 1 ounce /f. oz. 
 20 ounces = 1 pint O. 
 
 8 pints = 1 gallon C. 
 
 HAY AND STRAW WEIGHT. 
 
 36 lbs. avoir. = 1 truss of straw 
 56 lbs. = 1 truss of old hay 
 
 60 lbs. = 1 truss of new hay 
 
 36 trusses = 1 load 
 
 Hay sold befween the begirning of June 
 and the end of August, of that gear's 
 growth, is reckoned new. 
 
 TIME. 
 
 60 seconds sec. = 1 minute mi. 
 60 minutes = 1 hour ho. 
 
 24 hours =. 1 day da. 
 
 7 days = 1 week we. 
 
 4 weeks = 1 co. month mo. 
 
 365 days, or 52 ] 
 
 weeks and 1 >-= 1 co. year t/e. 
 day j 
 
 365J days = 1 Julian year 
 
 366 days = 1 leap year 
 
 The year is divided into 12 cal 
 endar months, viz. : 
 
 QUARTERLY TERMS. 
 
 In England. 
 Lady-day, March 25. 
 
 Midsummer, June 24. 
 
 Michaelmas, September 29. 
 
 Christmas, December 25. 
 
 In Scotland. 
 Candlemas, February 2. 
 
 Whitsunday, May 15. 
 
 Lammas, August 1. 
 
 Martinmas, November 11. 
 
 FLOUR & BREAD WEIGHT. 
 A peck-loaf = 17 lb. 6 oz. avoird. 
 A half-peck do. = 8 11 — 
 
 A quarter-loaf = 4 5J — - 
 
 A peck of flour is 14-44 lb,, or 
 14J lbs. nearly, and a bushel 57J lbs. 
 very nearly. Five bushels make a 
 sack, which ought to weigh 288-8 
 lbs. avoirdupois. 
 
 The number of days in each month may be easily remembered from 
 the following lines : 
 
 Thirty days hath September, 
 April, June, and November; 
 All the rest have thirty-one, 
 Excepting February alone, 
 Which hath but 28 days clear, 
 And 29 in each leap year. 
 
 365 days 5 hours 48 min. 50 sec. = 1 solar or tropical year. 
 
 January 31 days. 
 February 28 — 
 March 31 — 
 April 30 — 
 May 31 — 
 
 June 30 — 
 
 July 31 days. 
 August 31 — 
 Septem.30 — 
 October 31 — 
 Novem. 30 — 
 Decern. 31 — 
 
 MISCELLANEOUS TABLE. 
 
 24 sheets 
 
 20 quires 
 
 10 reams 
 
 12 articles 
 
 20 articles 
 
 12 dozen 
 
 12 gross 
 
 120 articles 
 
 500 bricks 
 
 1000 tiles 
 
 : 1 quire of paper 
 
 : 1 ream 
 
 : 1 bale 
 
 : 1 dozen 
 
 : 1 score 
 
 : 1 gross 
 
 r 1 great gross 
 
 = 1 great hundred 
 
 : 1 load 
 
 = 1 load 
 
 500 herrings = 
 
 500 red do. = 
 
 10(X) sprats = 
 
 60 herrings = 
 
 100 lbs. avoir.: 
 
 56 lbs. = 
 
 64 lbs. = 
 
 256 lbs. = 
 
 112 lbs. r 
 
 19i cwt. = 
 
 : 1 barrel 
 
 : 1 cade 
 
 : 1 cade 
 
 :1 keg 
 
 : 1 bari. gunpowder 
 
 : 1 firkin of butter 
 
 : 1 firkin of soap 
 
 : 1 baiTel of soap 
 
 : 1 barrel of raisins 
 
 : 1 foddftr of lead 
 
 ♦ AocordiiMi to the British Pharmacopoeia (18C4>. 
 
ARITHMETICAL TABLES. 
 
 Farthings. 
 
 Pence. 
 
 qrs 
 
 d. 
 
 d. s. d. 
 
 4= 
 
 = 1 
 
 12=1 
 
 6. 
 
 .. 1; 
 
 13.. .1 1 
 
 6. 
 
 .. It 
 
 14.. .1 2 
 
 7. 
 
 .. 1: 
 
 15.. .1 3 
 
 8. 
 
 .. 2 
 
 16.. .1 4 
 
 9. 
 
 .. 2J 
 
 17.. .1 5 
 
 10. 
 
 .. 2% 
 
 18.. .1 6 
 
 11. 
 
 .. 2| 
 
 19.. .1 7 
 
 12. 
 
 .. 3 
 
 20.. .1 8 
 
 13. 
 
 .. 3i 
 
 21.. .1 9 
 
 14. 
 
 . 3$ 
 
 22.. .1 10 
 
 15. 
 
 . 3| 
 
 23.. .1 11 
 
 IG. 
 17. 
 18. 
 19. 
 
 . 4 
 
 24... 2 
 25.. .2 1 
 26.. .2 2 
 27.. .2 3 
 
 20. 
 21. 
 
 . 5 
 . 5i 
 
 28.. .2 4 
 29.. .2 5 
 
 22. 
 
 . 5 J 
 
 30.. .2 6 
 
 23. 
 
 . 61 
 
 31.. .2 7 
 
 24. 
 
 . 6 
 
 32.. .2 8 
 
 25. 
 
 . 6J 
 
 33.. .2 9 
 
 26. 
 
 . ^ 
 
 34.. .2 10 
 
 27. 
 
 • 4 
 
 35.. .2 11 
 
 28. 
 
 . 7 
 
 36.. .3 
 
 29. 
 
 • 7} 
 
 37.. .3 1 
 
 30. 
 
 • 7} 
 
 38.. .3 2 
 
 31. 
 
 • n 
 
 39.. .3 3 
 
 82. 
 
 . 8 
 
 40... 3 4 
 
 33. 
 
 • 8i 
 
 41.. .3 5 
 
 34.. 
 
 . 8} 
 
 42.. .3 6 
 
 35.. 
 
 • n 
 
 43.. .3 7 
 
 36.. 
 
 . 9 
 
 44.. .3 8 
 
 37.. 
 
 • H 
 
 45... 3 9 
 
 38.. 
 
 . 9f 
 
 46.. .3 10 
 
 39.. 
 
 • n 
 
 47. ..3 11 
 
 40.. 
 
 .10 
 
 48... 4 
 
 41. 
 
 •lOi 
 
 49.. .4 1 
 
 42. 
 
 •lOJ 
 
 50... 4 2 
 
 43. 
 
 .io| 
 
 51. ..4 3 
 
 44 
 
 .11 
 
 52... 4 4 
 
 45. 
 
 .llj 
 
 53... 4 5 
 
 46. 
 
 .11} 
 
 54... 4 6 
 
 47. 
 
 .lll 
 
 55.. .4 7 
 
 48. 
 
 .12 
 
 56.. .4 8 
 
 MONEY TABLE. 
 
 d. s. 
 57=4 
 58.. .4 
 59.. .4 
 60... 5 
 61.. .5 
 62.. .5 
 63..,5 
 64.. .5 
 65.. .5 
 66.. .5 
 67.. .5 
 68.. .5 
 69.. .5 
 70.. .5 
 71.. .5 
 72.. .6 
 73... 6 
 74.. .6 
 75.. .6 
 76.. .6 
 77.. .6 
 78.. .6 
 79.. .6 
 80... 6 
 81.. .6 
 82.. .6 
 83... 6 
 84.. .7 
 85.. .7 
 86.. .7 
 87.. .7 
 88.. .7 
 89.. .7 
 90.. .7 
 91.. .7 
 92.. .7 
 93... 7 
 94... 7 
 95.. .7 
 96.. .8 
 97.. .8 
 98.. 8 
 99... 8 
 100.. .8 
 101.. .8 
 
 
 Shillings. 1 
 
 . d. 
 
 sk. 
 
 £ s. 
 
 9 
 
 20= 
 
 =1 
 
 10 
 
 21. 
 
 ..1 1 
 
 11 
 
 22. 
 
 ..1 2 
 
 
 
 23. 
 
 ..1 3 
 
 1 
 
 24. 
 
 ..1 4 
 
 2 
 
 25. 
 
 ..1 5 
 
 3 
 
 26. 
 
 ..1 6 
 
 4 
 
 27. 
 
 ..1 7 
 
 5 
 
 28. 
 
 ..1 8 
 
 6 
 
 29. 
 
 ..1 9 
 
 7 
 
 30. 
 
 ..110 
 
 8 
 
 31. 
 
 ..1 11 
 
 9 
 
 32. 
 
 ..1 12 
 
 10 
 
 33. 
 
 ..1 13 
 
 11 
 
 34. 
 
 .1 14 
 
 
 
 35. 
 
 ..1 15 
 
 1 
 
 36. 
 
 .116 
 
 2 
 
 37. 
 
 .1 17 
 
 3 
 
 38. 
 
 .1 18 
 
 4 
 
 39. 
 
 .1 19 
 
 5 
 
 40. 
 
 .2 
 
 6 
 
 41. 
 
 .2 1 
 
 7 
 
 42. 
 
 .2 2 
 
 8 
 
 43. 
 
 .2 3 
 
 9 
 
 44. 
 
 .2 4 
 
 10 
 
 45. 
 
 .2 5 
 
 11 
 
 46. 
 
 .2 6 
 
 
 
 47. 
 
 .2 7 
 
 1 
 
 48. 
 
 .2 8 
 
 2 
 
 49. 
 
 .2 9 
 
 3 
 
 50. 
 
 .2 10 
 
 4 
 
 51. 
 
 .2 11 
 
 5 
 
 52. 
 
 .2 12 
 
 6 
 
 53. 
 
 .2 13 
 
 7 
 
 54.. 
 
 .2 14 
 
 8 
 
 55. 
 
 .2 15 
 
 9 
 
 56. 
 
 .2 16 
 
 10 
 
 57. 
 
 .2 17 
 
 11 
 
 58. 
 
 .2 18 
 
 
 
 59. 
 
 .2 19 
 
 1 
 
 60. 
 
 .3 
 
 2 
 
 61. 
 
 .3 1 
 
 3 
 
 62. 
 
 .3 2 
 
 4 
 
 63. 
 
 .3 3 
 
 5 
 
 64. 
 
 .3 4 
 
 sh. 
 
 65= 
 
 66. 
 
 67. 
 
 68. 
 
 69. 
 
 70. 
 
 71. 
 
 72. 
 
 73. 
 
 74. 
 
 75. 
 
 76. 
 
 77. 
 
 78. 
 
 79. 
 
 80. 
 
 81. 
 
 82. 
 
 83. 
 
 84. 
 
 85., 
 
 86., 
 
 87., 
 
 88., 
 
 89., 
 
 90., 
 
 91., 
 
 92.. 
 
 93.. 
 
 94.. 
 
 95.. 
 
 96.. 
 
 97.. 
 
 98.. 
 
 99.. 
 100.. 
 101.. 
 102.. 
 103.. 
 104.. 
 105.. 
 106.. 
 107.. 
 108.. 
 109., 
 
 £ 
 =3 
 .3 
 .3 
 
 ..3 
 ,.3 9 
 .3 10 
 ,.3 11 
 .3 12 
 ,.3 13 
 .3 14 
 .3 15 
 .3 16 
 .3 17 
 .3 18 
 .3 19 
 .4 
 .4 1 
 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 4 
 
 .4 10 
 .4 11 
 .4 12 
 .4 13 
 .4 14 
 .4 15 
 .4 16 
 .4 17 
 .4 18 
 .4 19 
 .5 
 
10 
 
 ARITHMETICAL TABLES. 
 
 NUMERATION TABLE. 
 
 Units 9 
 
 Tens 98 
 
 Hundreds 987 
 
 Thousands 9; 876 
 
 Tens of Thousands 98; 765 
 
 Hundreds of Thousands 987 ; 654 
 
 Millions 9 ; 876 ; 643 
 
 Tens of Millions 98; 765; 432 
 
 Hundreds of Millions 987 : 654 ; 321 
 
 Billions 9; 876; 543; 210 
 
 Tens of Billions 98; 765; 432; 109 
 
 Hundreds of Billions 987; 654; 321; 098 
 
 Trillions 9; 876; 543; 210; 987 
 
 EOMAN NOTATION. 
 
 The Eomans used the following letters only for numbers, viz. 
 I one, V five, X ten, L fifty, C a hundred, D or Iq five hundred, 
 and M or CI^ a thousand. 
 
 Any letter followed by another of equal or less value denoted 
 the sum of their separate values ; thus III three, LXXVl 
 seventy-six. 
 
 Any letter followed by another of greater value denoted the 
 liflerence of their separate values ; thus XL forty, XC ninety. 
 
 Every 3 annexed to Iq, and every C and 3 joined to CIq, 
 increased the value ten times ; thus 1q3 five thousand, CCIq;;) 
 ten thousand. 
 
 A line drawn over a letter denoted that its simple value was 
 increased a thousand times ; thus X ten thousand, XL forty 
 thousand. 
 
 1 
 
 or 1 
 
 XVII 
 
 or 17 
 
 II 
 
 .. 2 
 
 XVIII 
 
 .. 18 
 
 III 
 
 .. 3 
 
 XIX 
 
 .. 19 
 
 IV 
 
 .. 4 
 
 XX 
 
 .. 20 
 
 V 
 
 .. 5 
 
 XXI 
 
 .. 21 
 
 VI 
 
 .. 6 
 
 XXII 
 
 .. 22 
 
 VII 
 
 .. 7 
 
 XXIII 
 
 .. 23 
 
 VIII 
 
 .. 8 
 
 XXIV 
 
 .. 24 
 
 IX 
 
 .. 9 
 
 XXV 
 
 .. 25 
 
 X 
 
 .. 10 
 
 XXVI 
 
 .. 26 
 
 XI 
 
 .. 11 
 
 XXVII 
 
 .. 27 
 
 XII 
 
 .. 12 
 
 XXVIII 
 
 .. 28 
 
 XIII 
 
 .. 13 
 
 XXIX 
 
 .. 29 
 
 XIV 
 
 .. 14 
 
 XXX 
 
 .. 30 
 
 XV 
 
 .. 15 
 
 XL 
 
 .. 40 
 
 XVI 
 
 .. 16 
 
 L 
 
 .. 50 
 
 LX or 
 
 60 
 
 LXX 
 
 70 
 
 LXXX 
 
 80 
 
 XC 
 
 90 
 
 C 
 
 100 
 
 CI, &c. 
 
 101 
 
 CC, &c. 
 
 200 
 
 CCCC or CD .. 
 
 400 
 
 lO or D 
 
 500 
 
 l0CorDC,&c. .. 
 
 600 
 
 loCCCC, DCCCC, 
 
 or CM 900 
 
 CIo or M 
 
 1000 
 
 CIoCorMC,&c... 
 
 1100 
 
 MM or II, &c. .. 
 
 2000 
 
 loo 0^ ^» «^c. .. 
 
 5000 
 
 lODO or L, &c. .. 
 
 50,000 
 
ARITHMETIC. 
 
 Arithmetic, as a science, explains the propei'ties of num- 
 bers, and as an art, the methods of computing by them. 
 
 The fundamental rules are. Numeration, Notation, Ad- 
 dition, Subtraction, Multiplication, and Division. 
 
 The characters by which all numbers are expressed are, 
 1, one or unit; 2, two; 3, three; 4, four; 5, Jive; 6, six, 
 7, seven; 8, eight; 9, nine; 0, cipher or nought. 
 
 NUMERATION 
 Is the art of reading a number expressed in figures. 
 
 Trillions. Billions. Millions. Thousands. Units. 
 
 604; 450; 360; 412; 474. 
 
 Read or write in words the following : 
 24079 — Twenty-four thousand and seventy-nine. 
 79_97_18— 24— 81— 67— 76— 35— 67— 26— 53— 91 — 19 
 —48—101—208—84—110—802 — 111 — 109—119 — 125 — 
 152—319—913—301—310—4617—4107—4170—28410— 
 20814—5106—74125—47010—2097431—501746-730087— 
 1730086—9704010—21070—20202020—5170409 — 2017101 
 — 74107 — 1074010 — 29654301 — 102030401 — 157301074 
 —748017018—547207542—63710073001—54872193543270. 
 
 NOTATION 
 Is the art of expressing any given number in figures. 
 
 Express in fig^ires the following : 
 Five thousand and sixty-four — 5064. 
 Seventy-four — ninety-six — one hundred and one — one 
 hundi-ed and ten — one hundred and eleven — two hundred 
 and eight — one hundred and eighteen — one hundred and 
 thirty-one — one hundred and thirteen — seven hundred and 
 eight — nine hundred and eighty — two thousand, three hun- 
 dred and twenty-one — nine thousand and seven — twenty- 
 one thousand and ten — one hundred and fifty thousand 
 and five — six millions, forty thousand and thirty — eighty- 
 niue millions, one hundred and forty thousand and twenty- 
 six — seven hundred billions, ten millions, eleven thousand, 
 one hundred and one — four hundred and one millions, seventy 
 thousand and seventeen — eight trillions, twenty billions, 
 sixty-nine millions, four thousand and sixty-three. 
 
 B 
 
12 
 
 SIMPLE ADDITION 
 Is the method of finding a number equal to several num- 
 bers taken togetlier. The number found is called the 
 sum or amount. 
 
 
 
 EXERCISES ON THE ADDITION TABLE. 
 
 
 
 1. 2. 
 
 3. 4. 5. 6. 7. 8. 9. 10. 11. 
 
 12. 
 
 13. 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2 
 
 3 
 
 4 
 
 5 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 
 
 2 
 
 3 
 
 4 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 4 
 
 1 
 
 2 
 
 3 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2 
 
 5 
 
 1 
 
 2 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 3 
 
 2 
 
 5 
 
 7 
 
 7 
 
 14 
 
 21 
 
 28 
 
 35 
 
 42 
 
 49 
 
 56 
 
 63 
 
 19 
 
 22 
 
 26 
 
 34 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 7 
 
 6 
 
 9 
 
 5 
 
 4 
 
 9 
 
 7 
 
 7 
 
 6 
 
 3 
 
 6 
 
 2 
 
 6 
 
 2 
 
 4 
 
 3 
 
 3 
 
 5 
 
 2 
 
 2 
 
 1 
 
 3 
 
 4 
 
 4 
 
 4 
 
 2 
 
 1 
 
 7 
 
 3 
 
 5 
 
 9 
 
 8 
 
 4 
 
 1 
 
 7 
 
 2 
 
 8 
 
 8 
 
 8 
 
 5 
 
 7 
 
 2 
 
 8 
 
 4 
 
 6 
 
 6 
 
 4 
 
 3 
 
 4 
 
 1 
 
 4 
 
 1 
 
 2 
 
 7 
 
 9 
 
 3 
 
 3 
 
 9 
 
 5 
 
 7 
 
 5 
 
 2 
 
 6 
 
 8 
 
 6 
 
 6 
 
 5 
 
 1 
 
 3 
 
 6 
 
 1 
 
 4 
 
 1 
 
 6 
 
 8 
 
 4 
 
 1 
 
 2 
 
 3 
 
 8 
 
 7 
 
 4 
 
 1 
 
 5 
 
 8 
 
 2 
 
 6 
 
 2 
 
 7 
 
 9 
 
 2 
 
 6 
 
 1 
 
 7 
 
 5 
 
 5 
 
 2 
 
 3 
 
 4 
 
 7 
 
 2 
 
 1 
 
 3 
 
 8 
 
 2 
 
 8 
 
 8 
 
 8 
 
 9 
 
 9 
 
 8 
 
 6 
 
 3 
 
 2 
 
 3 
 
 3 
 
 2 
 
 4 
 
 9 
 
 4 
 
 4 
 
 4 
 
 7 
 
 6 
 
 3 
 
 3 
 
 9 
 
 4 
 
 1 
 
 4 
 
 4 
 
 3 
 
 5 
 
 1 
 
 5 
 
 7 
 
 5 
 
 3 
 
 8 
 
 2 
 
 6 
 
 7 
 
 2 
 
 1 
 
 5 
 
 4 
 
 4 
 
 6 
 
 2 
 
 6 
 
 1 
 
 2 
 
 6 
 
 2 
 
 7 
 
 4 
 
 3 
 
 1 
 
 2 
 
 6 
 
 2 
 
 5 
 
 7 
 
 3 
 
 7 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 33. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 38. 
 
 39. 
 
 40. 
 
 41. 
 
 42. 
 
 43. 
 
 7 
 
 4 
 
 7 
 
 8 
 
 1 
 
 7 
 
 4 
 
 7 
 
 9 
 
 9 
 
 6 
 
 3 
 
 5 
 
 7 
 
 9 
 
 2 
 
 2 
 
 9 
 
 7 
 
 9 
 
 2 
 
 2 
 
 9 
 
 7 
 
 2 
 
 7 
 
 8 
 
 2 
 
 2 
 
 5 
 
 6 
 
 3 
 
 6 
 
 6 
 
 6 
 
 1 
 
 9 
 
 6 
 
 5 
 
 8 
 
 4 
 
 1 
 
 1 
 
 9 
 
 4 
 
 1 
 
 1 
 
 5 
 
 2 
 
 3 
 
 8 
 
 9 
 
 3 
 
 6 
 
 6 
 
 8 
 
 7 
 
 4 
 
 8 
 
 6 
 
 8 
 
 8 
 
 4 
 
 1 
 
 4 
 
 4 
 
 8 
 
 8 
 
 3 
 
 8 
 
 2 
 
 4 
 
 7 
 
 5 
 
 7 
 
 3 
 
 7 
 
 2 
 
 3 
 
 8 
 
 2 
 
 7 
 
 7 
 
 8 
 
 4 
 
 4 
 
 2 
 
 9 
 
 3 
 
 2 
 
 9 
 
 5 
 
 1 
 
 8 
 
 7 
 
 1 
 
 5 
 
 2 
 
 7 
 
 2 
 
 8 
 
 6 
 
 8 
 
 1 
 
 1 
 
 5 
 
 4 
 
 3 
 
 4 
 
 2 
 
 3 
 
 6 
 
 9 
 
 4 
 
 2 
 
 2 
 
 9 
 
 3 
 
 4 
 
 3 
 
 6 
 
 2 
 
 9 
 
 6 
 
 1 
 
 8 
 
 7 
 
 8 
 
 5 
 
 8 
 
 6 
 
 8 
 
 6 
 
 7 
 
 5 
 
 4 
 
 1 
 
 5 
 
 2 
 
 6 
 
 2 
 
 8 
 
 4 
 
 8 
 
 7 
 
 5 
 
 3 
 
 9 
 
 2 
 
 7 
 
 5 
 
 3 
 
 2 
 
 1 
 
 1 
 
 1 
 
 5 
 
 6 
 
 3 
 
 4 
 
 1 
 
 7 
 
 4 
 
 3 
 
 9 
 
 3 
 
 8 
 
 1 
 
 8 
 
 8 
 
 6 
 
 4 
 
 3 
 
 7 
 
 6 
 
 2 
 
 9 
 
 8 
 
 9 
 
 6 
 
SIMPLE ADDITION. 
 
 13 
 
 Example. Add together 847, 478, 19, and 951. Ans. 229 
 Solution. Arrange the numbers as in the margin ; 
 adding the units' or right-hand column, 1 and 9 are 
 10 and 8 are 18 and 7 are 25 ; write down 5 and carry 
 2 to the second column : 2 and 5 are 7 and 1 are 8 
 and 7 are 15 and 4 are 19 ; write down 9 and carry 
 1 to the third column : 1 and 9 are 10 and 4 are 14 
 and 8 are 22 ; write down 22, and the answer is 2295. 
 
 The work may be checked by adding the columns down^ 
 wards. 
 
 847 
 
 478 
 
 19 
 
 951 
 
 2295 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 234 
 
 754 
 
 869 
 
 649 
 
 214 
 
 314 
 
 987 
 
 374 
 
 215 
 
 118 
 
 982 
 
 475 
 
 698 
 
 495 
 
 421 
 
 431 
 
 879 
 
 743 
 
 152 
 
 181 
 
 342 
 
 638 
 
 986 
 
 218 
 
 638 
 
 209 
 
 798 
 
 437 
 
 521 
 
 811 
 
 758 
 
 863 
 
 213 
 
 821 
 
 863 
 
 920 
 
 654 
 
 865 
 
 634 
 
 214 
 
 875 
 
 921 
 
 542 
 
 637 
 
 759 
 
 516 
 
 465 
 
 685 
 
 463 
 
 579 
 
 426 
 
 192 
 
 121 
 
 736 
 
 975 
 
 651 
 
 546 
 
 856 
 
 346 
 
 798 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 7486 
 
 2146 
 
 4816 
 
 5411 
 
 2222 
 
 8888 
 
 5555 
 
 4848 
 
 4867 
 
 6412 
 
 6184 
 
 2196 
 
 3333 
 
 9999 
 
 6666 
 
 5959 
 
 2194 
 
 1093 
 
 7298 
 
 3482 
 
 4444 
 
 nil 
 
 7777 
 
 6767 
 
 1942 
 
 3901 
 
 8735 
 
 9876 
 
 5555 
 
 2222 
 
 8888 
 
 7676 
 
 7368 
 
 2473 
 
 4567 
 
 3846 
 
 ^m^ 
 
 3333 
 
 9999 
 
 9595 
 
 3687 . 
 
 3742 
 
 8912 
 
 2198 
 
 7771 
 
 4444 
 
 1111 
 
 8484 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 26. 
 
 1234 
 
 7921 
 
 4869 
 
 1276 
 
 1874 
 
 2764 
 
 4872 
 
 6729 
 
 6678 
 
 1297 
 
 5728 
 
 2761 
 
 7481 
 
 6427 
 
 3481 
 
 6278 
 
 9012 
 
 3808 
 
 6372 
 
 3849 
 
 2310 
 
 3818 
 
 5834 
 
 6483 
 
 3456 
 
 8076 
 
 7184 
 
 4598 
 
 1046 
 
 2984 
 
 6287 
 
 7321 
 
 7890 
 
 6487 
 
 8296 
 
 6623 
 
 9875 
 
 4629 
 
 7821 
 
 1234 
 
 1234 
 
 7923 
 
 9543 
 
 6312 
 
 6793 
 
 9273 
 
 1234 
 
 6678 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 33. 
 
 34. 
 
 9847 
 
 2146 
 
 4121 
 
 1214 
 
 2009 
 
 .9817 
 
 9002 
 
 7189 
 
 6438 
 
 6148 
 
 1246 
 
 6421 
 
 9002 
 
 1789 
 
 2009 
 
 9871 
 
 5279 
 
 6437 
 
 3459 
 
 9543 
 
 4716 
 
 2138 
 
 6174 
 
 8312 
 
 7346 
 
 2977 
 
 9528 
 
 8259 
 
 6174 
 
 4817 
 
 4716 
 
 7184 
 
 8978 
 
 3888 
 
 6473 
 
 3746 
 
 8136 
 
 7864 
 
 6318 
 
 4687 
 
 6438 
 
 8436 
 
 8987 
 
 7898 
 
 2198 
 
 3189 
 
 8912 
 
 9813 
 
14 
 
 SIMPLE ADDITION. 
 
 35. 
 
 36. 
 
 37. 
 
 38. 
 
 39. 
 
 40. 
 
 41. 
 
 8729 
 
 4816 
 
 7286 
 
 9112 
 
 9876 
 
 5469 
 
 5726 
 
 7298 
 
 3729 
 
 3465 
 
 2968 
 
 2187 
 
 3874 
 
 6275 
 
 4165 
 
 5412 
 
 2187 
 
 4627 
 
 4632 
 
 5286 
 
 3874 
 
 2189 
 
 8046 
 
 7129 
 
 3729 
 
 2893 
 
 9684 
 
 9873 
 
 3145 
 
 4208 
 
 1408 
 
 8463 
 
 3984 
 
 5836 
 
 3521 
 
 8729 
 
 9807 
 
 1076 
 
 2198 
 
 5726 
 
 2194 
 
 1234 
 
 42. 
 
 8768 
 7543 
 2189 
 9138 
 
 4672 
 8279 
 
 43. 
 
 44. 
 
 45. 
 
 46. 
 
 47. 
 
 48. 
 
 49. 
 
 50. 
 
 7284 
 
 4869 
 
 2790 
 
 4286 
 
 5216 
 
 2149 
 
 1876 
 
 2168 
 
 4563 
 
 4964 
 
 4623 
 
 6384 
 
 2615 
 
 9186 
 
 3848 
 
 8614 
 
 3629 
 
 5208 
 
 2347 
 
 2198 
 
 3842 
 
 3456 
 
 2193 
 
 2196 
 
 9245 
 
 2080 
 
 5867 
 
 5486 
 
 2876 
 
 7289 
 
 1984 
 
 5483 
 
 5483 
 
 1897 
 
 3867 
 
 2173 
 
 3184 
 
 9738 
 
 4876 
 
 3146 
 
 2196 
 
 7986 
 
 9218 
 
 4817 
 
 7296 
 
 4865 
 
 3842 
 
 8965 
 
 51. 
 
 52. 
 
 53. 
 
 54. 
 
 55. 
 
 56. 
 
 57. 
 
 58. 
 
 9726 
 
 6295 
 
 4872 
 
 2138 
 
 4965 
 
 9876 
 
 3097 
 
 2974 
 
 8643 
 
 4368 
 
 2198 
 
 5483 
 
 3846 
 
 6298 
 
 9808 
 
 9084 
 
 5273 
 
 7348 
 
 8169 
 
 9654 
 
 3876 
 
 6786 
 
 4097 
 
 9840 
 
 2736 
 
 2763 
 
 2367 
 
 3672 
 
 6723 
 
 7236 
 
 1876 
 
 9489 
 
 1894 
 
 9653 
 
 6539 
 
 4875 
 
 9864 
 
 2198 
 
 8965 
 
 1284 
 
 9867 
 
 2198 
 
 4963 
 
 2186 
 
 4372 
 
 7234 
 
 8629 
 
 5814 
 
 3095 
 
 1986 
 
 9631 
 
 8472 
 
 3729 
 
 2139 
 
 6243 
 
 8145 
 
 59. 
 
 60. 
 
 61. 
 
 62. 
 
 63. 
 
 64. 
 
 65. 
 
 66. 
 
 7486 
 
 2981 
 
 7298 
 
 2184 
 
 4763 
 
 4863 
 
 3456 
 
 9871 
 
 2193 
 
 1892 
 
 8917 
 
 4218 
 
 8769 
 
 6348 
 
 7890 
 
 2179 
 
 4728 
 
 3720 
 
 2347 
 
 5763 
 
 2986 
 
 2176 
 
 1234 
 
 5046 
 
 2089 
 
 4175 
 
 5486 
 
 3698 
 
 4863 
 
 8472 
 
 5678 
 
 6804 
 
 9082 
 
 5176 
 
 3847 
 
 7296 
 
 3648 
 
 2784 
 
 9012 
 
 8470 
 
 4754 
 
 2347 
 
 9176 
 
 4738 
 
 2198 
 
 5168 
 
 3456 
 
 1986 
 
 7538 
 
 6129 
 
 7153 
 
 7219 
 
 1927 
 
 3615 
 
 7891 
 
 3459 
 
 67. 
 
 63. 
 
 69. 
 
 70. 
 
 71. 
 
 72. 
 
 73. 
 
 74. 
 
 1874 
 
 2112 
 
 7411 
 
 2119 
 
 86 
 
 834 
 
 2174 
 
 2487 
 
 7486 
 
 331 
 
 1721 
 
 9112 
 
 186 
 
 4747 
 
 4187 
 
 87 
 
 8291 
 
 2897 
 
 862 
 
 7486 
 
 5681 
 
 6363 
 
 83 
 
 7428 
 
 9182 
 
 987 
 
 48 
 
 3849 
 
 2196 
 
 5995 
 
 3189 
 
 83 
 
 3748 
 
 729 
 
 5496 
 
 486 
 
 987 
 
 559 
 
 5 
 
 4876 
 
 1876 
 
 8297 
 
 7486 
 
 42 
 
 91 
 
 87 
 
 1765 
 
 42 
 
 741 
 
 54 
 
 59 
 
 3798 
 
 8746 
 
 63 
 
 6789 
 
 9899 
 
 3496 
 
 7289 
 
 876 
 
 7983 
 
 3904 
 
 7298 
 
 49 
 
 114 
 
SIMPLE ADDITION. 
 
 15 
 
 75. 
 
 76. 
 
 77. 
 
 78. 
 
 79. 
 
 80. 
 
 87469 
 
 18734 
 
 89846 
 
 19876 
 
 98846 
 
 11421 
 
 84697 
 
 81423 
 
 72844 
 
 28674 
 
 21174 
 
 21896 
 
 33442 
 
 47884 
 
 51168 
 
 54869 
 
 38965 
 
 69847 
 
 21756 
 
 58337 
 
 27489 
 
 96843 
 
 56897 
 
 38176 
 
 67498 
 
 21486 
 
 98472 
 
 21876 
 
 21984 
 
 47897 
 
 39846 
 
 68742 
 
 21224 
 
 48638 
 
 51478 
 
 38189 
 
 27485 
 
 89638 
 
 18769 
 
 88768 
 
 31894 
 
 49898 
 
 58744 
 
 48621 
 
 97652 
 
 21777 
 
 98499 
 
 98974 
 
 81. 
 
 82. 
 
 83. 
 
 84. 
 
 85. 
 
 86. 
 
 74985 
 
 71279 
 
 84120 
 
 98797 
 
 98724 
 
 34563 
 
 12345 
 
 48694 
 
 21796 
 
 38468 
 
 84786 
 
 78908 
 
 67890 
 
 38848 
 
 69845 
 
 21896 
 
 86749 
 
 42809 
 
 90876 
 
 97120 
 
 38471 
 
 54868 
 
 87498 
 
 90786 
 
 65217 
 
 17208 
 
 18769 
 
 98976 
 
 98863 
 
 36094 
 
 71489 
 
 80967 
 
 48684 
 
 48698 
 
 97377 
 
 27158 
 
 38594 
 
 74689 
 
 18769 
 
 38489 
 
 98776 
 
 38646 
 
 48684 
 
 98467 
 
 38478 
 
 89765 
 
 19864 
 
 64583 
 
 87. 
 
 88. 
 
 89. 
 
 90. 
 
 91. 
 
 92. 
 
 47216 
 
 90804 
 
 49899 
 
 48899 
 
 87748 
 
 47189 
 
 86143 
 
 79048 
 
 98765 
 
 37744 
 
 51123 
 
 98765 
 
 31487 
 
 21886 
 
 34775 
 
 44768 
 
 17648 
 
 38486 
 
 21879 
 
 66477 
 
 21984 
 
 89443 
 
 48679 
 
 34896 
 
 39842 
 
 38896 
 
 56348 
 
 34886 
 
 15015 
 
 69847 
 
 23876 
 
 59769 
 
 84237 
 
 29876 
 
 27987 
 
 97849 
 
 54875 
 
 27998 
 
 73486 
 
 54869 
 
 92764 
 
 38488 
 
 16846 
 
 54889 
 
 54997 
 
 12345 
 
 89898 
 
 21776- 
 
 93. 
 
 94. 
 
 95. 
 
 96. 
 
 97. 
 
 98. 
 
 94863 
 
 42174 
 
 8989 
 
 49864 
 
 97867 
 
 8765 
 
 8639 
 
 7148 
 
 98798 
 
 644 
 
 1008 
 
 219 
 
 86394 
 
 837 
 
 654 
 
 6449 
 
 976 
 
 38480 
 
 7563 
 
 1896 
 
 94568 
 
 21786 
 
 54890 
 
 10846 
 
 75638 
 
 61784 
 
 28 
 
 38486 
 
 12789 
 
 8973 
 
 6387 
 
 4721 
 
 2875 
 
 9876 
 
 76 
 
 87997 
 
 29846 
 
 12 
 
 38486 
 
 54868 
 
 38147 
 
 738 
 
 4875 
 
 38469 
 
 94783 
 
 987 
 
 21898 
 
 84778 
 
 99. 7368+ 8451+5184+6372+ 3147+1763 + 2189. 
 
 100. 5436+ 2195+7964+6830+ 8347+5146+ 798. 
 
 101. 73847+85487+3486+5763+84695+3146+ 495. 
 
 b2 
 
16 
 
 SIMPLE ADDITION. 
 
 102. 
 
 103. 
 
 104. 
 
 105. 
 
 106. 
 
 714816 
 
 187621 
 
 876548 
 
 971028 
 
 918765 
 
 148617 
 
 317849 
 
 721473 
 
 876980 
 
 187659 
 
 548389 
 
 948647 
 
 374869 
 
 487694 
 
 876591 
 
 821864 
 
 218698 
 
 968768 
 
 527389 
 
 243876 
 
 217784 
 
 384869 
 
 486842 
 
 938765 
 
 438762 
 
 548987 
 
 198768 
 
 172986 
 
 387659 
 
 387624 
 
 987786 
 
 2147-29 
 
 348697 
 
 647548 
 
 876554 
 
 489754 
 
 987486 
 
 374898 
 
 475486 
 
 554433 
 
 457986 
 
 579864 
 
 548694 
 
 754864 
 
 765432 
 
 107. 
 
 108. 
 
 109. 
 
 110. 
 
 111. 
 
 314579 
 
 869457 
 
 304756 
 
 274816 
 
 908076 
 
 145793 
 
 694578 
 
 475630 
 
 748163 
 
 807069 
 
 457931 
 
 945786 
 
 756309 
 
 481634 
 
 760908 
 
 579314 
 
 457869 
 
 563098 
 
 816345 
 
 219374 
 
 894632 
 
 578694 
 
 630987 
 
 123456 
 
 475432 
 
 946328 
 
 786945 
 
 789063 
 
 234567 
 
 173849 
 
 463284 
 
 123456 
 
 890637 
 
 345678 
 
 948386 
 
 632846 
 
 789012 
 
 637890 
 
 876543 
 
 872198 
 
 328466 
 
 345678 
 
 378906 
 
 765432 
 
 749865 
 
 778998 
 
 901234 
 
 906378 
 
 654321 
 
 384976 
 
 112. 
 
 113. 
 
 114. 
 
 115. 
 
 116. 
 
 548637 
 
 493128 
 
 795846 
 
 497864 
 
 998776 
 
 486378 
 
 931284 
 
 598467 
 
 864794 
 
 887769 
 
 863789 
 
 312849 
 
 218694 
 
 468479 
 
 776698 
 
 637890 
 
 128493 
 
 580308 
 
 684947 
 
 433821 
 
 749087 
 
 740086 
 
 984678 
 
 218624 
 
 388466 
 
 490876 
 
 409648 
 
 394867 
 
 374186 
 
 218968 
 
 471874 
 
 218408 
 
 973842 
 
 987384 
 
 478149 
 
 548643 
 
 184820 
 
 298765 
 
 219864 
 
 941798 
 
 896847 
 
 123456 
 
 458738 
 
 718698 
 
 217486 
 
 376849 
 
 654321 
 
 219986 
 
 398748 
 
 989999 
 
 729287 
 
 987489 
 
 487219 
 
 216847 
 
 874865 
 
 117.47563+74298+98254+214865+652193+381964 
 +300892+476983+396847+734682. 
 
 118. 2 14736 + 637240 + 509984 +998447 + 219863 + 
 863214+792186+197235+748692+897628. 
 
 119. 742869+38475+8476+317286 + 863217 + 9846 
 +72354+748693+7486+95476+4721864. 
 

 SIMPLE ADDITION. 
 
 17 
 
 120. 
 
 121. 
 
 122. 
 
 123. 
 
 124. 
 
 786904 
 
 5744 
 
 217846 
 
 849784 
 
 216 
 
 72189 
 
 186473 
 
 3868 
 
 84 
 
 47386 
 
 2891 
 
 862 
 
 9 
 
 7698 
 
 472 
 
 749863 
 
 7648 
 
 778466 
 
 377669 
 
 8 
 
 2847 
 
 97448 
 
 47 
 
 4886 
 
 67489 
 
 47283 
 
 189654 
 
 3848 
 
 847334 
 
 738789 
 
 898647 
 
 347219 
 
 543896 
 
 27 
 
 48 
 
 98 
 
 386 
 
 8965 
 
 7846 
 
 2748 
 
 749 
 
 4 
 
 47 
 
 987654 
 
 64 
 
 7864 
 
 786473 
 
 889764 
 
 87654 
 
 736 
 
 987654 
 
 876 
 
 74869 
 
 78 
 
 876489 
 
 125. 7486 + 7489 + 9846 + 3748 + 5634+7486+ 9847 
 +5329+4675+3869+9873+8469+4683. 
 
 126. 5276+8943+9486+3114+98760+3456+72894 
 +729+89657+3846+47836+7584+48765. 
 
 127. 74486+311472+68476+38169+744869 + 1870 
 +542138+216746+9876+521869+31468. 
 
 128.7486957+75312984+9104763+7238641+521437 
 +43879654+9876+34819+9896543+47869847. 
 
 129. The population of London, in 1851, was 2,362,236 ; 
 of Dublin, 258,369 ; of Edinburgh and Leith, 191,221 ; 
 of Glasgow, 329,097; of Liverpool, 375,955; of Bir- 
 mingham, 232,841 ; of Manchester, 316,213 ; of Bristol, 
 137,328 ; and of Leeds, 172,270 : required the amount of 
 the whole. 
 
 130. Bought a house for £3150 ; what should it be 
 sold for to gain £275? 
 
 131. The number of wrecks and collisions on or near 
 the coasts of the United Kingdom in 1852 was 1015 ; in 
 1853, 832; in 1854, 987; in 1855, 1141; and in 1856, 
 1153 : find the whole number during these five years. 
 
 132. The total number of British Cavalry who joined 
 the Allied Army in the Crimean Campaign, was 4819 ; 
 Artillery, 7032 ; Sappers and Miners, 403 ; and Infantry, 
 43,726 : how many men joined in all? 
 
 133. In 1856, the passengers conveyed by Kail in 
 Scotland were. First Class, 1,664,005; Second Class. 
 1,952,240; Third Class, 9,476,226; Mixed, 4767: find 
 the total number. 
 
 c 
 
18 SIMPLE ADDITION. 
 
 134. In the same year the receipts were, First Class. 
 £232,130; Second Class,£171,588; Third Class,£436,564; 
 Mixed, £14,892 : required the whole sum. 
 
 135. Find the sum of twenty- seven thousand, eight 
 hundred and forty-nine — thirty-eight thousand, live 
 hundred and forty-six — eight thousand and nine — twelve 
 thousand, nine hundred and sixty-three — five thousand 
 and forty — five hundred and seventy-eight thousand and 
 forty-six — nineteen thousand and sixty — twenty-seven 
 thousand, eight hundred and forty-seven. 
 
 136. A merchant has £1275 in the bank ; his goods are 
 worth £2760 ; his household furniture, £565 ; and debts 
 owing to him, £674 : how much is he worth ? 
 
 137. What quantity of tea was consumed in the 
 United Kingdom in 1856, England having consumed 
 47,986,635 lbs. ; Scotland, 6,583,233 lbs. ; and Ireland, 
 8,708,344 lbs. ? 
 
 138. In 1856, the Emigrants to Canada consisted of 
 5555 English; 3872 Scotch ; 4357 Irish ; 3136 Prussians , 
 2806 Norwegians; 1249 Germans; 823 Belgians; 260 
 Swiss, and 381 Italians, French, &c. ; find the whole 
 number. 
 
 139. Two travellers start from the same place and 
 travel in opposite directions, the one travels 75 miles 
 the first day, 63 the second, and 45 the third ; while the 
 other travels 65 miles the first day, 180 the second, and 
 378 the third : how far distant will they then be from 
 each other ? 
 
 140. In 1856, the quantity of cofi*ee consumed in Eng- 
 land was 33,019,884 lb. ; in Scotland, 1,197,6851b. ; and 
 in Ireland, 778,385 lb. : what quantity was consumed in 
 the United Kingdom ? 
 
 141. In 1856, the tonnage of registered ships in the 
 British Empire was in England, 3,461,031 tons ; in 
 Scotland, 592,974 ; in Ireland, 250,455 ; in Jersey, Man, 
 &c., 62,496 ; and in the Colonies, 949,780 tons : find 
 the amount of tonnage. 
 
 142. A merchant owes to A £597, to B £694, to C 
 £748, to D £899, to E £1045, and to F £1303 j how 
 much does he owe in all? 
 
19 
 
 SIMPLE SUBTRACTION 
 Is the method of taking a less number from a greater. 
 
 The greater number is called the minuend^ the less, 
 the subtrahendj and the number found, the remainder or 
 difference. 
 
 Ex. 
 
 From 7986734 
 Take 2463212 
 Diflf. 5523522 
 
 Ex. 607482678 minuend. 
 
 5140346 subtrahend. 
 602342332 remainder. 
 
 217486973489 
 105342341056 
 
 46798765483 
 23214342352 
 
 85179684729 
 23123461304 
 
 600796857439 
 342526125 
 
 10008694758 
 3242745 
 
 85069857497 
 3042354443 
 
 Ans. 9890771. 
 
 Ex. From 10574363 take 683592. 
 
 Sol. 2 from 3 leaves 1, write 
 down 1 ; 9 from 6 we cannot, but 9 
 from ten leayes 1 and 6 are 7 ; write 
 down 7 ; having borrowed ten, carry 
 one to 5 is 6 from 3 we cannot, but 
 6 from ten leaves 4 and 3 are 7 ; 
 write down 7 and carry one to 3 is 4 from 4, &c. 
 
 The work may be checked by adding the lower nurnber 
 and remainder together, or by subtracting the remainder from 
 the upper number. 
 
 From 
 
 Take 
 
 Difference 
 
 Proof 
 
 Proof 
 
 10574363 
 
 683592 
 
 9890771 
 
 10574363 
 683692 
 
 217634821643 90000000000 
 124368412781 47654321809 
 
 47386743841 
 31728698748 
 
 10. 11. 12. 
 
 987214638475 1 47869386481 63112141763 
 298765428969 j 18976248656 32197648763 
 
 13. 14. 15. 
 
 804765786935 30241704862 47214127004 
 276548674876 18702930409 21807163047 
 
 16. 17. 18. 
 
 172876548734 20468754874 53748688714 
 89658714968 9876547185 31765948976 
 
20 
 
 SIMPLE SUBTRACTION. 
 
 374869040735 
 9876524698 
 
 10074021004 21047386943 
 734861047 987654897 
 
 22. 23. 24. 
 
 734869548647 20417386984 15473846731 
 27486009829 1763047098 7348209872 
 
 25. 
 
 111473869875 
 9174869989 
 
 26. 27. 
 
 21765483642 1 60000472986 
 9176254961 | 73864786 
 
 28. 29. 30. 
 
 300712684734 10203040506 60708090104 
 987000487 1020304050 6070809017 
 
 31. 32. 33. 
 
 10000473698 1 34072986410 20172345604 
 784629 1 29738047306 1073647298 
 
 70047216384 17047386473 40100721647 
 1976006548 8721738462 1700876109 
 
 87. 38. 39. 
 
 21734007201 21738400078 40072173867 
 9172073167 4764873091 74169081 
 
 40. 41. 42. 
 
 100002402503 600043216753 100000643289 
 76543209 67429768 854989 
 
 43. From 
 
 44. From 
 
 45. From 
 
 46. From 
 
 47. From 
 
 48. From 
 
 49. From 
 
 50. From 
 
 51. Take 
 
 52. Take 
 
 53. Take 
 
 54. Take 
 
 55. Take 
 
 748163486 take 79106474 and 549876. 
 2104738400 take 219846736 and 2173844. 
 2174863 take 478654+312842+176348. 
 548629+748634take318467+21986+73894 
 2198641+200473take54876+78698+9846. 
 
 8047- 
 5278- 
 9873- 
 
 7048+5734 take 2174+3846- 
 
 ■8497. 
 
 9176+8796 take 8976+7421+1121. 
 
 •7894+2198 take 4987+8746+1471. 
 2173+4173+9876from 78469+2174+8459. 
 74867382176983 from 4879684721674974. 
 58217384698746 from 5763847218698481. 
 91047384687690 from 9476347869485203. 
 20734076948763 from 9846738479894210. 
 
SIMPLE SUBTRACTION. 21 
 
 56. The battle of Waterloo was fought in 1815, and 
 the battle of the Alma in 1854 ; how many years elapsed 
 between them ? 
 
 57. A merchant owed £2476, but has paid £1587 ; 
 how much does he still owe ? 
 
 58. A man born in 1775, died in 1858; what was his age? 
 
 59. Napoleon I. born in 1769, died in 1821 ; what was 
 his age ? 
 
 60. A man was 98 years old in 1858 ; when was he born ? 
 
 61. Americawas discovered in 1492; howlongis it since? 
 
 62. A piece of cloth contained 1074 yards ; 274 yards 
 were sold to one person and 123 yards to another ; how 
 many yards remained ? 
 
 63. From Edinburgh to York by rail is 209 miles, and 
 to London 413 miles ; how far distant is York from 
 London ? 
 
 64. A ship sails from London to Sydney, a distance of 
 13,640 miles ; after sailing 7684 miles, how far has she 
 still to sail ? 
 
 65. What number added to 354896 will make 432678? 
 
 66. The sum of two numbers is 4789246, and the less 
 is 849758 ; what is the greater ? 
 
 67. Howlong is it since the invention of printing in 1430? 
 
 68. In 1856, the number of Post-office Orders issued 
 in the United Kingdom was 6,178,982 ; the number 
 issued in England and Ireland was 5,693,459 : how many 
 were issued in Scotland ? 
 
 69. The receipts from passengers and goods by rail 
 in Scotland amounted to £2,319,217 in 1856, and from 
 goods alone £1,464,041 ; find the receipts from passen- 
 gers alone. 
 
 70. How long is it since the invention of gunpowder in 
 1400? 
 
 71. B was born when A was 27 years old ; what age is 
 A when B is 51, and how old is B when A is 76 ? 
 
 72. A merchant owed to A £7486, but has paid him 
 £4736; to B, £5746, but has paid him £3721; to C, 
 £10,844, but has paid him £7483 ; to D, £5748, but has 
 paid him £4106 ; to E, £5120, but has paid him £3980; 
 and to F, £11,111, but has paid him £9879 ; how much 
 does he owe to each, and how much in all ? 
 
22 
 
 SIMPLE MULTIPLICATION 
 
 Is a short method of finding the sum of any given num- 
 ber when repeated as many times as there are units in 
 another given number. 
 
 The number to be repeated is called the multiplicand^ 
 the other number, the multiplier^ and the result is called 
 the product. 
 
 The two given numbers are also called factors of the 
 product. 
 
 Case L When multiplier does not exceed 12. 
 
 Ex. Multiply 5974587 by 8. Ans. 47796696. 
 
 Sol. 8 times 7 are 56, write Multiplicand 5974587 
 
 down 6 and carry 5 ; 8 times 8 Multiplier 8 
 
 are 64 and 5 are 69, write down Product 47796696 
 
 9 and carry 6 ; 8 times 5 are 40 = 
 and 6 are 46, &c. 
 
 1. 384607592176 X 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 2. 597260875486 X 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3. 
 
 These Exercises may all be checked by Addition. 
 
 Case II. When the multiplier is found in the table. 
 Ex. Multiply 74867384 by 14. Ans. 1048143376. 
 74867384 X 14 = 2 X 7 
 
 Ex. Mult. 748673 by 20 
 20 
 
 149734768 prod, by 2 
 7 
 
 1048143376 prod, by 14 
 
 14973460 
 
 1. 748674869 
 
 2. 530472937 
 
 3. 374216487 
 
 4. 796548737 
 
 5. 975318642 
 
 6. 759386154 
 
 7. 649587596 
 
 8. 927635849 
 
 9. 123456789 
 10. 987654321 
 
 X16, 
 X15, 
 X22, 
 
 X33, 
 X25, 
 
 X35, 
 X36, 
 X48, 
 X55, 
 X64, 
 
 18, 24. 
 21, 32. 
 30, 28. 
 42, 45. 
 36, 49. 
 27, 44. 
 40, 42. 
 54, 56. 
 60, 63. 
 m, 70. 
 
 11.219703842 
 12.504382796 
 13. 846593742 
 14. 142857142 
 15.846153846 
 16. 952380952 
 17.543207159 
 18.791364857 
 19. 517369428 
 20. 629752837 
 
 X72, 77, 81. 
 X84, 88, 90. 
 X96, 99,110. 
 X96, 81, 63. 
 X80, 96, 77. 
 X 81,121,144. 
 X 99,132,121. 
 X 84,110,100. 
 X56, 54,132. 
 X 45,121, 81. 
 
SIMPLE MULTIPLICATION. 
 
 '23 
 
 Case III. When the multiplier is not found in the 
 table, and does not exceed 156, or 12 X 12 + 12. 
 
 Ex. 74238476X26=5X6+1 
 
 5 
 
 371192380= 5 times 
 5 
 
 1855961900 = 25 >^ 
 74238476= 1 " 
 
 Ex. 67584937X38=6X6+2 
 
 6 
 
 405509622 = 6 times 
 6 
 
 2433057732 = 36 »* 
 135169874 = 2 ,' 
 2568227606 = 38 times 
 
 1930200376 = 26 times 
 
 1. 674295386 X 17, 23, 26, 29, 31, 34, 37, 43, 46. 
 
 2. 965830295 X 38, 47, 62, 58, 62, 68, 74, 79, 83. 
 
 3. 534869738 X 39, 59, 69, 75, 87, 93, 103, 105, 115. 
 
 4. 275963849 X 19, 38, 47, 59, 74, 87, 95, 137, 149. 
 Case IV. When the multiplier exceeds 156. 
 
 Ex. 3210421765X235 
 235 
 
 16052108825= 5 times 
 9631265296 = 30 « 
 6420843530 =200 « 
 754449114775=235 times 
 
 1. 74863847 X 
 
 2. 43958172 X 
 8. 79586216 X 
 
 4. 31596857 X 
 
 5. 74951084 X 
 
 6. 16847593 X 
 
 7. 39416809 X 
 
 8. 20537958 X 
 
 9. 53104009 X 
 
 10. 69073854 X 
 
 11. 90768300 X 
 
 12. 71765184 X 
 
 364, 729. 
 513, 624. 
 734, 856. 
 807, 965. 
 760, 398. 
 976, 304. 
 854, 930. 
 216, 648. 
 729, 356. 
 457, 390. 
 278, 936. 
 548, 690. 
 
 25. 51948673X7040908. 
 
 26. 94076803X4667890. 
 
 27. 72584692X1234667. 
 
 1. My income is £29 per week ; what is it per annum ? 
 
 2. 87 parishes are each assessed £37 ; what is the whole 
 assessment ? 
 
 Ex. 48769486X407500 
 407500 
 24384743000 
 341386402 
 195077944 
 19873565545000 
 
 13. 5976843 X 2798, 6005. 
 
 14. 3179648 X 4035, 3907. 
 
 15. 5271809 X 4576, 7689. 
 
 16. 6485937 X 3090, 7406. 
 
 17. 7268369 X 6480, 4729. 
 
 18. 5184736X2751, 6043. 
 
 19. 4958674X1234, 6678. 
 
 20. 6396274X9560, 8009. 
 
 21. 7261587X8154, 6700. 
 
 22. 8430957 X 8900, 3007. 
 
 23. 9376864X7461, 6893. 
 
 24. 1069769 X 9876, 4500. 
 
 28. 40769864 X 70049000. 
 
 29. 36947582 X 84000960. 
 
 30. 52749683 X 90004396. 
 
24 SIMPLE MULTIPLICATION. 
 
 3. How many sheaves are in a field containing 327G 
 Bhocks, each 12 sheaves ? 
 
 4. How many miles does a ship sail in 17 days at the 
 rate of 169 miles a-day ? 
 
 5. How many hours are there in a year ? 
 
 6. How often does the seconds hand of a watch re- 
 volve in a day and in a year ? 
 
 7. A railway train travels at the rate of 35 miles an 
 hour ; how many miles does it travel in 56 hours ? 
 
 8. A ship's cargo consists of 435 boxes, each contain- 
 ing 598 apples ; find the number of apples. 
 
 9. How many letters are there in a volume of 436 
 pages, each page 39 lines, and each line 52 letters ? 
 
 10. Sound moves at the rate of 1142 feet in a second; 
 how many feet will it move in 75 seconds ? 
 
 11. A peal of thunder is heard 35 seconds after seeing 
 the flash of lightning ; how far distant is the cloud ? 
 
 12. A train consists of 13 carriages having each 3 com- 
 partments, each containing 12 seats ; how many passen- 
 gers would find seats ? 
 
 13. What is the value of an estate, containing 7564 
 acres at £56 per acre ? 
 
 14. A ship's crew of 375 men is provisioned for 115 
 days, now each man is to receive 16 ounces a-day; how 
 many ounces have they in all ? 
 
 15. A ship after sailing 37 hours at the rate of 7 miles 
 an hour, encounters a storm, which drives her back 
 during 7 hours at the rate of 12 miles an hour ; she then 
 sails at her original rate during 5 hours ; how many miles 
 will she now be upon her voyage ? 
 
 16. How many shots does a fleet of 3 ships of 72 guns 
 each, 5 of 91 and 7 of 42, fire in 93 rounds ? 
 
 17. How many soldiers are there in 12 regiments of 
 9 companies each, and each company consisting of 95 
 men? 
 
 18. How much powder does a sixteen gun-battery of 
 18 pounders expend in 18 hours, if each gun is discharged 
 22 times iji an hour, the charge for an 18 pounder being 
 6 lbs. ? 
 
25 
 
 Divisor. Dividend. 
 
 7)47286492 
 6755213^ 
 
 7 
 
 Quot. 
 
 SIMPLE DIVISION 
 
 Is the method of finding how often one number is con- 
 tained in another. 
 
 The number we divide by is called the divhor, the num- 
 ber to be divided, the dividend^ and the result, the quotienU 
 
 Case I. When the divisor does not exceed 12. 
 
 Ex. Divide 47286492 by 7. 
 
 Sol. 7 is not contained in 4, but 
 7 in 47 is 6 and 5 over; place 5 
 before 2, then 7 in 52 is 7 and 3 
 over ; 7 in 38 is 5 and 3 over, &c. 
 
 The work is proved by multiply- 
 ing the quotient by the divisor and 
 adding in the remainder, 
 
 1. 7298763408 ~ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 2. 5487219876 — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 3. 9846798764 -^ 12, 6, 2, 3, 11, 9, 10, 8, 5, 4, 7. 
 
 Case II. When the divisor is found in the table. 
 Ex. Divide 74263849 by 14. 
 2 )74263849 ^14=2X7 
 7 )37131924 — 1 quot. by 2 
 5304560— 4 ... 14 
 
 47286492 Proof. 
 
 20 
 
 4X2+1=8+1=9 rem. 
 
 1. 34867896-M5, 16, 18. 13. 47654876- 
 
 2. 48678963-^20, 21, 24. 14. 76548764 ■ 
 
 3. 86789634-^-25, 27, 28. 15. 98765432 - 
 
 4. 21750486-H30, 32, 33. 16. 23457219 - 
 
 5. 30975219-^35, 36, 40. 17. 34807280- 
 
 6. 93048765-r42, 44, 45. 18. 48702083 - 
 
 7. 12345678-^48, 50, 54. 19. 54621487 - 
 
 8. 23456789-^56, 60, 63. 20. 18765486- 
 
 9. 34567890-^64, 66, 70. 21. 33144777 - 
 
 10. 51146784-^72, 77, 80. 22. 11847654- 
 
 11. 38712967-1-81, 84, 88. 23. 28048694 ■ 
 
 12. 76921783+90, 96, 99. 24. 78648769 • 
 
 Ex. 275473 - 
 
 2,0) 27547,3 
 
 13773^§ Quot. 
 
 100,108,110. 
 120, 121, 132. 
 144, 121, 108. 
 
 72, 81, 50. 
 
 54, 96, 44. 
 108, 88, 77. 
 132, 81, 56. 
 144, 54, 48. 
 121, 36, 32. 
 120, 64, ^Q. 
 110, 72, 42. 
 108, 99, 35. 
 c2 
 
26 SIMPLE DIVISION. 
 
 Case III. When the divisor is not contained in the table. 
 
 Ex. Divide 48769847 by 7486. 
 
 Divisor. Dividend. 
 7486)48769847( 
 7486 X 6 = 44916 
 
 Ans. 6514f 043, 
 
 Quotient. 
 6ol4f£|? 
 7486 Divisor. 
 
 
 38538 
 
 ... X5 = 
 
 37430 
 
 
 11084 
 
 ... Xl = 
 
 7486 
 
 
 35987 
 
 ... X4 = 
 
 29944 
 
 Kemainder. 
 
 6043 
 
 39084 
 52112 
 26056 
 45598 
 
 6043 Rem. 
 48769847 Dividend. 
 
 1.77486694- 
 2.54809678- 
 3.48096785- 
 4.57486786- 
 5.38492136- 
 6.48675846- 
 7.21486483- 
 8.54862187- 
 9.48765486- 
 10.30846298- 
 11.74869548- 
 12.34112118- 
 13.21476548- 
 14.58643876- 
 15.79864879- 
 16.54867384- 
 17.79847684- 
 18.54867486- 
 
 ■23, 31, 43. 
 ■26, 37, 47. 
 •29, 39, 51. 
 •17, 19, 13. 
 •52, 53, 57. 
 ■61, 75, 69. 
 •73, 74, 78. 
 •79, 82, 83. 
 ■85, 86, 87. 
 ■89, 91, 95. 
 ■97, 92, 98. 
 ■93, 74, 94. 
 ■784, 842. 
 •542, 876. 
 ■325, 498. 
 ■173, 156. 
 •139, 147. 
 •163, 184. 
 
 73846548 
 65482173 
 87460094 
 86754800 4- 
 38476700 -^ 
 48216784 -^ 
 
 25. 7384698700 
 
 26. 4869873846 
 
 27. 7298740000 
 
 28. 3216504000 
 
 29. 2190874860 
 
 30. 5486384766 
 
 31. 4768754867 
 
 32. 7321987645 
 
 33. 5419738473 
 
 34. 2176548698 
 
 35. 1876487693 
 
 36. 3175486987 
 
 217, 298. 
 248, 263. 
 376, 483. 
 800, 900.' 
 600, 390. 
 740, 500. 
 - 17640. 
 
 - 47687. 
 
 - 87000. 
 
 - 36500. 
 - 17000. 
 -37480. , 
 - 176487. 
 
 - 279864. 
 
 - 548637. 
 
 - 248765. 
 
 - 764869. 
 
 - 987654. 
 
 1. A product is 4822150080, and one of the factors 704 ; 
 what is the other? 
 
 2. My yearly income is £364 ; what is that per week ? 
 
 3. Great Britain and Ireland contain a population of 
 27,675,780, and their surface is 121,385 square miles; how 
 many inhabitants is that on an average to the square mile? 
 
 4. France contains a population of 35,700,000, at the 
 rate of 175 to the square mile ; how many square miles 
 is the surface of France ? 
 
SIMPLE DIVISION. 27 
 
 ft. If a floor 40 feet long require 1280 stones, each a 
 foot square, to pave it; what is its length? 
 
 6. The number of letters in a volume containing 746 
 pages is 1,846,350 ; how many letters are in a page? 
 
 7. An assessment for the poor of £5616 is raised from 
 48 parishes ; how much is levied from each parish ? 
 
 8. If a pigeon fly at the rate of 56 miles an hour, what 
 time would it take between Edinburgh and the Cape of 
 Good Hope, a distance of 5544 miles ? 
 
 9. Divide £6725 equally among 25 men. 
 
 10. In how many days will a ship accomplish a voy- 
 age of 4473 miles, sailing 213 miles in a day? 
 
 11. How many loaves, each weighing 69 ounces, can 
 be made from 16,491 ounces of flour? 
 
 12. The circumference of a wheel is 13 feet ; how 
 often does it revolve on a road 68,640 feet long ? 
 
 13. A tax of £7791 is to be levied from 53 parishes; 
 how much must each pay ? 
 
 14. Divide 343 oranges equally among 7 boys. 
 
 15. How many carriages, each containing 36 passen- 
 gers, would be required to convey 648 persons ? 
 
 16. A gentleman's income is £6205 per annum ; how 
 much is it per day ? 
 
 17. One man alone can build a wall in 378 hours ; in 
 how many hours would 7 men do the same ? 
 
 18. 7 regiments, consisting of 716 men each, are to be 
 reduced into 4 others of equal strength ; how many men 
 will be in each new regiment ? 
 
 19. How often can 375 be subtracted from 744375? 
 
 20. 15,855 ounces of beef are divided among 755 sol- 
 diers ; what is the weight of each man's ration ? 
 
 21. How many dozens of wine are in 64 pipes, each 
 containing 756 bottles ? 
 
 22. A product is 2632938, and one of the factors 246 ; 
 what is the other factor ? 
 
 23. A ship sails 5712 miles in 28 days ; how many 
 miles is this on an average per day ? 
 
 24. The circumference of the Earth is 25,000 miles 
 nearly ; how long would a person take to travel this dis- 
 tance at the rate of 40 miles per hour ? 
 
28 
 
 SUPPLEMENT TO MULTIPLICATION AND DIVISION. 
 
 I. When the multiplier 
 contains a fraction. 
 Ex. 6487536 X 8f 
 
 5 )19462608 = 3 times. 
 38925213- = I times. 
 51900288" = 8 times. 
 557928091 Product. 
 
 1.7486948X 
 2.5721987X 
 3.7121846X 
 4. 5987648 X 
 5.3842198X 
 6. 4876529 X 
 7.7214867X 
 8.4962184X 
 9. 4763148 X 
 10.2147634X 
 11.9847693X 
 12.6478796X 
 13. 5463784 X 
 14. 8754964 X 
 15. 8075084 X 
 
 41 
 
 63, 8i. 
 
 _, 71,10^. 
 41, n, 6|. 
 
 84,121,2^. 
 
 37A, 46^. 
 
 65^1,304^. 
 113^\,312if 
 416^V 549if 
 1791, 484^'^. 
 
 44U, 574j. 
 
 41 1, 59 A- 
 
 84A, 93,\. 
 108ii,275A. 
 
 II. When the divisor con- 
 tains a fraction. 
 Ex. 487654-^-31 
 30 487654 
 
 _5 5 
 
 16 f 2)2438270= prod, by 5 
 (8 )1219135 
 
 1523911 Quotient. 
 
 l.4765847-^- 
 2.5862190-^ 
 3. 4948645-^ 
 4. 5482169-:- 
 5.7928465^ 
 6. 5786478-f- 
 7.87486736^ 
 8. 57638469. 
 9.78621475- 
 10. 86275846- 
 11.51840963- 
 12.78219865- 
 13.21973465 
 14.34758694 
 15.97986089 
 
 Q 3 K 6 m 3 
 
 As Q6 
 "T25 ^85 
 
 . - 12i. 
 13i, 14f, 155. 
 244|. 
 18J. 
 56i^ 
 94i«. 
 
 104,11 
 
 -^ 17 
 
 631 
 
 84i 
 
 — 71 6 
 
 ^58^^, 644H. 
 ^ 251^,5124^. 
 
 -^7364 3674^. 
 
 EXERCISES ON THE PRECEDING RULES. 
 
 1. In 1856, the number of seamen registered in Eng- 
 land was 156,913; in Scotland, 29,987; in Ireland, 13,403; 
 in Jersey, Man, &c. 5424 ; and in the Colonies, 62,032 : 
 lind the whole number. 
 
 2. In 1851, the population of the South-eastern 
 Counties of Scotland was : Linlithgow, 30,590 ; Edin- 
 burgh, 259,493 ; Haddington, 36,363 ; Berwick 36,165; 
 Peebles, 10,804 ; and Selkirk, 9802 : find the sum. 
 
 3. In 1856, the number of births registered in Scot- 
 land was 52,301 males and 49,447 females ; and the 
 number of deaths was 29,417 males and 29,039 females : 
 find the excess of births over deaths in that year. 
 
EXERCISES. 29 
 
 4. How many passengers are in a train consisting ot 
 4 first class carriages, each containing 18 persons ; 3 
 second class containing 30 each, and 2 third class con- 
 taining 40 each ? 
 
 5. In 1856, the number of marriages in the 33 coun- 
 ties of Scotland was 20,487 ; what was the average 
 number in each ? 
 
 6. The British Army at the battle of the Alma was 
 composed as follows : — Light Division, 5454 men; 1st 
 Division, 4711; 2d, 4222 ; 3d, 3794; 4th, 4419 ; Cavalry, 
 1100; Artillery, 2700; Sappers and Miners, 400; how 
 many men were engaged in all ? 
 
 7. At the same battle, the loss of the British amounted 
 to 2196 killed and wounded; how many effective men 
 remained ? 
 
 8. How many yards are in 15 pieces of cloth, each 
 containing 56 yards ? 
 
 9. Mercury's distance from the Sun is 36,793,000 miles, 
 Mars' distance is 108,031,000 miles greater than Mer- 
 cury's, and Neptune's is 2,710,114,000 miles greater than 
 Mars' ; find the distances of Mars and Neptune from the 
 Sun. 
 
 10. In 1856, the number of Post-ofiice Orders issued 
 in Ireland was 461,723; the number in Scotland was 
 23,800 more than in Ireland, and the number in England 
 exceeded that in Scotland and Ireland together by 
 4,284,490 : how many were issued in Scotland, in Eng- 
 land, and in the United Kingdom ? 
 
 11. How many times is Mount Blanc, 15,732 feet in 
 height, higher than Arthur Seat, which is 820 feet high ? 
 
 12. At the battle of the Alma, the Fusilier Guards 
 lost 11 officers and 170 non-commissioned officers and 
 men killed and wounded ; the Grenadiers, 3 officers and 
 126 men ; and the Coldstreams, 3 officers and 27 men : 
 at Inkerman, the Fusiliers lost 9 officers and 169 men ; 
 the Grenadiers, 9 officers and 223 men ; and the Cold- 
 streams, 13 officers and 178 men. How many of the 
 Guards fell at Inkerman more than at Alma? 
 
 13. A pear-tree one year produced 14,861 pears, aver- 
 aging 11 to the pound ; how many lbs. were produced? 
 
 ^4- In how many days will a boy read through the 
 
 D 
 
30 EXERCISES. 
 
 Bible, which contains 31,173 verses, if he reads 39 verses 
 daily? 
 
 15. How often does the hammer of a clock strike in a 
 day and in a year y 
 
 16. One female can cut out 300 gross of blanks for steel 
 pens in a day ; how many will she cut out in a year of 
 313 days? 
 
 17. A steel pen manufactory sends out 180,000,000 
 pens yearly ; how many boxes, each containing a gross 
 or 12 dozen, would they fill ? 
 
 18. A gentleman has 3 farms containing 675 acres ; 
 the first and second together contain 490 acres; and 
 the second and third 425 acres . how many acres are in 
 each farm ? 
 
 19. The gallant Sir John Moore fell at the battle of 
 Corunna in 1809, at the age of 48 ; in what year was he 
 born? 
 
 20. The Sun's diameter is 882,000 miles ; how many 
 times is it greater than the Earth's diameter, which is 
 7920 miles ? 
 
 21. Divide 1584d. among 3 girls and 5 boys, giving 
 each girl twice the number which a boy gets. 
 
 Sol. Since each girl gets 2 boys' shares, 3 girls have 
 2X3 = 6 boys' shares ; the number of boys' shares is 
 therefore 6 + 5 = 11. Hence each boy gets 1584 4- 11 = 
 144d., and each girl 144 X 2 = 288d. 
 
 22. How much grain will a farm of IG fields, each 29 
 acres, produce, if one acre produces 9 quarters of grain ? 
 
 23. A gentleman gave £484 to two charities, and to 
 one he left 3 times as much as to the other ; what did 
 he leave to each ? 
 
 24. Several volumes contain 10,192 pages ; in how 
 many days would a person read the whole, reading 4 
 hours a day and 7 pages an hour ? 
 
 25. In a church there are 12 windows ; in the lower 
 sash there are 12 panes and in the upper 18 ; how many 
 panes of glass are there in all ? 
 
 26. A gentleman has 4 farms, containing 240, 375, 408, 
 and 425 acres respectively, and he wishes to divide them 
 into as many others of equal size ; how many acres will 
 there be in each farm ? 
 
EXERCISES. 31 
 
 27. In one class there are 150 boys, in another 145, 
 in a third 140, in a fourth 135, and in a fifth 130; how 
 many are there on an average in each ? 
 
 28. The sum of two numbers is 2779, and their difi'erence 
 is 293 ; what are the numbers ? 
 
 Sol. 2779 2779 
 
 Add 293 Subtract 293 
 
 2 ) 3072 2 ) 2486 
 
 1536 is the greater. 1243 is the less. 
 
 29. At an election, the successful candidate had a ma- 
 jority of 84 votes out of 572 votes ; how many had each 
 of the two candidates ? 
 
 80. The loss of the French and Sardinians at the battle 
 of the Tchernaya or of Traktir Bridge, amounted to 
 1792 men killed and wounded; the French loss was 
 1292 more than the Sardinian : what was the loss of each? 
 
 31. Divide 204 apples among 4 girls and 5 boys, giving 
 each girl 3 times as many as a boy. 
 
 32. Galileo died in 1642, and Newton in 1725; how 
 long is it since each of these events, and how many years 
 elapsed between them ? 
 
 33. A gentleman dying, left £45,000 ; to his widow he 
 bequeathed ^ of his estate, and the remainder was to be 
 equally divided among his 4 children ; how much did he 
 leave to each ? 
 
 34. A ship at sea fires a gun, the report of which is 
 heard 12| seconds after seeing the flash ; how far distant 
 is the ship, sound moving at the rate of 1142 feet per 
 second? 
 
 35. Two casks of wine contain together 151 gallons, 
 and one contains 31 gallons more than the other; how 
 many gallons does each contain ? 
 
 36. What number being divided by 337 gives 9472 for 
 the quotient, and 108 for the remainder ? 
 
 37. Divide £416 among 6 men and 8 women, giving 
 each man 4 times as much as a woman. 
 
 38. Two brothers being asked their ages, said that the 
 sum of their ages was 63, and that the difference of their 
 ages was 9 ; find their ages. 
 
Ex.Red.l9718farth.to£. 
 4 )19718 Farth. 
 12 ) 4929 ^ Pence. 
 2,0) 41,0s. 9|d. 
 
 £20, 10s. 9§d. 
 
 32 
 
 COMPOUND NUMBERS 
 
 I. STERLING MONEY. 
 
 REDUCTION 
 
 Is the method of bringing numbers from one denomina- 
 tion to another without altering their value. 
 
 To bring higher to lower denominations multiply. 
 
 To bring lower to higher denominations divide. 
 
 Ex. Red. £20, 10s. 9id. to farth 
 Mult, by 20 and add 10s. 
 
 410 Shillings. 
 Mult, by 12 and add 9d. 
 4929 Pence. 
 
 Mult, by 4 and add 2f. 
 
 19718 Farthings. 
 
 1. Reduce£35, 17s. 4id.; £28,lls.ll|d.; £40, 10s. lOf d.; 
 €200. 10s. 8fd.; £574, 19s. 11^.; £409, 17s. 4id. ; 
 £147', 10s. lOid. ; and £105, 2s. 4id. to farthings. 
 
 2. Reduce £470, 10s. O^d. ; £270, lis. 6d. ; £672, 18s. 
 9^.; £486, 12s. l^d. ; 12s. 4id. ; 17s. S^d. ; lis. lid. 
 £700, 10s. 2d. ; £21, 15s. S^d. to halfpence. 
 
 3. Reduce £87, 19s. lO^d. ; £11, lis. lid. ; £50, 19s. 6d. 
 £47, 15s. 9id. ; £400, 10s. O^d. ; £290, 16s. 4d. ; £403, 
 lis. ll^d.; 16s. 8id. ; lis. S^d. ; 13s. 4^d. ; £43, 12s. 4d. 
 and 15s. 8^d. to halfpence and farthings. 
 
 4. Reduce 4786; 3040; 7098; 48769; 73846; 4098 
 7214 ; and 38463 farthings to pence, shillings, and pounds 
 
 5. Reduce 4876; 7487; 3562; 1749; 3689; 2177 
 5848 ; 7216 ; 111111 ; 33333 halfpence to d. s. and £. 
 
 6. Reduce 78469 ; 738467; 87698; 714086 farthings: 
 48763; 21764; 50487; 140715 halfpence: 729374; 89214; 
 47865; and 571640 pence to sovereigns. 
 
 7. Reduce £2716, 2s. 2id. ; £4176, 12s. S^d. ; £3108, 
 14s. 7id. ; £176, Os. 2id. ; £417, Os. O^d. ; £49, 17s. 6d. ; 
 and £2010, 10s. 6|d. to halfpence and farthings. 
 
 8. Reduce 41763 ; 58462 ; 71209 ; 17268 ; 38467 ; 
 84762; 47219; and 876213 farthings to sovereigns. 
 
REDUCTION. 33 
 
 Ex. Red. £2475 to crowns and guineas. 
 
 2. £2475 X 20 
 
 £2475 
 
 20 
 
 5 )49500 s. 
 Ans. 9900 cr. 
 
 f 3)49500 s. 
 17 )16500 
 Ans. 2357 gu. 3 s. 
 
 9. Reduce £7485; £3876; £4921; £3817; and £3760 
 to crowns and guineas. 
 
 10. Reduce 17486; 887; 2130; 2491; 2168; and 
 7430 guineas to pounds. 
 
 Ex. Red. £21, 17s. 6d. to sixpences. Ans. 875 sixd. 
 £21, 17 s. 6d. Proof. 
 
 20 2 )875 sixd. 
 
 437 s. 2,0)4Vs. 6d. 
 
 2 (sixd. in Is.) £21, 17s. 6d . 
 
 Ans. 875 sixd. c===; 
 
 11. Reduce £121 ; £45, 7s. 6d. ; £56, 18s. 6d. ; £79, 
 18s. ; £84, 5s. 6d. ; and £99, 19s. 6d. to sixpences. 
 
 12. Reduce 448; 977; 2163; 3729; 4125; and 5763 
 sixpences to shil. and pounds. 
 
 13. How many half-crowns in £42, 7s. 6d. ; £54, 12s. 
 6d. ; £67, 15s. ;"'and in £99, 17s. 6d. ? 
 
 14. Reduce 528 ; 1254; 3453; 4869; 5871; and 7459 
 half-crowns to pounds, &c. 
 
 15. How many threepences are in £49, 7s. ; £54, 6s. 3d. ; 
 £72, 19s. 6d. ; and in £84, 14s. 9d. ? 
 
 16. Reduce 1748; 2153; 3785; 5142; 6897; and 7455 
 threepences to shillings and pounds. 
 
 17. How many florins are in £170 ; £144 ; 6743 far- 
 things ; 1786 pence ; and in 436 shillings ? 
 
 18. Reduce 43 guineas ; 77 gu. 8s. l^d, ; £37, 2s. 6d. ; 
 93 gu. 2s. 4»d. ; 78 gu. 18s. 9|d. ; and 18s. 9|d. to farth. 
 
 19. Find the sum of £18, 19s. 4^d.+5 crowns+17 half- 
 crowns-f-234 florins-}-! 7 guineas, in farthings and pounds. 
 
 20. How many pounds will a man save yearly, by lay- 
 ing aside 5s. 9M. weekly ? 
 
 21. How many penny stamps may be obtained for 
 £49, 17s. 7d.? 
 
34 
 
 COMPOUND ADDITION. 
 
 Example. 
 Sol. The sum of the farthings is 10 = £381 17 s. 6id. 
 2^d., write down ^d. and carry 2 to the 148 12 9^ 
 
 pence. The sum of the pence is 44 = 412 16 7| 
 
 3s. 8d., write down 8d. and carry 3 to the 319 11 ll| 
 
 shil. The sum of the units column of the 470 19 9f 
 
 shil. is 28, write down 8s. and carry 2 to £1733 18 8^ 
 the tens of the shil. : the sum is 7 ten shil. ===== 
 pieces = £3 and 1 ten shil. piece, write down 1 and carry 
 3 to the pounds. The sum of the pounds is £1733, and the 
 whole answer is £1733, 18s. 8^d. — The results in Compound 
 numbers may be checked as in Simple numbers. 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s. d. 
 
 24 11 4 J 
 
 31 17 lU 
 
 27 15 1\ 
 
 14 19 111 
 
 16 18 9i 
 
 13 14 lOi 
 
 72 18 10 
 
 12 16 Si 
 
 61 10 2| 
 
 42 16 9.f 
 
 36 11 5i 
 
 29 11 5A 
 
 32 17 lU 
 
 24 12 4i 
 
 63 10 4^ 
 
 18 18 8£ 
 
 45 16 3i 
 
 56 18 Hi 
 
 41 17 lOi 
 
 15 14 10 
 
 96 11 41 
 
 49 19 111 
 
 68 16 Si 
 
 15 14 9 
 
 69 13 7i 
 
 94 13 7 
 
 86 15 51 
 
 19 17 lOi 
 
 12 16 10 
 
 17 11 lU 
 
 74 11 91 
 
 91 19 6i 
 
 14 18 n 
 
 16 15 5i 
 
 47 16 10 
 
 51 14 lU 
 
 29 15 6i 
 
 18 18 Hi 
 
 51 10 4i 
 
 18 13 2\ 
 
 31 17 111 
 
 81 17 lOi 
 
 15 8 111 
 
 81 10 9| 
 
 9. 
 
 10. 
 
 11. 
 
 12. 
 
 17 18 HI 
 
 42 18 9i 
 
 29 10 8^ 
 
 14 12 Si 
 
 16 13 7i 
 
 36 17 2| 
 
 34 8 11^ 
 
 17 13 61. 
 
 19 12 41 
 
 34 16 3| 
 
 76 7 7i 
 
 98 19 2 
 
 20 11 3| 
 
 43 12 111 
 
 82 11 10| 
 
 84 10 6| 
 
 31 17 Si 
 
 45 19 101 
 
 49 17 71 
 
 18 11 111 
 
 17 16 111 
 
 53 11 4| 
 
 63 13 91 
 
 19 10 81 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 45 17 SI 
 
 40 21 
 
 51 S 3| 
 
 82 12 llf 
 
 49 16 4| 
 
 38 19 11 
 
 64 19 111 
 
 4M8 71 
 
 38 18 71 
 
 51 15 5| 
 
 73 17 10^ 
 
 72 16 9 
 
 64 4 llf 
 
 86 16 7 
 
 84 16 91 
 
 S8 11 4f 
 
 39 17 6i 
 
 13 14 101 
 
 18 18 11| 
 
 22 15 101 
 
 83 11 4f 
 
 89 19 6 
 
 17 14 10| 
 
 16 18 7i 
 

 COMPOUND ADDITION. 
 
 35 
 
 17. 
 
 18. 19. 
 
 20. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s. d. 
 
 274 13 lOf 
 
 426 16 4J 
 
 410 10 lOf 
 
 329 19 111 
 
 476 12 8J 
 
 246 13 3^ 
 
 104 17 4f 
 
 293 18 11 
 
 567 11 4| 
 
 642 17 8f 
 
 816 11 \\\ 
 
 932 17 6i 
 
 658 13 Ik 
 
 351 9 lU 
 
 681 13 4 
 
 456 16 10| 
 
 549 18 7i 
 
 513 12 Al 
 
 168 12 lOJ 
 
 564 13 3i 
 
 721 16 111 
 
 135 11 lU 
 
 473 2 U 
 
 645 17 6 
 
 213 19 lOf 
 
 497 18 101 
 
 734 3 0^ 
 
 897 13 4i 
 
 132 15 7i 
 
 974 19 9i 
 
 347 11 111 
 
 978 19 9^ 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 476 11 llf 
 
 847 13 6| 
 
 984 17 m 
 
 484 15 4| 
 
 725 13 4i 
 
 472 19 2i 
 
 845 15 0| 
 
 846 13 8| 
 
 870 11 9| 
 
 756 14 llf 
 
 756 13 21- 
 
 725 16 10^ 
 
 708 17 lOi 
 
 793 18 5A 
 
 384 11 5i 
 
 857 11 Ak 
 
 534 16 3i 
 
 904 15 81 
 
 479 18 lOi 
 
 583 3 9i 
 
 729 19 111 
 
 405 12 lOi 
 
 721 19 111 
 
 879 16 8| 
 
 297 18 4| 
 
 762 16 81 
 
 562 13 8i 
 
 405 17 Ik 
 
 972 15 3| 
 
 636 17 9^ 
 
 629 16 9i 
 
 896 19 111 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 325 14 71 
 
 420 12 7J 
 
 508 19 71 
 
 874 13 6 
 
 256 15 81 
 
 500 13 8^ 
 
 850 11 2 
 
 847 16 8i 
 
 719 11 61 
 
 721 16 6| 
 
 793 16 71 
 
 856 17 101 
 
 971 13 lOi 
 
 217 18 lU 
 
 918 13 41 
 
 865 11 21 
 
 47*2 16 8i 
 
 172 16 4| 
 
 981 17 10 
 
 832 18 6 
 
 749 18 111 
 
 901 17 21 
 
 974 18 Q^ 
 
 823 7 4| 
 
 426 19 9^ 
 
 847 19 111 
 
 953 12 111 
 
 748 16 3 
 
 273 17 10^ 
 
 487 15 lOi 
 
 947 13 3^ 
 
 784 17 4| 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 219 13 111 
 
 549 16 2 J 
 
 Ill 11 111 
 
 204 8 0| 
 
 192 16 5^ 
 
 495 17 10 
 
 222 17 10^ 
 
 420 -3 n\ 
 
 921 17 4 
 
 954 11 2| 
 
 363 18 2| 
 
 569 18 21 
 
 476 13 &l 
 
 867 18 31 
 
 746 12 91 
 
 931 13 11 
 
 764 18 lOi 
 
 678 19 3i 
 
 805 13 7| 
 
 139 15 4| 
 
 647 11 11 
 
 786 12 9 
 
 508 19 61 
 
 721 4 8^ 
 
 513 17 101 
 
 954 13 81 
 
 741 10 41 
 
 801 12 7 
 
 315 19 8^ 
 
 987 16 10 
 
 417 11 U 
 
 971 19 101 
 
 33. £473, 18s. 10|d.+£972, lis. 4id.+£987, 19s. llid. 
 +£852, 17s. 9id. + £112, 15s. 61d. + £521, 14s. 8|d. -f 
 £846, 13s. 7|d. + £613, 12s. 9^d. + £716, 17s. ll|d. 
 
36 
 
 COMPOUND ADDITION. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ 8. d. 
 
 540 13 llf 
 
 321 17 8i 
 
 463 18 9 
 
 897 11 81 
 
 419 19 9 
 
 123 16 3i 
 
 364 19 lOi 
 
 879 12 71 
 
 914 13 41 
 
 231 15 4i 
 
 643 11 2i 
 
 798 13 4| 
 
 411 12 2 
 
 213 18 11 
 
 634 17 10 
 
 789 16 llf 
 
 114 8 6| 
 
 312 16 8J 
 
 346 18 9i 
 
 978 4 2 
 
 701 13 4 
 
 132 11 2i 
 
 436 12 71 
 
 987 11 4| 
 
 158 17 llf 
 
 474 13 6 
 
 183 16 8 
 
 363 15 71 
 
 815 16 8 
 
 744 11 3f 
 
 831 15 41 
 
 633 18 9f 
 
 38. 
 
 39. 
 
 40. 
 
 41. 
 
 948 12 71 
 
 574 11 lOf 
 
 530 11 4f 
 
 876 11 llf 
 
 489 13 61 
 
 457 16 41 
 
 504 17 111 
 
 768 19 lOl 
 
 894 19 91 
 
 739 19 9 
 
 876 19 91 
 
 687 14 41 
 
 276 15 41 
 
 395 11 10| 
 
 743 12 lOf 
 
 527 13 8 
 
 568 17 llf 
 
 953 14 41 
 
 549 13 61 
 
 498 19 llf 
 
 729 19 9 
 
 476 15 11| 
 
 985 19 llf 
 
 409 17 lOf 
 
 276 11 111 
 
 729 13 8i 
 
 859 18 10| 
 
 490 17 101 
 
 467 13 41 
 
 297 16 41 
 
 764 13 81 
 
 385 13 4f 
 
 42. 
 
 43. 
 
 44. 
 
 45. 
 
 210 11 5i 
 
 741 18 11 
 
 116 17 41 
 
 901 18 71 
 
 101 13 61 
 
 387 16 5f 
 
 161 13 5f 
 
 910 13 41 
 
 354 16 21 
 
 862 10 101 
 
 600 17 21 
 
 864 12 111 
 
 726 15 111 
 
 629 17 61 
 
 560 13 81 
 
 648 17 6f 
 
 367 18 10| 
 
 748 15 5f 
 
 74 11 3f 
 
 899 11 11 
 
 481 19 111 
 
 796 17 llf 
 
 9 8 6 
 
 988 15 7^ 
 
 816 15 81 
 
 869 19 10 
 
 408 12 llf 
 
 749 18 llf 
 
 964 17 lOf 
 
 176 17 8f 
 
 780 16 91 
 
 548 17 61 
 
 489 19 111 
 
 298 11 41 
 
 473 18 111 
 
 721 16 21 
 
 984 12 61 
 
 476 10 6f 
 
 729 16 71 
 
 387 19 9i 
 
 571 18 llf 
 
 80 16 101 
 
 780 13 31 
 
 807 12 111 
 
 709 11 41 
 
 89 13 61 
 
 10 16 71 
 
 840 15 llf 
 
 742 18 91 
 
 476 13 4- 
 
 47. 
 
 48 19 41 
 
 480 13 61 
 
 408 15 91 
 
 72 11 41 
 
 568 17 111 
 
 367 13 2f 
 
 673 18 81 
 
 469 12 lOf 
 
 576 19 8f 
 
 864 13 4j 
 
 61 
 
 7: 
 
 48. 
 
 500 11 llf 
 499 9 " 
 
 72 18 
 308 15 
 
 38 12 
 380 11 
 596 12 
 
 65 13 
 962 18 
 
 298 14 llf 
 
 If 
 
 49. 
 
 344 18 101 
 436 19 111 
 
 87 13 " 
 728 12 
 864 11 111 
 
 86 13 41 
 987 12 
 
 49 14 
 986 17 
 806 4 
 
 91 
 61 
 2i 
 
COMPOUND ADDITION. 37 
 
 50. A owes to B £743, lis. 6id., to C £325, 4s. 8|d., 
 to D £750, 19s. lOfd., to E £113, lis. lljd., to F £1041, 
 13s. 8fd., to G £89, 16s. 8d., to H £1430, 153. ll|d., and 
 to I £740, 16s. lOd. ; how much does he owe in all ? 
 
 51. A paid to B £675, 13s. 7id., to C £298, 16s. lOid., 
 to D £749, 13s. 7id., to E £97, 18s. 6|d., to F £987, 13k. 
 Hid., to a £75, 13s. 8|d., to H £1279, 17s. 4fd., and 
 to I £684, 13s. ll^d. ; how much did he pay in all? 
 
 52. A person collected in January £744, lis. 8fd., in 
 February £896, 17s. lO^d., in March £472, 17s. 4id., in 
 April £583, 16s. llfd., in May £739, 17s. 6fd., in June 
 £1096, 13s. 8id., in July £578, 12s. 8^d., in August 
 £1374, 18s. 5jd.,in September £458, lis. llid.,in October 
 £735, 13s. 4id., in November £2179, 16s. 4id., and in 
 December £532, lis. Ijd. ; how much did he collect? 
 
 53. I received from A £736, 15s. lid., from B £874, 
 13s. 8fd., from C £879, 17s. lOid., from D £84, Us. 2|d., 
 from E £98, 17s. lOfd., from F £921, 16s. llid., from 
 G £1093, 10s. 4^d., and from H £729, 8s. lid. ; how 
 much did I receive in all ? 
 
 54. A owes me £274, lis. lOid., B £89, 13s. 7d., C 
 £74, lis. lid., D £96, 18s. 9^d., E £65, lis. 2id., F 
 £418, 4s. 6fd., G £173, 13s. 4id., H £748, 17s. 6fd., 
 K £847, 13s. 4id., and I have in the bank £7486, 17s. 
 ll|d. ; how much am I worth? 
 
 55. A housekeeper's account was, for beef, &c., £4, 
 2s. 7id. ; tea and coffee, 21s. 3d. ; sugar, 17s. 7|d. ; 
 potatoes, 5s. 6|d. ; butter, lis. l^d.', fruit, 21s. 3^d. ; 
 and bread, 43s. 7d. ; find the amount. 
 
 56. A corn merchant laid out on wheat, £597, lis. 6^d. ; 
 on barley, £409, 17s. 4|d. ; and on oats, £347, 9s. llfd. : 
 what should he sell the whole for to gain £79, 18s. 11 ^d. ? 
 
 57. A gentleman left to his widow, £7692, 17s. 4id. ; 
 to each of his two sons, £3000, 17s. 6d. ; to each of his 
 four daughters, £2559, 18s. 7^d. ; and to his other rela- 
 tives, £4975, 8s. 4id. : how much was this in all? 
 
 58. A gentleman owes his tailor, £23, 14s. 8^d. ; his 
 bootmaker, £14, 7s. 3jd. ; his grocer, £48, 17s. 7|d. ; 
 his baker, £35, 16s. 8^d. ; his house-rent is £115, 17s. 
 6d. : how much must he draw from the bank to pay 
 these sums ? 
 
38 
 
 COMPOUND SUBTRACTION 
 
 Ex. From £429 17s. Sjd. 
 Take 145 12 3i 
 Diff. 
 
 £284 5 5^ 
 
 Ex. From £501 15s. 6^d. 
 Take 250 4 Gj 
 Diff. 
 
 £251 11 Oi 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 £ ». d. 
 
 £ 5. d. 
 
 £ s. d. 
 
 £ 5. d. 
 
 146 12 7i 
 
 247 16 lOf 
 
 375 15 6i 
 
 508 6 7| 
 
 73 5 2^ 
 
 184 5 3^ 
 
 183 10 4^ 
 
 348 3 7i 
 
 Ex.From£742,15s.8id.take£653,17s.9id.Ans.£88,17s.l0|d. 
 
 From £742 15s. S^d. 
 Take 653 17 9| 
 Diff. £88 17 lo| 
 
 Sol. 2f. from If. we cannot, but 2f. 
 
 from 4f. (or Id.) is 2f. and If. is |d.; 
 
 write down |d., and carry 1 to 9d. is 
 
 lOd. from 8d. we cannot, but lOd. from 
 
 12d. (or Is.) is 2d. and 8d. are lOd. ; write do^Am lOd., and 
 
 carry 1 to 17s. is 18s. from 15s. we cannot, but 18s. from 20s. 
 
 (or £1) is 28. and 15s. are 17s. ; write down 17s., and carry 
 
 1 to £653 
 
 is £654 from £742 are £88 ; write down £88. 
 
 
 
 5. 
 
 
 
 6. 
 
 
 
 7. 
 
 
 
 8. 
 
 
 427 
 
 13 
 
 4i 
 
 450 
 
 10 
 
 44 
 
 296 
 
 16 
 
 34 
 
 609 
 
 13 
 
 64 
 
 298 
 
 16 
 
 lOi 
 
 276 
 
 13 
 
 B| 
 
 109 
 
 11 
 
 114 
 
 379 
 
 14 
 
 7f 
 
 
 9. 
 
 
 
 10. 
 
 
 
 11. 
 
 
 
 12. 
 
 
 825 11 
 
 6 
 
 742 
 
 17 
 
 84 
 
 408 
 
 18 
 
 10 
 
 504 
 
 16 
 
 74 
 
 296 
 
 13 
 
 6i 
 
 486 
 
 13 
 
 94 
 
 298 
 
 19 
 
 9| 
 
 329 
 
 16 
 
 8f 
 
 
 13. 
 
 
 
 14. 
 
 
 
 15. 
 
 
 
 16. 
 
 
 742 
 
 13 
 
 84 
 
 200 
 
 
 
 
 
 804 10 
 
 14 
 
 476 
 
 17 
 
 7f 
 
 427 
 
 12 
 
 n 
 
 99 
 
 12 
 
 04 
 
 721 
 
 13 
 
 6 
 
 298 
 
 17 
 
 11 
 
 
 17. 
 
 
 
 18. 
 
 
 
 19. 
 
 
 
 20. 
 
 
 547 
 
 10 
 
 
 
 976 
 
 15 
 
 4 
 
 705 
 
 
 
 44 
 
 325 
 
 6 
 
 04 
 
 238 
 
 11 
 
 Of 
 
 762 
 
 18 
 
 K 
 
 396 17 
 
 2^ 
 
 298 
 
 13 
 
 04 
 
 
 21. 
 
 
 
 22. 
 
 
 
 28. 
 
 
 
 24. 
 
 
 610 
 
 17 
 
 3| 
 
 542 
 
 16 
 
 04 
 
 726 
 
 17 
 
 104 
 
 789 
 
 11 
 
 5| 
 
 496 
 
 16 
 
 lU 
 
 486 
 
 16 
 
 04 
 
 498 
 
 17 
 
 11 
 
 499 
 
 11 
 
 74 
 
 
 25. 
 
 
 
 26. 
 
 
 
 27. 
 
 
 
 28. 
 
 
 271 
 
 13 
 
 0^ 
 
 542 
 
 16 
 
 04 
 
 980 15 
 
 6 
 
 832 
 
 17 
 
 64 
 
 148 
 
 17 
 
 0| 
 
 347 
 
 19 
 
 111 
 
 890 
 
 15 
 
 6| 
 
 328 
 
 18 
 
 7f 
 
 
 29. 
 
 
 
 30. 
 
 
 
 31. 
 
 
 
 32. 
 
 
 532 16 
 
 7 
 
 424 
 
 19 
 
 10 
 
 173 
 
 16 
 
 14 
 
 410 
 
 12 
 
 44 
 
 325 
 
 11 
 
 9| 
 
 248 
 
 19 
 
 104 
 
 99 
 
 17 
 
 Of 
 
 147 
 
 13 
 
 74 
 
COMPOUND SUBTKACTION. 
 
 39 
 
 83. 
 
 34. 
 
 35. 
 
 3a. 
 
 £ s. d. 
 
 £ s. d. 
 
 £ s, d. 
 
 £ s. d. 
 
 901 18 0| 
 
 386 16 4 
 
 409 11 H 
 
 251 13 4^ 
 
 496 18 U 
 
 293 17 2| 
 
 359 11 6 
 
 151 17 9| 
 
 109 13 10 
 96 13 lOi 
 
 38. 
 
 499 17 3i 
 399 17 61 
 
 39. 
 
 256 11 2i 
 193 4 7i 
 
 40. 
 
 704 14 4 
 407 14 9i 
 
 
 41. 
 
 
 
 42. 
 
 
 
 43. 
 
 
 
 44. 
 
 
 275 
 
 12 
 
 ^ 
 
 326 
 
 9 
 
 3 
 
 533 
 
 4 
 
 0^ 
 
 214 
 
 17 
 
 11 
 
 186 
 
 11 
 
 7i 
 
 263 
 
 18 
 
 H 
 
 353 
 
 7 
 
 6f 
 
 142 
 
 17 
 
 iH 
 
 
 45. 
 
 
 
 46. 
 
 
 
 47. 
 
 
 
 48. 
 
 
 973 
 
 
 
 2^ 
 
 841 
 
 1 
 
 0^ 
 
 711 
 
 5 
 
 2 
 
 817 
 
 
 
 
 
 739 
 
 3 
 
 If 
 
 418 
 
 1 
 
 n 
 
 117 
 
 5 
 
 lU 
 
 718 
 
 
 
 03 
 
 49. £748, 13s. 6id.— £589, 15s. 8|cl. 
 
 50. £721, 15s. 8d. —£629, 13s. lUd. 
 
 51. £721, 17s. 6|d.+£853, 13s. l|d.— £684, 13s. 6id. 
 +£789, 17s. lid. 
 
 52. £987, 2s. lid.+£305, 2s. Hid.— £896, 12s. 8id 
 +£296, 17s. 9id. 
 
 53. A merchant bought goods for £578, 15s. 6^d., and 
 sold them for £642, 8s. 7Jd. ; what did he gain ? 
 
 54. Borrowed 500 guineas and paid £125, 17s. 4id. at 
 one time and £298, 14s. 5id. at another ; what is still 
 due? 
 
 55. The receipts of a railway one year amounted to 
 £48,984, 17s. 8id. ; and the year followmg to £50,492, 
 2s. 3d. ; find the increase. 
 
 56. A housekeeper went to market with £5 ; she paid 
 for beef 17s. 6id. ; mutton, 12s. 7id. ; fish, 7s. ^^L.', 
 tea, 6s. 5d. ; coffee, 2s. 3^d. ; sugar, 7s. l^d. ; vegetables, 
 7s. 3|d. and sundries, 4s. l|d. ; with what sum did she 
 return ? 
 
 57. A owed to B £748, 16s. 7id., but has paid £398, 
 17s. 6^d. ; to C £1000, but has paid £899, 17s. 4id. ; to 
 D £470, lis. 4id., but has paid £381, 13s. 4£d. ; to E 
 £721, 18s. 7|d., but has paid £643, lis. 9id. ; to F £896, 
 13s. 2id., but has paid £799, 17s. l|d. ; how much does 
 he still owe to each and in all? 
 
 58. A merchant has in cash £7328, 17s. 11 Jd., goods 
 worth £12,748, 16s. lOd., furniture £574, 18s. lljd. ; 
 
40 COMPOUND SUBTRACTION 
 
 A owes him £112, 17s. 6id., B £327, 18s. 7Ad., C £486 
 13s. 8|d., D £89, 16s. lO^d. and E £136, 18s. 8id. ; at 
 the same time he owes to F £574, 18s. 11 ^d., to G £324, 
 lis. 7|d., to H £723, 18s. 6d., to I £327, 17s. 4|d., and 
 to K £587, 10s. 3fd. : how much is he worth? 
 
 59. A gentleman's yearly income is £500, his household 
 expenses £294, 13s. 7:|d., rent £54, 13s. 6d., taxes £20, 
 lis. 8id., servants' wages £25, 17s. lid., tradesmen's ac- 
 counts £52, lis. 7fd., and incidental expenses £24, 17s. 
 ll^d. ; how much does he save yearly? 
 
 60. Three ponies cost £35, 15s. 6d ; the first and second 
 cost £26, 10s. 4d. and the second and third £30, 3s. 9d. ; 
 find the price of each. 
 
 61. A, B, and C contributed £109, 18s. l^d. to a 
 charity ; A and B contributed £61, 3s. 3^d. and A's 
 contribution was £21, 10s. lO^d. less than C's: how 
 much did each contribute? 
 
 62. A bankrupt's debts amount to £19,728, 15s. 7jd. 
 and his effects to £12,899, 17s. 8|d. ; how much is he de- 
 ficient ? 
 
 63. A gentleman dying left £17,584, 17s. 6d. ; to his 
 widow he left £3756, l8s. 9d. ; to each of his three sons, 
 £2573, 7s. 6d, ; to each of his two daughters, £2000, 
 14s. 3d. ; and the remainder to his other relatives : how 
 much was this ? 
 
 64. A bankrupt owes to A, £329, 10s. 7^d. ; to B, 
 £748, 17s. ll^d. ; to C, £876, 17s. lOjd. ; to D, £1783, 
 17s. Hid.; to E, £578, 19s. 3|d. ; to F, £1047, 18s. 
 6jd. ; and to Gr, £1270, 8s. 8^d. : at the same time he 
 has in cash, £520, 17s. S^d. ; in bills, £325, 16s. lO^d. ; 
 goods valued at £984, 17s. 6d. ; H owes him £44, 16s. 
 7id.; I,£72,lls.7|d.; K, £84, 13s. 4id. ; and L, £105, 
 17s. llfd. How much will his creditors lose by him? 
 
 65. A tax of £975, 17s. lO^d. is raised from 5 towns ; 
 the first town pays £190, 14s. 8^d. ; the second, £204, 
 15s. 7|d.; the third, £199, 17s. 8f d. ; and the fourth, 
 £219, 15s. 3id. : how much does the fifth town pay? 
 
 66. A merchant laid out £756, 18s. 9^d. on wheat, bar- 
 ley, and oats ; the sum laid out on wheat and barley was 
 £437, 6s. 2d., and on barley and oats, £540, 12s. l^d. : 
 how much was laid out on each ? 
 
41 
 
 COMPOUND MULTIPLICATION. 
 Case I. When the multiplier is not greater than 12. 
 
 Ex. Multiply £8, 17s. 9id.by 9. Ans. £79, 19s. lUd. 
 
 Sol. 9 times If. = 9f. or 2Jd. ; write down £8 17s. 9id, 
 Jd., and carry 2d. 9 times 9d. are 81d. and 9 
 
 2d. are 83d. or 6s. lid. ; write down lid., and £79 19 \i^ 
 carry 6s. 9 times 7s. are 63s. and 6s. are = 
 
 69s. ; write down 9s. and carry 6 9 times 1 are 9 and 6 
 are 15 ten s. pieces = £7, 10s. ; write down 1 before 9s. and 
 carry £7. 9 times £8 are £72 and £7 are £79. 
 
 1. Multiply £27, 17s. 8jd.by2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 2. Multiply£36,15s.ll|d. by 7,5,2,9, 6,11,4,10, 8, 12,3. 
 
 Case II. When the multiplier does not exceed 156. 
 
 Ex. Multiply £3, 16s. 7id. by 16 and by 26. 
 
 2. £3 16s. 7id.X26=5x5-f 1 
 
 1. £3 16s. 7jd.Xl6 = 4X4 | 
 
 
 
 _5 
 
 
 4 
 
 19 
 
 3 
 
 0| = 5 times. 
 
 15 6 
 
 5 = 4 times. 
 4 
 
 5 
 
 
 95" 
 3 
 
 15 
 16 
 
 1 J = 25 // 
 
 £61 5 
 
 8 =16 times. 
 
 7i= 1 '/ 
 
 
 d. 
 
 £99 
 
 11 
 
 8i = 26 times. 
 
 £ 5. 
 
 £ 
 
 5. 
 
 d. 
 
 1.27 11 
 
 4iX 14, 18, 20 
 
 13.42 
 
 18 
 
 6iX 17, 23, 26 
 
 2.31 17 
 
 2|X 24, 27, 30 
 
 14.36 
 
 15 
 
 lliX 29, 31, 34 
 
 3.19 18 
 
 6iX 32, 25, 36 
 
 15.25 
 
 13 
 
 lOfX 38, 43, 39 
 
 4.34 14 
 
 lliX 42, 45, 48 
 
 16.38 
 
 11 
 
 OiX 47, 59, 68 
 
 5.28 19 
 
 lOiX 49, 54, 65 
 
 17.45 
 
 12 
 
 8IX 67, 69, 74 
 
 6.74 13 
 
 8|X 56, 60, 64 
 
 18.56 
 
 18 
 
 6iX 75, 76, 79 
 
 7.16 19 
 
 lliX 63, 66, 72 
 
 19.73 
 
 16 
 
 4|X 83, 87, 86 
 
 8.35 
 
 OfX 70, 77, 81 
 
 20.84 
 
 19 
 
 llfX 89, 93, 98 
 
 9.54 19 
 
 OiX 80, 90, 96 
 
 21.91 
 
 13 
 
 4iX 94,103,107 
 
 10.47 13 
 
 111X108,121,144 
 
 22.94 
 
 15 
 
 2iXll5, 95,106 
 
 11.45 15 
 
 6|X110, 99,132 
 
 23.96 
 
 17 
 
 81X117,127,139 
 
 12.39 17 
 
 10|X 84, 77, 81 
 
 24.99 
 
 19 
 
 11|X148,126,137 
 
42 COMPOUND MULTIPLICATION. 
 
 Case III. When the multiplier exceeds 156. 
 
 Ex. Multiply £2, 13s. 4|d. by 536. Ans. £1431, Os. 2d 
 
 £2 13s. 4|d.X6 = £16 Os. 4id.= 6 times. 
 10 
 
 
 26 13 11^ X3= 80 1 lOi = 30 times. 
 10 
 
 £266 19 7 X5= 1334 17 11 = 500 times. 
 
 £1431 2 =536 times. 
 
 1. 
 
 2. 
 3. 
 4. 
 
 £ s. d. 
 
 5 18 11| X 583, 742 
 
 6 5 2^X 879, 986 
 
 3 13 4i X 1004, 2963 
 
 4 17 9| X 3125, 7518 
 
 £ *. d, 
 
 5. 7 19 lOfX 7384, 6472 
 
 6. 10 11 lliX 5809, 4365 
 
 7. 13 16 8iX 9416,10738 
 
 8. 16 17 101X27580,74087 
 
 Find the price of, 
 
 1. 27 cwt. of sugar at £3, 16s. 6d. per cwt. 
 
 2. 38 tons of steel at £25, 17s. lid. per ton. 
 
 3. 45 quarters of wheat at £3, 6s. 7^d. per quarter. 
 
 4. 67 dozen Madeira at £6, 8s. llf d. per dozen. 
 
 5. 53 gallons whisky at 12s. 2f d. per gallon. 
 
 6. 86 acres of turnips at £17, 16s. 8d. per acre. 
 
 7. 57 cwt. butter at £4, 5s. 8Jd. per cwt. 
 
 8. 67 lbs. tea at 7s. ll^d. per lb. 
 
 9. 58 acres of grass at £7, 8s. 7id. per acre. 
 
 10. 75 cwt. Carolina rice at £2, 15s. 7^d. per cwt. 
 
 11. 46 sugar loaves, each 17^ lbs., at ll^d. per lb. 
 
 12. 17 boxes pimento, each 87 lbs. at lljd. per lb. 
 
 13. 19 cwt. potashes at £1, 7s. llfd. per cwt. 
 
 14. 116 cwt. tallow at £2, 10s. 7id. per cwt. 
 
 15. 73 gallons rum at 18s. O^d. per gallon. 
 
 16. 59 ounces of gold at £3, 17s. ll|d. per oz. 
 
 17. 153 bushels malt at 7s. A^d. per bushel. 
 
 18. The daily pay of a foot soldier is Is. Id. ; how 
 much is this yearly ? 
 
 19. A farm of 379 acres is rented at £3, lOs. 7^d. per 
 acre ; how much is the whole rent ? 
 
 20. A merchant bought 25 pieces of cloth, each con- 
 taining 20 yards at £1, 2s. t^d. a-yard, and sold the 
 whole for £612, 10s. ; what was his gain? 
 
COMPOUND MULTIPLICATION. 43 
 
 21. If the weekly forage of a horse be 14s. 6^d. ; what 
 sura will be required to keep a regiment of 750 horses 
 for a year ? 
 
 22. The rent of a house is £1, 10s. 6Jd. per week ; how 
 much is that in the year ? 
 
 23. How much will a farmer pay for cutting down his 
 crop, if he employs 53 reapers for 3 weeks at 2s. llfd. 
 each per day ? 
 
 24. If an hospital contains 80 boys, and each on an 
 average costs Is. 3^d. a-day for food and clothing; how 
 much will each, and also the whole, cost in the year ? 
 
 25. How much will a tax on property of £8746 yearly 
 value amount to, at 2s. 2f d. per pound ? 
 
 26. A clerk's salary is £2, 17s. 9d. a-week ; how much 
 is it yearly ? 
 
 27. Find the price of 7 pieces of cloth, each 45 yards, 
 at £1, 2s. 7^d. per yard. 
 
 2i». The pay of an Ensign in the Foot Guards is 5s. 6d. 
 per day ; what is it yearly ? 
 
 29. A bankrupt owes his creditors £4876, and pays 
 them 8s. 6^d. per pound ; how much does he pay in all? 
 
 30. How much does the pay of a regiment of 895 men 
 amount to in a year, at the rate of Is. l^d. to each man 
 per day ? 
 
 31. Find the value of a lac of rupees, that is 100,000, 
 at Is. llfd. each. 
 
 32. How much will a farmer receive for a field of wheat 
 containing 16 acres, if each acre produces 7^ quarters, 
 and the price of wheat is £2, 16s. 7d. per quarter? 
 
 33. A farmer has a field of potatoes containing 1000 
 drills ; now if each drill produces 19 bushels, how much 
 will he receive for each drill, and also for the whole, at 
 the rate of 4s. 7Jd. per bushel ? 
 
 84. A butcher purchases 4 oxen for 49 guineas, and 
 sells the beef, which amounted to 165 stones, at 6s. llfd. 
 per stone, and he gets besides £2, 3s. 5|d. for the hide, 
 &c. of each ; what is his net gain ? 
 
 35. The weekly receipts of a railway are £1768, 17s. 
 8id. ; how much is this per annum ? 
 
 36. Find the value of 17 tons of coal at 15s. 3d. per 
 ton. 
 
44 
 
 COMPOUND MULTIPLICATION. 
 
 37. What should 7 chests of tea, each containing 74 lb., 
 cost, at 3s. lOd. per lb. ? 
 
 38. An hospital contains 165 boys, and each requires 
 for food and clothing Is. 2Jd. a-day; the governor's 
 salary is £368, 7s. 6d. yearly, and 4 teachers have each 
 £182, 14s. 8d. yearly ; the porters' and servants' wages 
 and board amount to £215, lis. 6d. per annum ; and the 
 treasurer's salary amounts to £400 yearly : what is the 
 annual income of the hospital, supposing the yearly sur- 
 plus to be £597, 18s. 9d. ? 
 
 COMPOUND DIVISION. 
 
 Case I. When the divisor does not exceed 12. 
 Ex. Divide £27, 13s. 7id. by 5. Ans. £5, 10s. SJd. 
 Sol. 5 in £27 is 5 times and £2 
 over; £2 
 
 :40s. and 13s. are 53s. 5 
 in 53s. is 10 times and 3s. over; 3s. 
 = 36d. and 7d. are 43d. 5 in 43d. is 
 8 times and 3d. over; 3d. = 12f. and 
 If. are 13f. 5 in 13f. is 2 times and 3 over. 
 
 5 )£27 13s. 7|d . 
 £5 10 8i I 
 
 5 
 
 Proof £27 13 7i 
 
 1. Divide £35, 17s. 8id. by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 2. // 74 15 7i by 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 12. 
 
 Case II. When the divisor is found in the table. 
 Ex. Divide £30, lis. 8id. by 18. Ans. £1, 13s.ll|d.^\. 
 2 )£30 lis. Sj d. -M8 = 2 X 9 
 9)15 5 10^- 1 quot. by 2. 
 £ 1 13 11 1- 1 " by 18. 
 1X2 + 1 = 2 + 1=3 rem. 
 
 £ s. d. 
 
 9.612 16 3i-r 80, 84, 90 
 
 10.714 13 10^+ 70,121,144 
 
 11.896 11 2i+ 20, 42, 81 
 
 12.968 17 9|-f- 88,108,132 
 
 13.742 16 8i+ 63, 72, 81 
 
 14.845 17 9^+120, 44, 56 
 
 15.874 5 6f+ 36, 88,108 
 
 16.997 19 1U-+121, 132, 144 
 
 1. 374 16 
 
 2. 456 18 
 
 d. 
 
 3.354 11 lOf+32,35,40 
 4. 729 19 9i+30, 36, 44 
 6.847 17 llf-f-45,48,49 
 
 6. 783 11 9 ■ 
 
 7. 874 14 10*- 
 
 8. 956 15 4| 
 
 16,21,25 
 ■24, 27, 28 
 
 ■54, 55, 56 
 ■60, 63, 64 
 •50, 66, 72 
 
COMPOUND DIVISION. 
 
 45 
 
 Case III. When the divisor is not contained in the table. 
 Ex. Divide £27, 13s. 7id. by 17. Ans. £l,12s.6id.-rV 
 17)£27, 13s. lid. ( £1 12s. Gfd.^^'y 
 
 17X1 = 
 
 10 
 
 6 10 
 
 3=4 times. 
 
 Mult, by 20 
 
 
 4 
 
 213 s. 
 
 .26 1 
 
 = 16 " 
 
 17 X 1= 17 
 
 1 12 
 
 6i=l . 
 
 43 
 
 
 |Rem. 
 
 17X2= 34 
 
 £27 13 
 
 7i Proof. 
 
 Mult, by 
 17X6 = 
 Mult, by 
 17X3 = 
 
 £ s. 
 
 476 13 
 
 764 17 
 
 1387 11 
 
 17 
 i 
 
 r 
 
 t: 
 \' 
 
 9 
 12 
 115 d. 
 102 
 13 
 _4 
 54 f. 
 51 
 3 rem. 
 
 d. 
 
 8^-7-13,19,23 
 8i-rl7,26,29 
 4i-^37, 46, 58 
 4. 7480 16 lOi-f-67, 78, 89 
 5.5387 14 11^47,58,69 
 6. 6892 17 4i-^53, 57, 59 
 7.9673 8 lU-^73,75,79 
 a 2723 4 U-f-83,91,95 
 
 £ s. 
 9.9873 18 
 10.3725 17 
 11.4876 11 
 12.5983 13 
 13.6473 12 
 
 571, 
 219, 
 432, 
 729, 
 
 843 
 343 
 
 563 
 
 984 
 
 d. 
 
 llf-f- 
 6 -^ 
 
 41-^8463,1729 
 14.7893 17 10i-^- 2748, 9740 
 15.8739 16 11^^5490,6753 
 16.9378 11 71-^4386,9897 
 Case IV. To divide one sum of money by another. 
 Ex. How often does £99, 8s. 5id. contain £1, lis. 6|d. 
 £1, lis. 6|d. ) £99, 8s. 5Jd. 
 
 20 
 31s. 
 12 
 378 d. 
 
 4 
 
 1515 f. 
 
 20 
 
 1988 s. 
 12 
 
 23861 d. 
 4 
 
 )95445 f. (63 times. 
 9090 
 
 4545 
 
 4545 
 
46 
 
 COMPOUND DIVISION. 
 
 £ 8. 
 
 d. 
 
 £ s. 
 
 d. 
 
 £ s. 
 
 d. 
 
 £ s. d. 
 
 1. 113 12 
 
 6 - 
 
 - 2 10 
 
 6 
 
 9. 402 2 
 
 - 
 
 -4 3 9i 
 
 2. 51 7 
 
 3 - 
 
 - 12 
 
 2| 
 
 10. 103 14 
 
 0|- 
 
 -0 18 4i 
 
 3. 630 7 
 
 8^ 
 
 - 1 14 
 
 6^ 
 
 11. 308 15 
 
 0- 
 
 -2 7 6 
 
 4. 248 17 
 
 3^ 
 
 -72 
 
 2^ 
 
 12.9093 12 
 
 - 
 
 -2 12 1\ 
 
 5. 484 19 
 
 4^ 
 
 -13 17 
 
 H 
 
 13. 201 9 
 
 9^- 
 
 -3 9 5f 
 
 6.2855 7 
 
 o^ 
 
 -27 14 
 
 4 
 
 14.4349 1 
 
 n- 
 
 -6 3 8| 
 
 7. 2673 1 
 
 6 - 
 
 - 7 13 
 
 n 
 
 15.4539 8 
 
 4 - 
 
 -0 18 7i 
 
 8.8866 
 
 0^ 
 
 - 1 5 
 
 Oi 
 
 16.4574 15 
 
 3^- 
 
 -2 11 2^ 
 
 17. How many moidores, each 27s., are in £149, 17s. 
 sterling ? 
 
 18. How many francs, each 9|d., are equal to £9, 15s. ? 
 
 19. How many books at 3s. 6d. are equal in value to 
 868 at Is. 9d.? 
 
 20. £lj 3s. 4d. was distributed among a number of 
 boys, each received Is. 8d. ; how many were there? 
 
 21. How many pounds Irish, each 21s. 8d., are equal 
 to 1404 pounds Scotch, each Is. 8d. ? 
 
 22. The railway fares of a certain number of passengers 
 amounted to £26, 12s. 6d. ; the fare of each was 35s. 6d. : 
 how many were there ? 
 
 SUPPLEMENT TO COMPOUND MULTIPLICATION AND DIYISION. 
 
 Ex. £4 17s. e^d. X 4g 
 
 4| 
 
 3)9 15 1 =2 times. 
 
 3 5 
 19 10 
 
 Oii 
 2 
 
 £22 15 21 J = 4§ times. 
 
 Ex. £27, 10s. lljd. -r4|. 
 4| )£27 108.11id. 
 
 5^ 5 
 
 22 [2 )137 14 8^ =5 tunes. 
 1 1 1)68 17 4'g -l \b_ 
 £6 5 2^/22 
 
 
 £ 5. d. 
 
 
 £ 8. 
 
 d. 
 
 
 1. 
 
 4 8 7iX 41, 
 
 5f 
 
 1. 270 18 
 
 llf- 
 
 - 4i, 5^ 
 
 2. 
 
 6 17 10| X 6^, 
 
 H 
 
 2. 384 13 
 
 lOi- 
 
 - 9i, 114 
 
 8. 
 
 7 14 IH X 7^, 
 
 H 
 
 3.487 11 
 
 5^- 
 
 " 9f, 10| 
 
 4. 
 
 8 19 7i X 8f, 
 
 9f 
 
 4. 592 13 
 
 n- 
 
 -llf, 13| 
 
 6. 
 
 9 12 1\ X 111, 
 
 12t\ 
 
 5. 756 17 
 
 lu- 
 
 -16i, 29^ 
 
 6. 
 
 12 14 7i X 16y% 
 
 27A 
 
 6. 847 11 
 
 9^- 
 
 -47|, 59i 
 
 7. 
 
 17 18 11|X 19f, 
 
 26^ 
 
 7. 967 11 
 
 H- 
 
 -84t?^,97t*, 
 
 6. 
 
 24 11 7^ X 46 ,V 
 
 52^ 
 
 8. 989 17 
 
 lU- 
 
 r8U\,89^\ 
 
COMPOUND DIVISION. 47 
 
 1. Divide £746, lis. 6d. equally among 48 men. 
 
 2. If 38 cwt. sugar cost £108, 16s. 8d. ; what is that per 
 cwt.? 
 
 3. If 32 quarters of wheat cost £110, lis. 6d. ; what is 
 that per quarter ? 
 
 4. A gentleman spends £960 a-year ; what is that a- 
 week, and a-day ? 
 
 5. A gentleman's income is £1000 ; what should his 
 daily expenses be to save £340 a-year ? 
 
 6. A labourer earns 15s. 7^d. per week, but he must 
 save £12 a-year for house-rent and clothes; how much 
 may he spend per week ? 
 
 7. If 46i lbs. tea cost £18, 17s. 6id. ; what is that 
 per lb. ? 
 
 8. If27| gallons Cognacbrandycost £33, 17s. 6d.;what 
 is that per gallon ? 
 
 9. If 34 men gain £1360 in a year; what does each gain 
 per week, and per day ? 
 
 10. Divide £255, 17s. 6d. among 7 marines and 75 
 sailors, giving each marine twice as much as a sailor. 
 
 11. A farm of 156 acres is let for £375, 18s. 3d. ; what 
 is that per acre ? 
 
 12. A joint-stock company consists of 527 shares, and 
 the capital is £500,000 ; what is the value of a share ? 
 
 13. A merchant bought 6 pieces of cloth, each 56 yards, 
 for £308, 12s. 6d., and sold it at 19s. llfd. per yard; 
 how much did he gain upon the whole, and per yard ? 
 
 14. How much cloth at 15s. 6i d. per yard can be bouglit 
 for£95, lis. 7id.? 
 
 15. How much wine at £2, 2s. 6d. per dozen can be 
 purchased. for £297, 10s.? 
 
 16. In £59, 17s., how many crowns, half-crowns, and 
 florins, and of each an equal number? Ans. 126 of each. 
 
 Sc*L. 1 crown = 60d. £59, 17s. 
 
 1 h.-cr. = 30 _20 
 
 1 florin =_24 1197 s. 
 
 ll4d. )14364d . 
 
 126 of each. 
 
 17. How many guineas, half-gumeas, crowns and florins, 
 and of each an equal number, are in £25, 6d. ? 
 
48 COMPOUND DIVISION. 
 
 18. How many gallons of brandy can be bought for 
 £625, 19s. 6d. at 36s. 6d. the gallon? 
 
 19. The revenues of an hospital amount to £1807, 8s. 
 yearly ; how many boys wiU it maintain, if each costs 
 £18, 16s. 6^d. ? 
 
 20. A gentleman distributed £19, 14s. 6d. among some 
 poor people, giving each 10s. ll^d. ; how many poor 
 were there ? 
 
 21. Divide £73, 7s. 44 d. among 3 men, 5 women, and 
 10 boys, giving each man twice a woman's share, and 
 each woman 3 times a boy's share. 
 
 22. If a man gains 2s. 6d. a-day, and spends Is. lO^d.; 
 how many days must he labour to pay a debt of £11, 
 7s. 6d. ? 
 
 23. A farmer, who employed 49 reapers for 4 weeks to 
 cut down his crop, paid them in aU £158, 12s. 9d. ; how 
 much was that to each reaper, and what was the daily 
 wages of each ? 
 
 24. A merchant pays for gas £12, 17s. 6d. yearly, at the 
 rate of 10s. per 1000 cubic feet; how many cubic feet does 
 he consume in the year ? 
 
 25. The wages of an equal number of men, women, 
 and children amounted to £24, 7s. 6d. ; each man earned 
 Is. 6d., each woman Is., and each child 9d. : how many 
 were there of each ? 
 
 26. A house and its furniture are worth £3750, 16s. 
 8d., but the house is worth 7 times as much as the 
 furniture ; what is the value of each ? 
 
 27. If 1000 muskets are worth £3333, 6s. 8d. ; what 
 is the price of each ? 
 
 28. A corn merchant lays out £581, 17s. on equal 
 quantities of wheat at 42s. per quarter, barley at 36s. 
 6d. per quarter, and oats at 29s. 3d. per quarter ; what 
 quantity of each did he buy ? 
 
 29. How many gallons of ale at 3s. 6d. a-gallon should 
 be exchanged for 75 gallons brandy at 38s. 6d. per 
 gallon ? 
 
 30. A person spends £8, 12s. 6d. weekly ; what must 
 his daily income be that in 12 years he may lay by 
 £312 r 
 
49 
 
 BILLS OF PARCELS. 
 
 Mr James Scott 
 
 14 gallons malt aqua 
 13 rum 
 
 12 hollands 
 
 9 brandy 
 
 15 dozen port wine 
 16 sherry 
 
 Edinburgh, Jan. 2, 1858. 
 Bought of William Oliver^ 
 
 @ 15/6 £ 
 
 .. 18/6 
 
 .. 24/6 
 
 .. 55/6 
 
 .. 47/6 
 
 .. 36/6 
 
 Mr Andreio Turnhull 
 
 Bought of John Smart & Co, 
 27J yards superfine black cloth @ 21/8. ..£ 
 
 17| blue do. .. 23/6... 
 
 15| olive do. ..14/9... 
 
 23» mixt do. ..17/10.. 
 
 343 bl. cassimere .. 6/4i... 
 
 3n 
 
 .drab do. ..5/9^... 
 
 
 
 £ 
 
 Mr John Williamson 
 
 
 
 Bought of J. & W, Allan, 
 
 17 reams large thick post HP. 
 
 . @41/7.... 
 
 ..£ 
 
 23 small do. do. 
 
 .. 32/9.... 
 
 
 13 foolscap ruled 
 
 .. 20/3.... 
 
 
 16 coloured yellow 
 
 .. 25/8i... 
 
 
 18 do. green 
 
 ..24/111. 
 
 
 21 marbled 
 
 .. 19/11... 
 
 
 
 £ 
 
 Mr John Anderson 
 
 
 
 Bought of William Tod, 
 
 13j lbs. green tea 
 
 @ 6/61.... 
 
 ..£ 
 
 17^ hyson skin 
 
 .. 5/3^... 
 
 
 26 1 souchong 
 
 .. 4/lU... 
 
 
 191 pekoe 
 
 .. 5/8^... 
 
 
 27 raw sugar 
 
 .. 6^... 
 
 
 35 refined do. 
 
 .. 8.... 
 
 
 
 £ 
 
50 
 
 BILLS OF PARCELS. 
 
 Mr William Brown 
 
 56 cwt. raw sugar 
 
 29 boxes oranges 
 
 5 lemons 
 
 150 sugar loaves ea. IS^lbs 
 
 52^ cwt. of molasses 
 
 A chest of black tea, ST^lbs. 
 
 Bouglit of Drysdale & Co. 
 
 @ 50/8 £ 
 
 .. 34/lU 
 
 .. 19/4i 
 
 .. 8|p.lb. 
 .. 17/6 p. cwt. 
 .. 4/3jp.lb... 
 
 Mr George Thomson 
 
 Bought of David Wright, 
 
 54i yds. superfineBrussels carpet @4/10|..£ 
 
 71 fine do. do. ..3/9 
 
 67f superfine English do. .. 2/11 J.. 
 
 294 
 
 fine 
 
 do. 
 
 17^ floor-cloth 
 
 15J.. 
 
 V crumb-cloth 
 
 do. 
 
 ■2/M 
 . 5/71... 
 . 8/9i... 
 
 Mr David Simpson 
 
 52 quarters wheat 
 
 47 barley 
 
 39 oats 
 
 17 pease 
 
 19 beans 
 
 117 stones hay 
 
 Bought of Richard Davidson, 
 
 @46/6 £ 
 
 .. 43/5., 
 .. 27/8. 
 .. 45/3. 
 .. 46/8. 
 
 9i.. 
 
 Miss Murray 
 
 14^ yds. pink sarcenet 
 
 17f green silk 
 
 25 printed calico 
 
 23 J ..... Norwich crape 
 
 19 gingham 
 
 24| do. striped 
 
 27| silk velvet 
 
 Bought of Thomas Watson, 
 
 @3/7i £ 
 
 .. 4/2i 
 
 .. l/2i 
 
 .. 3/2i 
 
 .. llf 
 
 •• 10^ 
 
 .. 14/8^ 
 
61 
 
 II. WEIGHTS AND MEASTJKES. 
 
 KEDUCTION. 
 
 Ex. Eed. 8472 grs. to ib. 
 f 4)8472 grs. 
 (6)2118 
 
 16 )2118 
 2,0)35,3 dwt. 
 12)17 oz. 13 dwt. 
 lib. 5 oz. 13 dwt 
 
 Ex. Red. 3 lb. 4 oz. 5 dwt. to gi'S. 
 Mult. by 12 and add 4 oz. 
 
 40 oz. 
 Mult, by 20 and add 5 dwt. 
 
 805 dwt 
 Mult. by 24 
 
 19320 grs. 
 
 1. Reduce 27 lbs. ; 14 lbs. 10 oz. 13 dwts. ; 57 lbs. 8 oz. 
 12 dwts. 16 grs. ; 82 lbs. 3 oz. 15 dwts. 20 grs. troy re- 
 spectively to grains. 
 
 2. Reduce 27653 dwts. ; 476890 grs. ; 478670 oz. ; 
 72586 grs. ; 5147G0 dwts. ; and 738469 grs. to pounds. 
 
 3. Reduce 29 lbs. 2 oz. 3 drs. 1 scr. 18 grs. ; 18 lbs. 
 4drs, ; 461bs. 4oz. 2 scrs. ; and 205 lbs. 15 grs. to grains 
 apothecaries' weight. 
 
 4. Reduce 4968 drs. ; 72190 scrs. ; 618764 grs. ; 5489 
 oz. ; 73864 drs. ; and 892164 grs. to pounds. 
 
 5. Reduce 24 tons ; 6 tons, 3 cwt. 2 qrs. 14 lbs. 12 oz. 
 12 drs. ; 15 cwt. 27 lbs. 14 drs. ; 27 lbs. 13 oz. 15 drs. to 
 drams avoirdupois. 
 
 6. Reduce 21704736 drs.; 41876 lbs.; 219864 oz. , 
 518764 lbs. ; 21983 qrs. ; 714867846 drs. to tons. 
 
 7. Reduce 3 fur. 34 po. 3 yds. 2 ft. ; 17 miles, 2 fur. 28 
 po. 2 yds. 9 in. ; and 81 mis. 1 fur. 26 po. 3 yds. 2 ft. 6 in. 
 to inches. 
 
 8. Reduce 71846 yds. ; 4189628 inches ; 4596327 ft. ; 
 8476 po. ; 51486973 in. ; and 7184896 ft. to miles. 
 
 9. Reduce 4 yds. 2 qrs. 1 nl. ; 24 yds. 3 nls. ; 25 Eng. 
 ells, 3 qrs. 2 nls. ; 53 Fie. ells, 2 qrs. 3 nls. ; 56 yds. 3 qrs. 
 3 nls. to nails. 
 
 10. Reduce41764 nls. ; 5174 qrs. ; 318769 inches ; 49864 
 nls.; 217384 inches; and 8172144 nls. to yards and 
 English ells. 
 
 11. Reduce 27 ac. 3 ro. 16 per. ; 84 ac. 2 ro. 24 per. 28 
 yds. ; 108 ac. 1 ro. 36 per. 25 yds. 5 ft. 84 in. to square 
 inches. 
 
52 REDUCTION. 
 
 12. Reducel47847684sq.inches; 218764yds.; 5189764 
 ft. ; 31874 per. ; and 84726084 inches to acres. 
 
 13. Reduce 48 cub. yds. ; 403 cub. yds. 21 ft. 908 in. , 
 700 tons of ship. ; 672 loads of hewn timber ; and 876 
 do. of rough, to cubic inches. 
 
 14. Reduce 17486936 cu. in.; 784693 cu. ft.; 874869684 
 cu. in. ; and 784627 cu. ft. to cubic yards and tons of 
 shipping. 
 
 15. Reduce 8 qrs. 3 bu. 2 pk. 1 ga. ; 208 qrs. 7 bu. 3 pk. 
 1 ga. 3 qts. ; 409 bu. 2 pk. 1 ga. 3 qts. 1 pt. to pints. 
 
 16. Reduce 7486984 pts. ; 87634 pks. ; 918764 gals. ; 
 8176 bu. ; 514876 pts. ; and 784673 qts. to quarters. 
 
 17. Reduce 208 galls. 3 qts. 1 pt. ; 476 galls. 2 qts. ; and 
 749 galls. 1 qt. 1 pt. to pints. 
 
 18. Reduce 74869 pints ; 586476 pints ; 3486 qts. ; and 
 79040 pints to gallons. 
 
 19. Reduce 42 signs 39° 36' ; 81^ 15° 49' 59'^ ; 208s 20° 
 56' 28''; and 315^ 19° 34' 38'' to seconds. 
 
 20. Reduce 718460"; 87654'; 374°; 8178640"; 71860'; 
 7186940"; and 7184° to signs and circles. 
 
 21. Reduce 36 co. ye. 219 da. 18ho. 15 min. 27 sec. ; 380 
 CO. ye. 219 da. 23 ho. 29 min. 36 sec. ; and 7184 Julian 
 years to seconds. 
 
 22. Reduce 71847630 sec. ; 48196219 min. ; 81468 ho. ; 
 31817640 sec. ; and 7187210 min. to com. and Jul. years. 
 
 23. How long would it require to count 800 millions of 
 sovereigns, at the rate of 120 in a minute? 
 
 24. How many seconds have elapsed since the birth of 
 Christ or in 1858 Jul. years? 
 
 25. The distance of Jupiter from the sun is 494,513,000 
 miles ; express this in feet. 
 
 26. Saturn revolves round the sun in 10,756 days, 5 ho. 
 16 m. 32 sec. ; how many seconds is this ? 
 
 27. In Scotland there are 29,167 square miles j how 
 many acres does it contain ? 
 
 28. The polar axis of the Earth is 41,706,360 feet ; 
 express this in miles, &c. 
 
 29. Light travels at the rate of 192,000 miles per sec. ; 
 in what time will it travel between the Sun and Saturn, 
 the distance being 906,643,000 miles ? 
 
53 
 
 COMPOUND ADDITION. 
 
 TROY WEIGHT. 
 2. 
 
 lbs. 
 
 oz. 
 
 dwt. 
 
 gr. 
 
 lbs. 
 
 oz. 
 
 dwt. 
 
 gr. 
 
 lbs. 
 
 oz. 
 
 dwt. 
 
 gr. 
 
 27 
 
 10 
 
 11 
 
 18 
 
 31 
 
 10 
 
 19 
 
 23 
 
 67 
 
 8 
 
 13 
 
 22 
 
 36 
 
 11 
 
 16 
 
 17 
 
 53 
 
 8 
 
 17 
 
 19 
 
 76 
 
 9 
 
 18 
 
 20 
 
 41 
 
 8 
 
 18 
 
 23 
 
 35 
 
 4 
 
 15 
 
 20 
 
 18 
 
 11 
 
 15 
 
 23 
 
 34 
 
 9 
 
 10 
 
 12 
 
 20 
 
 3 
 
 4 
 
 6 
 
 81 
 
 4 
 
 12 
 
 14 
 
 26 
 
 5 
 
 8 
 
 19 
 
 25 
 
 9 
 
 16 
 
 17 
 
 15 
 
 3 
 
 13 
 
 13 
 
 37 
 
 11 
 
 16 
 
 15 
 
 48 
 
 11 
 
 19 
 
 21 
 
 56 
 
 11 
 
 4 
 
 8 
 
 47 
 
 10 
 
 18 
 
 22 
 
 84 
 
 10 
 
 16 
 
 18 
 
 9 
 
 10 
 
 8 
 
 17 
 
 APOTHECARIES' WEIGHT. 
 
 
 4. 
 
 
 
 
 5. 
 
 
 
 
 6. 
 
 
 
 lbs. 
 
 oz. 
 
 dr. 
 
 Bcr. 
 
 oz. 
 
 dr. 
 
 sc. 
 
 gr- 
 
 lbs. 
 
 oz. 
 
 dr. 
 
 Bcr. 
 
 18 
 
 9 
 
 4 
 
 1 
 
 11 
 
 7 
 
 2 
 
 19 
 
 56 
 
 10 
 
 7 
 
 2 
 
 17 
 
 8 
 
 7 
 
 2 
 
 10 
 
 4 
 
 1 
 
 15 
 
 84 
 
 11 
 
 5 
 
 1 
 
 26 
 
 5 
 
 4 
 
 
 
 8 
 
 3 
 
 2 
 
 18 
 
 96 
 
 10 
 
 6 
 
 2 
 
 62 
 
 11 
 
 7 
 
 2 
 
 7 
 
 5 
 
 1 
 
 17 
 
 31 
 
 8 
 
 4 
 
 1 
 
 25 
 
 10 
 
 4 
 
 1 
 
 9 
 
 4 
 
 2 
 
 15 
 
 28 
 
 9 
 
 7 
 
 2 
 
 64 
 
 11 
 
 2 
 
 2 
 
 11 
 
 6 
 
 1 
 
 18 
 
 86 
 
 11 
 
 7 
 
 2 
 
 AVOIRDUPOIS WEIGHT. 
 
 
 7 
 
 
 
 
 8 
 
 
 
 
 s 
 
 . 
 
 
 ton. 
 
 cwt. 
 
 qrs. 
 
 lbs. 
 
 cwt. 
 
 qrs. 
 
 lbs. 
 
 oz. 
 
 qrs. 
 
 lbs. 
 
 oz. 
 
 dr. 
 
 74 
 
 18 
 
 2 
 
 25 
 
 27 
 
 2 
 
 18 
 
 14 
 
 14 
 
 14 
 
 14 
 
 14 
 
 87 
 
 16 
 
 3 
 
 27 
 
 31 
 
 3 
 
 26 
 
 15 
 
 27 
 
 26 
 
 15 
 
 15 
 
 65 
 
 13 
 
 1 
 
 20 
 
 46 
 
 1 
 
 24 
 
 13 
 
 38 
 
 22 
 
 13 
 
 12 
 
 29 
 
 11 
 
 
 
 18 
 
 49 
 
 2 
 
 27 
 
 11 
 
 47 
 
 11 
 
 12 
 
 13 
 
 94 
 
 17 
 
 3 
 
 26 
 
 37 
 
 
 
 24 
 
 12 
 
 31 
 
 18 
 
 15 
 
 11 
 
 38 
 
 14 
 
 2 
 
 19 
 
 84 
 
 3 
 
 16 
 
 10 
 
 72 
 
 27 
 
 13 
 
 15 
 
 45 
 
 19 
 
 1 
 
 27 
 
 93 
 
 1 
 
 27 
 
 15 
 
 29 
 
 22 
 
 10 
 
 4 
 
 LINEAL MEASURE. 
 
 
 10. 
 
 
 
 11 
 
 
 
 
 12. 
 
 
 
 mis. 
 
 fu. po. 
 
 yds. 
 
 fu. 
 
 po. 
 
 yds. 
 
 ft. 
 
 po. 
 
 yds. 
 
 ft. 
 
 in. 
 
 45 
 
 3 27 
 
 4 
 
 17 
 
 18 
 
 2 
 
 1 
 
 39 
 
 '2 
 
 1 
 
 7 
 
 76 
 
 7 39 
 
 5 
 
 25 
 
 36 
 
 1 
 
 2 
 
 45 
 
 4 
 
 2 
 
 11 
 
 64 
 
 5 29 
 
 3 
 
 64 
 
 31 
 
 3 
 
 1 
 
 53 
 
 3 
 
 1 
 
 10 
 
 85 
 
 6 34 
 
 2 
 
 45 
 
 39 
 
 5 
 
 2 
 
 32 
 
 5 
 
 2 
 
 8 
 
 58 
 
 7 26 
 
 4 
 
 74 
 
 26 
 
 4 
 
 
 
 25 
 
 4 
 
 2 
 
 y 
 
 69 
 
 3 37 
 
 2 
 
 55 
 
 34 
 
 5 
 
 2 
 
 74 
 
 5 
 
 2 
 
 11 
 
 73 
 
 5 33 
 
 4 
 
 79 
 
 18 
 
 1 
 
 1 
 
 43 
 
 2 
 
 1 
 
 9 
 
54 
 
 COMPOUND ADDITION. 
 
 CLOTH MEASURE. 
 
 
 13 
 
 
 
 
 14 
 
 
 
 
 
 15. 
 
 
 yds. 
 
 qrs. 
 
 nls. 
 
 in. 
 
 En.ell 
 
 qrs. 
 
 nls. 
 
 in. 
 
 Fr.ell. 
 
 qrs. 
 
 nls. 
 
 in. 
 
 27 
 
 3 
 
 3 
 
 2 
 
 45 
 
 3 
 
 2 
 
 1 
 
 48 
 
 5 
 
 3 
 
 2 
 
 73 
 
 1 
 
 
 
 1 
 
 36 
 
 4 
 
 3 
 
 2 
 
 76 
 
 3 
 
 2 
 
 
 
 48 
 
 
 
 2 
 
 
 
 75 
 
 2 
 
 1 
 
 1 
 
 51 
 
 4 
 
 1 
 
 1 
 
 86 
 
 2 
 
 1 
 
 1 
 
 64 
 
 4 
 
 3 
 
 2 
 
 36 
 
 5 
 
 3 
 
 2 
 
 74 
 
 2 
 
 3 
 
 2 
 
 38 
 
 4 
 
 1 
 
 2 
 
 71 
 
 4 
 
 1 
 
 
 
 39 
 
 1 
 
 2 
 
 
 
 76 
 
 3 
 
 3 
 
 1 
 
 67 
 
 1 
 
 
 
 2 
 
 76 
 
 1 
 
 3 
 
 2 
 
 69 
 
 4 
 
 2 
 
 2 
 
 84 
 
 5 
 
 3 
 
 2 
 
 
 
 
 SQUARE OR LAND MEASURE. 
 
 
 
 
 
 16. 
 
 
 17. 
 
 
 u 
 
 I 
 
 
 ac. 
 
 ro. 
 
 pe. 
 
 yds. 
 
 ro. 
 
 pe. yds. 
 
 ft. 
 
 pe. 
 
 yds. 
 
 ft. 
 
 in. 
 
 36 
 
 3 
 
 39 
 
 30 
 
 14 
 
 27 18 
 
 4 
 
 27 
 
 29 
 
 8 
 
 67 
 
 45 
 
 2 
 
 33 
 
 24 
 
 25 
 
 11 19 
 
 8 
 
 31 
 
 30 
 
 4 
 
 96 
 
 72 
 
 3 
 
 27 
 
 29 
 
 32 
 
 17 21 
 
 4 
 
 27 
 
 27 
 
 1 
 
 99 
 
 85 
 
 1 
 
 36 
 
 30 
 
 36 
 
 38 29 
 
 7 
 
 38 
 
 11 
 
 7 
 
 84 
 
 96 
 
 3 
 
 38 
 
 27 
 
 48 
 
 28 26 
 
 6 
 
 29 
 
 26 
 
 3 
 
 47 
 
 71 
 
 2 
 
 31 
 
 25 
 
 86 
 
 39 30 
 
 8 
 
 36 
 
 30 
 
 8 
 
 98 
 
 78 
 
 3 
 
 39 
 
 30 
 
 74 
 
 36 28 
 
 7 
 
 39 
 
 30 
 
 8 
 
 99 
 
 MEASURE OF CAPACITY. 
 
 
 19 
 
 
 
 
 20 
 
 
 
 
 21. 
 
 
 qrs. 
 
 bu. 
 
 pe. 
 
 Ra. 
 
 bu. 
 
 pe. 
 
 ga. 
 
 qt. 
 
 pe. 
 
 ga. qt. 
 
 pt. 
 
 56 
 
 7 
 
 3 
 
 
 56 
 
 2 
 
 1 
 
 2 
 
 74 
 
 1 3 
 
 
 74 
 
 6 
 
 2 
 
 
 39 
 
 1 
 
 
 
 3 
 
 38 
 
 1 2 
 
 
 45 
 
 3 
 
 1 
 
 
 47 
 
 3 
 
 1 
 
 2 
 
 84 
 
 1 3 
 
 
 63 
 
 7 
 
 3 
 
 
 76 
 
 1 
 
 1 
 
 1 
 
 48 
 
 1 2 
 
 
 34 
 
 6 
 
 2 
 
 
 79 
 
 3 
 
 
 
 3 
 
 56 
 
 1 3 
 
 
 
 47 
 
 7 
 
 3 
 
 
 34 
 
 1 
 
 1 
 
 
 
 75 
 
 2 
 
 
 38 
 
 5 
 
 2 
 
 
 49 
 
 3 
 
 1 
 
 3 
 
 63 
 
 1 3 
 
 
 
 
 
 
 TIME. 
 
 
 
 
 
 
 22. 
 
 
 
 23. 
 
 
 
 24 
 
 
 
 co.ye. da. 
 
 ho. 
 
 m. 
 
 da. 
 
 ho. m. 
 
 sec. 
 
 da. 
 
 ho. 
 
 m. 
 
 sec. 
 
 28 96 
 
 18 
 
 15 
 
 84 
 
 12 56 
 
 59 
 
 55 
 
 18 
 
 54 
 
 11 
 
 38 27 
 
 16 
 
 53 
 
 96 
 
 18 41 
 
 36 
 
 73 
 
 19 
 
 49 
 
 56 
 
 45 99 
 
 23 
 
 59 
 
 72 
 
 23 59 
 
 59 
 
 85 
 
 16 
 
 46 
 
 55 
 
 76 84 
 
 11 
 
 52 
 
 67 
 
 22 48 
 
 45 
 
 98 
 
 17 
 
 41 
 
 36 
 
 35 219 
 
 16 
 
 18 
 
 36 
 
 21 18 
 
 47 
 
 87 
 
 22 
 
 28 
 
 39 
 
 74 361 
 
 15 
 
 55 
 
 79 
 
 20 29 
 
 55 
 
 76 
 
 20 
 
 18 
 
 49 
 
 84 278 
 
 11 
 
 46 
 
 93 
 
 23 51 
 
 42 
 
 65 
 
 23 
 
 54 
 
 51 
 
COMPOUND ADDITION. 
 
 55 
 
 25. A corn merchant bought 208 qrs. 3 bu. 1 pk. of 
 barley ; 336 qrs. 2 pk. of wheat ; 236 qrs. 4 bu. of oats ; 
 125 qrs. 1 bu. 3 pks. of rye ; 86 qrs. 1 bu. 1 pk. of pease ; 
 and 79 qrs. 2 bu. 2 pk. of beans : how many quarters 
 did he buy ? 
 
 26. The distance from A to B is 2 ml. 1 fu. 30 po. 5 yds. ; 
 from B to C, 7 fu. 4 yds ; from C to D, 1 ml. 25 po. ; 
 and from D to E, 3 ml. 1 fu. 2 yd. : find the distance 
 from A to E. 
 
 27. A clothier, at various times, bought 28 yds. 2 qrs. 
 1 nl. of cloth ; 37 yds. 2 qrs. ; 47 yds. 1 nl. ; 37 yds, 
 1 qr. 2 nl. ; and 67 yds. 2 qrs. 2 nl. : how much did he 
 buy in all ? 
 
 28. London is in latitude 51° 30^ 48'' N., and Sydney 
 is in lat. 33° 51^ 40'^ S. ; what is the diflference ? 
 
 COMPOUND SUBTRACTION. 
 
 TROY WEIGHT. 
 
 
 1. 
 
 
 
 2. 
 
 
 
 3. 
 
 lb. 
 
 oz. dwt. 
 
 gr. 
 
 lb. 
 
 oz. dwt. 
 
 gr. 
 
 lb. 
 
 oz. dwt. gr. 
 
 96 
 
 10 13 
 
 14 
 
 36 
 
 5 17 
 
 21 
 
 82 
 
 2 1 16 
 
 47 
 
 10 19 
 
 21 
 
 19 
 
 7 18 
 
 23 
 
 79 
 
 11 14 20 
 
 
 
 
 apothecaries' weight. 
 
 
 
 
 
 4. 
 
 
 
 5. 
 
 6. 
 
 
 
 lb. 
 
 oz. 
 
 dr. 
 
 scr. 
 
 lb. 
 
 oz. dr. Bcr. 
 
 oz. 
 
 dr. 
 
 scr. 
 
 pr. 
 
 39 
 
 2 
 
 3 
 
 1 
 
 52 
 
 7 7 
 
 41 
 
 6 
 
 2 
 
 18 
 
 29 
 
 7 
 
 5 
 
 2 
 
 46 
 
 8 7 1 
 
 34 
 
 7 
 
 1 
 
 19 
 
 84 
 65 
 
 avoirdupois weight. 
 
 
 7. 
 
 
 8. 
 
 
 
 9. 
 
 
 ton. 
 
 cwt. qrs. lb. 
 
 cwt. 
 
 qrs. lb. 
 
 oz. 
 
 qrs. 
 
 lb. oz. 
 
 dr. 
 
 84 
 
 13 2 11 
 
 46 
 
 1 23 
 
 12 
 
 17 
 
 21 11 
 
 10 
 
 69 
 
 14 3 25 
 
 29 
 
 2 22 
 
 15 
 
 9 
 
 22 13 
 
 14 
 
 10. 
 
 mis. fu. po. yds. 
 
 ^ 3 22 4 
 
 3 25 5 
 
 lineal measure. 
 11. 
 
 fa. po. yds. ft. 
 
 35 33 4 1 
 17 36 4 2 
 
 po. 
 
 39 
 19 
 
 12. 
 
 yds. ft. in, 
 
 2' 2 8 
 
 4 2 10 
 
56 
 
 COMPOUND SUBTRACTION. 
 
 
 
 
 CLOTH MEASURE. 
 
 
 
 
 
 13. 
 
 
 14. 
 
 
 15. 
 
 
 yds. 
 
 qrs. Ills. 
 
 in. 
 
 E.ell. qrs. nls. in. 
 
 Fr.ell. 
 
 qrs. nls. 
 
 in. 
 
 72 
 
 2 1 
 
 1 
 
 93 4 2 1 
 
 81 
 
 4 2 
 
 1 
 
 66 
 
 2 1 
 
 2 
 
 63 4 3 2 
 
 41 
 
 5 3 
 
 2 
 
 SQUARE OR LAND MEASURE. 
 17. 
 
 ae. 
 
 ro. pe. 
 
 yds. 
 
 ro. 
 
 pe. 
 
 yds. 
 
 ft. 
 
 pe. yds. 
 
 ft. 
 
 in. 
 
 65 
 
 2 31 
 
 21 
 
 53 
 
 18 
 
 27 
 
 3 
 
 25 21 
 
 4 
 
 10 
 
 36 
 
 3 31 
 
 24 
 
 19 
 
 28 
 
 29 
 
 5 
 
 8 29 
 
 4 
 
 11 
 
 MEASURE OF CAPACITY. 
 
 
 19. 
 
 
 
 20. 
 
 
 
 21. 
 
 
 qrs. 
 
 bu. pe. 
 
 pa. 
 
 bu. 
 
 pe. ga. 
 
 qt. 
 
 pe. 
 
 ga. qt. 
 
 pt. 
 
 21 
 
 3 2 
 
 
 
 54 
 
 2 1 
 
 2 
 
 18 
 
 3 
 
 
 
 18 
 
 4 3 
 
 1 
 
 49 
 
 2 1 
 
 3 
 
 9 
 
 1 3 
 
 1 
 
 22. 
 
 co.ye. da. ho. m. 
 
 41 138 14 25 
 
 18 147 16 46 
 
 TIME. 
 23. 
 da. ho. 
 
 90 13 43 21 
 40 18 25 46 
 
 m. sec. 
 
 da. 
 
 24. 
 
 ho. m. BBC. 
 
 70 19 15 55 
 
 31 22 15 59 
 
 25. The latitude of Edinburgh is 55° 57' 23'' N., and 
 the latitude of Pekin is 39° 54' 13'' N. ; find the difference. 
 
 26. Mars revolves round the sun in 686 da. 23 ho. 30 m. 
 41 sec, and Venus in 224 da. 16 ho. 49 ra. 10 sec. ; find 
 the difference. 
 
 27. Three farms contain 4536 ac. 3 ro. 25 per. ; the 
 1st and 2d contain 3327 ac. 30 per., and the 1st and 3d 
 2752 ac. 15 per. ; what is the size of each? 
 
 28. A merchant bought 756 qrs. 3 bu. 2 pk., and sold 
 to A 208 qrs. 3 bu. 1 pk., and to B 315 qrs. 2 bu. 2 pk. ; 
 what quantity has he left ? 
 
 29. A piece of silk measured 43 yds. 2 qrs. 1 nl. 1 in. ; 
 after 27 yds. 3 qrs. 2 nl. 2 in. have been sold: how much 
 remains ? 
 
 30. A traveller arrived at a railway station at 26 min. 
 and 32 sec. past 1 o'clock, and found that the train 
 did not start until a quarter past 2 o'clock ; how long 
 had he to wait ? 
 
57 
 
 COMPOUND MULTIPLICATION. 
 
 1. 17 lb. 8 oz. 15 dwt. 21 grs. X25, 27, 29, 47 
 
 2. 32 lb. 11 oz. 17 dwt. 19 grs. X 16, 24, 31, 38 
 
 3.25 lb. 4 oz. 3 drs. 2 scr. 18 grs. X 18, 22, 34, 43 
 
 4. 47 lb. 9 oz. 7 drs. 1 scr. 13 grs. X20, 28, 37, 41 
 
 6. 36 ton. 14 cwt. 2 qrs. 21 lb. 1 1 oz. 13 drs. X 30, 32, 39, 46 
 6.43ton. 16cwt. 3qrs. 261b. 13oz. 15 drs.X33, 35, 47, 51 
 7.21 mis. 5 fu. 29 po. 2 yds. 1 ft. 11 in. X36, 40, 52, 57 
 
 8.37 mis. 7 fu. 36 po. 3 yds. 2 ft. 8 in. X42, 45, 53, 58 
 9. 56 yds. 3 qrs. 2 nls. 2 inches X54, 56, 67, 71 
 
 10. 73 E. ells, 4 qrs. 3 nls. 1 inch X60, 64, 68, 17 
 
 11.47 Fr. ells, 5 qrs. 2 nls. 2 inches X^^, 70, 69, 73 
 
 12.38 Fl. ells, 2 qrs. 1 nl. 1 inch X72, 77, 19, 13 
 
 13. 56 ac. 2 ro. 31 pe. 23 yds. 5 ft. 47 in. X44, 48, 59, 61 
 U.87 ac. 3 ro. 39 pe. 27 yds. 8 ft. 126 in. X49, 50, 62, 65 
 15.43 qrs. 3 bu. 2 pe. 1 gal. 3 qts. 1 pint X80, 81, 75, 78 
 16.76 qrs. 4 bu. 1 pe. gal. 2 qts. 1 pint X84, 88, 79, 82 
 17. 34 CO. ye. 156 da. 21 ho. 56 min. 57 sec. X90, 96, 86, 98 
 18. 71 Ju. ye. 213 da. 19 ho. 42 min. 49 sec. X 108, 121, 107 
 
 19. A sovereign weighs 5 dwt. 3 grs. nearly ; find the 
 weight of 1000 sovereigns. 
 
 20. What is the weight of 35 brass guns, each weigh- 
 ing 6 cwt. 3 qrs. 9 lbs. ? 
 
 21. How far will a postman travel in a year, if he walks 
 9 mis. 3 fu. 8 po. 5 yds. daily ? 
 
 22. How much grain will a farm of 25 fields, each 12 
 acres, produce at the rate of 8 qrs. 7 bu. 2 pk. 1 gal. 
 per acre ? 
 
 23. A cubic foot of water weighs 2 qrs. 6 lbs. 8 oz. ; 
 what weight of water is there in a cistern whose content 
 is 72 cubic feet ? 
 
 24. How much cloth would be required to make coats 
 for a regiment of 875 soldiers, allowing 3 yds. 1 qr. 1 nl. 
 to each ? 
 
 25. A cartload of coal weighs 19 cwt. 2 qr. 18 lb. ; 
 how much will 37 cartloads weigh? 
 
 26. Find the content of 17 farms of 14 fields, each con- 
 taining 9 ac. 3 ro. 19 per. 4 yds. 
 
58 
 
 COMPOUND DIVISION. 
 
 1.387 lb. 4 oz. 13 dwts. 18 grs. 
 2. 496 lb. 11 oz. 19 dwts. 22 grs. 
 3.576 lb. 10 oz. 4 drs. 2 scr. 18 grs. - 
 4.765 lb. 8 oz. 7 drs. 1 scr. 12 grs. - 
 5.876ton.l5cwt..3qr.201b.l3oz.l2dr.- 
 6.987ton. 18cwt.2qr.261b.l5oz.8dr.- 
 7. 475 mis. 7 fu. 38 po. 3 yd. 2 ft. 11 in.- 
 8. 754 mis. 3 fu. 25 po. 2 yd. 1 ft. 10 iii.- 
 9. 375 yds. 3 qrs. 2 nls. 1 inch 
 10. 573 E. ells, 4 qrs. 3 nls. 2 inches 
 11. 876 Fr. ells, 5 qrs. 2 nls. 2 inches - 
 12.768 Fl. ells, 2 qrs. 1 nl. 1 inch 
 13. 476 ac. 3 ro. 36 pe. 25 yds. 4 ft. 96 in. ■ 
 u. 674ac. 2 ro. 24pe. 28yds. 5ft. 102 in.- 
 15. 987 qrs. 7 bu. 3 pe. 1 gal. 2 qts. 1 pint- 
 le. 879 qrs. 4 bu. 2 pe. gal. 3 qts. 1 pint- 
 17. 578 CO. ye. 134 da. 15 ho. 44 m. 58 sec- 
 18. 488 Ju.ye. 341 da. 21ho. 56m. 58 sec- 
 
 16, 18, 
 •15,14, 
 ■20, 22, 
 30, 42, 
 •28, 25, 
 27, 32, 
 ■33, 40, 
 •35, 36, 
 •44, 45, 
 •48, 49, 
 50,54, 
 -55, 56, 
 -60, 63, 
 -64, 70, 
 -66, 72, 
 -77; 80, 
 -81,84, 
 -88, 90, 
 
 23, 
 17, 
 31, 
 39, 
 37, 
 38, 
 43, 
 46, 
 53, 
 52, 
 98, 
 
 19 
 29 
 26 
 34 
 39 
 41 
 47 
 51 
 57 
 87 
 117 
 
 273, 181 
 371,811 
 713, 645 
 298, 364 
 756, 643 
 209,316 
 369, 691 
 
 19. 14 hhds. Jamaica sugar weigh 234 cwt. 2 qr. 14 lb. ; 
 find the weight of each. 
 
 20. How many canisters, each containing 1 qr. 7 lb., 
 can be filled from 37 cwt. 21 lb. ? 
 
 21. 133 bars of silver weigh 156 lb. 3 oz. 17 dwt. 2 grs. ; 
 w^hat is the weight of each ? 
 
 22. Find the circumference of a wheel which revolves 
 5267 times on a road 8 mis. 7 fu. 32 po. 5 yds. long. 
 
 23. An estate contains 5837 ac. 2 ro. 29 per. ; into how 
 many farms, each containing 32 ac. 3 ro. 37 per., may 
 it be divided ? 
 
 24. A spring yields 72 gallons of water an hour, and 
 supplies 675 families ; how much may each family use 
 daily ? 
 
 25. How many steps, each 2| feet, will a man take in 
 walking 9 miles ? 
 
 26. In 2 cwt. 2 qr. 5 lb. 4 oz. 8 drs. ; how many 
 parcels of 4 oz. 5 drs., 5 oz. 6 drs., 7 oz. 8 drs., and 8 
 oz. 5 drs., and of each an equal number ? 
 
59 
 
 MISCELLANEOUS EXERCISES. 
 
 1. A was born in 1805, and B 20 years after; when was 
 B born, and what are their present ages ? 
 
 2. A general, commanding an army of 45,550 men, fought 
 a battle, in which 5217 were killed, 11,781 wounded, and 
 518 amissing; he likewise threw 2157 into one garrison, 
 and 1786 into another; how many effective men remained 
 under his command in the field ? 
 
 3. What number being divided by 374 will give 8647369 
 for the quotient, and 76 for the remainder? 
 
 4. The product is 78469468, and one of the factors 4876 ; 
 what is the other? 
 
 5. Two persons start from the same place, and travel the 
 one 35 miles, and the other 42 miles a-day; how far will 
 they be distant from one another at the end of 44 days if 
 they both travel the same way, and how far if they travel 
 in opposite directions ? 
 
 6. A person, after paying to A £71, to B £84, to C £121, 
 to D £118, to E £217, and to F £196, has still remaining 
 £254 ; how much had he at first ? 
 
 7. In leap year how many days in each of the 12 calendar 
 months, and what is their sum ? 
 
 8. How many days from March 3d to November 1 9th ? 
 
 9. How many days from April 1st to December 29th? 
 
 10. A man was born in the year 1821, when will he be 85 
 years of age ? 
 
 11. A man was bom in 1815, what was his age in 1858 ? 
 
 12. A boy can point 1 6,000 pins in an hour, how many at 
 that rate will 16 boys point in a year of 365 days, if they 
 work ten hours each day ? 
 
 13. If the population of the globe is taken at one billion, 
 how many die yearly, if we suppose a generation to last 
 36 years? 
 
 14. At a game of cricket A, B, and C score 112 runs, A 
 and B score 79 runs and B and C 70 runs ; how many did 
 each score ? 
 
 15. The Iliad contains 15683 lines, and the -^neid 9882 
 lines, now if a boy reads 112 lines daily; in how many days 
 will he finish them ? 
 
 16. A merchant lodged in the bank on Monday £744, lis. 
 7^d., and drew out on Tuesday £579, 18s. 6|d. ; lodged on 
 Wednesday £1054, 17s. 8d., drew on Thursday £873, 198. 
 
60 MISCELLANEOUS EXERCISES. 
 
 9id. ; lodged on Friday £1786, 13s. 10|d., and drew out 
 on Saturday £1297, 13s. llfd. ; how much remained on 
 Tuesday, Thursday, and Saturday after drawing? 
 
 17. If a yard of cloth costs £1 , 2s. 6^d., what cost 85 yards ? 
 
 18. If 74 yards of cloth cost £84, 17s. 6d., what cost 
 lyard? 
 
 19. If 25 yards cost £24, 5s. lOd., what cost 5 yards? 
 
 20. What cost 93 cwt. of sugar at £2, 16s. 8^d. per cwt.? 
 
 21. What cost 1 lb. of tea at £96, lis. S^d. for 275 lb. ? 
 
 22. How many letters in a book of 21 volumes, each 840 
 pages, each page 48 lines, and each line 41 letters? 
 
 23. If a mason gains 18s. 6d. per week, and lays up 2s. T^d. 
 per week ; how much does he spend, and how much does he 
 lay up in a year ? 
 
 24. How many revolutions does a wheel, which is 2 J yards 
 in circumference, make in 3^ miles ? 
 
 25. A traveller walks 25 miles a-day, after travelling 75 
 miles, another follows him at the rate of 30 miles a-day ; 
 in how many days will the second overtake the first ? 
 
 26. If a man's wages are 21s. per week, how much may he 
 spend weekly to save £13, 13s. a-year? 
 
 27. A farm of 96 acres is let for £96, 16s. 6^d., what is 
 that per acre ? 
 
 28. Gained £274, 19s. 8id., but afterwards lost £189, 19s. 
 llfd. ; what is my net gain? 
 
 29. How much will a labourer earn in 219 days at 2s. l^d. 
 per day ? 
 
 30. A labourer earns £35, 17s. lO^d. a-year, how much 
 is that per week ? 
 
 31. 16 men purchased a lottery ticket for £25, which 
 turned out a prize of £3150; how much of the ticket did 
 each pay, and how much did each receive of the prize ? 
 
 32. A merchant has in cash £2385, 17s. llfd., in bills 
 £12,748, 16s. 6d., tea valued at £748, 16s. llfd., raw sugar 
 £289, 17s. 6|d., refined sugar £112, 17s. S^d., whisky £348, 
 17s. lOd., rum £240, lis. 7id., brandy £497, lis. 7|d., 
 gin £241, lis. 7^d., wines £1298, 3s. 4|d., porter £84, lis. 
 ll^d., ale £73, 16s. 9d., in other articles £876, 13s. 9^d., and 
 debts owing to him £2381, lis. lid.; at the same time ho 
 owes to A £481, 17s. llfd., to B £973, 16s. 7^^ ^o C £876, 
 16s. lOd., to D £584, 16s. 4|d., to E £683, 13s. ^d., to 
 F £297, 16s. lO^d., and in bills £7348, 16s. 7fd.; what is his 
 net worth ? 
 
 33. In £23, 2s., how many shillings, sixpences, and four- 
 pences, and of each an equal number ? 
 
MISCELLANEOUS EXERCISES. 61 
 
 34. "Wliat quantity of tea at 3s. 9§d. per lb. should be 
 exchanged for 728 lbs. of sugar at 6^d. per lb. ? 
 
 35. A took to market with him £148, 17s. lOfd., and he 
 there received from B £741, lis. lO^d., from C £629, 168. 
 S^d., from D £946, lis. 6d., from E £493, 16s. llfd., from 
 F £748, 16s. 9id., from G £387, 10s. 6fd., and from H 
 £876, lis. 7^d. ; but in coming home he was robbed of 
 £2587, lis. 8f d. : how much did he bring home with 
 him? 
 
 36. A person paid for a feu to build a house £1276, 17s. 
 6|d. ; the mason's bill amounted to £1485, 178. 3f d., the 
 joiner's to £487, 16s. 9fd., the plasterer's to £184, 19s. 9id., 
 the slater's to the same, the painter's to £120, lis. 7fd., the 
 plumber's to £56, lis. lO^d., besides other charges to £37, 
 lis. 9^d. ; now he wants to sell it so as to gain £470, lis. 
 9^d. : how much does he expect for it ? 
 
 37. A person gains £1, 5s. 7jd. per week, and spends 19s. 
 8^d. per week ; how much does he save in the year ? 
 
 38. A person gains £1, 2s. 7^d. per week, and spends £45, 
 17s. Ifd. in the year; how much does he save in the week? 
 
 39. Divide 91 lb. 7 oz. 11 dr. of tea among 12 men and 24 
 women, giving each man | of the share of a woman. 
 
 40. A merchant began business with a capital of £950, 
 17s. 6d. ; at the end of the year he had in cash £350, lis. 
 8id., in bills £256, 17s. 8^d., in goods £850, lis. 2^d., and 
 debts owing to him £572, lis. 7fd. ; at the same time he 
 owed in bills £381, 17s. 2Ad., to A £340, 18s. 7^d., to B 
 £120, lis. 4fd., to C £49, Hs. 6fd., to D £36, 17s. 8^., to 
 E £49, lis. 2^d., and to sundries £134, 18s. 6d. : whether 
 has he gained or lost, and how much ? 
 
 41. Bought 24 pieces of cloth, each containing 30 yards, 
 for £840, 17s. 6d., and sold 400 yards at £1, 4s. 3d. per yard ; 
 how must I sell the remainder per yard to gain £84, 2 s. 6d. 
 upon the whole ? 
 
 42. Bought 480 yards of cloth for £560, 6s. 8d., but 120 
 yards being damaged, I am obliged to sell them at a loss of 
 £20, 13s. 4d. ; how must I sell the remainder per yard so 
 as to gain £60, 16s. 8d. upon the whole, and what did the 
 damaged part sell at per yard ? 
 
 43. A merchant clears by his trade £1 590, 17s. 6f d. yearly ; 
 his household expenses amount to £580, 17s. 7|d., house 
 rent £120, lis. 9^, taxes £45, 17s. 8|d., shop rent £140, 
 lis. 9id., taxes £56, 17s. 8|d., servants' wages £175, lis. 
 llfd., tradesmen's accounts £170, lis. 9|d., and incidental 
 expenses £49, 17s. 8|<l. ; what is his net gain ? 
 
62 MISCELLANEOUS EXERCISES. 
 
 44. What is the value of 12 1 gallons of rum at 18s. 4d. 
 per gallon ? 
 
 45. Bought sugar at £3, 16s. 6d. per cwt., how much was 
 that per lb. ? 
 
 46. After paying at one time £847, lis. 8|d., at another 
 £650, 10s. 4id., at a third £549, 16s. T^d., at a fourth 
 £729, 18s. 4|d., at a fifth £1084, 19s. 8id., and at a sixth 
 £1578, 15s. 5id., there remained due £2196, 17s. lOfd.; 
 what was the original debt ? 
 
 47. What is the stock of a banking company, which con- 
 sists of 154 shares, each £578, 17s. 8^d. ? 
 
 48. Divide £17, 12s. lid. among 3 men, 4 women, and 5 
 children, giving each man 2 times the share of a woman, 
 and each woman 3 times the share of a child. 
 
 49. A gentleman gave £10, 10s. to pay for his lodging 
 from 1st May till 10th July, at Is. ll^d. per night; what 
 change should be returned to him ? 
 
 50. The longitude of New York is 74° 0' 3" W., and of Cal- 
 cutta, 88° 20' 27" E. ; find the difference. 
 
 51. Discounted six bills; the first amounted to £340, 17s. 
 8^d., the second to £473, lis. 9|d., the third to £576, 17s. 
 8|d., the fourth to £605, 15s. 4|d., the fifth to £680, 17s. 
 2|d., and the sixth to £720, Is. 9^d. ; the discount upon 
 each was respectively £7, 19s. lOf d. ; £9, 12s. ll^d.; £11, 
 18s.8|d.; £12, 16s. 8id.; £12, 19s. 9|d. ; and£13, 5s. ll|d. : 
 what was the net proceeds of each, and of the whole ? 
 
 52. A gentleman's yearly income is £1560, 16s. 8^d. ; how 
 much may he spend monthly, weekly, and daily, to save 
 £500 a-year ? 
 
 53. A gentleman gave his daughter for her fortune an es- 
 critoire, containing 12 drawers, each drawer was divided 
 into 18 compartments, in each of which was £24, 17s. 6fd. ; 
 what was the daughter's fortune? 
 
 54. Divide £1120, 10s. 6d. among 10 men and 3 boys, 
 giving each boy only ^ of a man's share. 
 
 55. How many guineas, half-guineas, crowns, and florins, 
 and of each an equal number, are contained in £36, lis. 6d. ? 
 
 56. Divide 886 ac. 3 ro. 25 per. of land among A, B, and 
 C, giving A 32 ac. 2 ro. 35 per. less than C, and B 98 ac. 3 
 ro. 15 per. more than C. 
 
 57. The freights received for a voyage were, from A 
 £127, 6s. 8H, from B £141, lis. 7fd., from C £174, 17s. 
 lO^d., from D £84, lis. 9|d., from E £79, 12s. 4id., from 
 F £112, 13s. 6id., and from G £14, lis. 2Jd.; how much 
 was the whole freight ? 
 
MISCELLANEOUS EXERCISES. 63 
 
 5^3. A merchant bought 87 yards of blue cloth for £1, 2s. 
 2^d. per yard; how must he sell it per yard to gam £12, 
 13s. 6d. on the whole? 
 
 59. The rent of a shop, including taxes, is £95, 19s. 7Jd, 
 a-year ; how much is tliat weekly and daily ? 
 
 60. Bought 9 pieces of cloth, each 35 yards, for £164, 12 s. 
 9^d., and sold 108 yards at lis. 2d. per yard; how must 1 
 sell the remainder per yard to gain £47, 8s. 7fd. in all? 
 
 61. In 20 lbs. 11 oz. 14 drs. of sugar, how many packages, 
 containing 2 lb., 9 oz., and 4 oz., and of each an equal 
 Qumber ? 
 
 62. A common consists of 440 ac. 2 ro. 20 per. ; into how 
 many fields, each containing 5 ac. 3 ro. 20 per. can it be 
 divided ? 
 
 63. Bought 44 pipes of wine for £2640, and gained by 
 selling them as much as 11 pipes cost me ; what was a pipe 
 of it sold for ? 
 
 64. A ship's company took a prize of £17,240, lis. 9d. ; 
 the captain got i of the whole, the 2 lieutenants got each 
 y*g of the remainder, the 3 midshipmen got each ^^g of what 
 was left, and the remainder was equally divided among i 
 crew of 218 men ; what was the share of each ? 
 
 65. Divide £172, 18s. 3d. among 4 men, 7 women, and 13 
 children, givmg each man 3 times the share of a woman, ami 
 each woman 5 times the share of a child. 
 
 66. A father divides his estate among his 3 sons ; the 
 eldest gets £6000, the second | of the eldest, and the third 
 f of the second ; what was the value of the estate, and the 
 shares of the two younger sons ? 
 
 67. A bankrupt who owed his creditors £7856, paid them 
 only £3250, 12s. 6d. ; what was that per pound? 
 
 68. A and B gain joinjtly £56, 17s. llfd., A and C £48, 
 17s. lO^d., and B and C £60, lis. 8Jd. ; what is the whole 
 gain, and the share of each ? 
 
 69. Received 147 yards of cloth at 14s. 6d. per yard in 
 exchange for 441 lbs. of tea ; find the price of the tea per lb. 
 
 70. An equal number of men, women, girls, and boys, are 
 employed at a manufactory, each man receives Is. 6d. per 
 day, each woman Is. 3d., each girl 7^d., and each I 
 now the sum required to pay their daily -^ ^ 
 £15, 63. l^d. : how many of each are empla 
 
 71. A merchant purchased 245 yards o^Sid^at 10^ T^dUi 
 per yard, now 20 yards became worthlesl^feena >being damj^ ^s -. 
 aged ; he sold the remainder for 18s. 9d. v- what did he gaintt a^ i 
 
 72. 14 lbs. of tea at 3s. lOd. per lb., 16 lbs. at 4s. 2d^^ 
 
64 MISCELLANEOUS EXERCISES. 
 
 lbs. at 4s. 6d., and 35 lbs. at 5s. 3d. are mixed together; 
 what should it be sold for per lb. ? 
 
 73. How many packages of coffee, containing respectively 
 2 lb., 1 lb., I lb., and ^ lb., and of each an equal number, can 
 be made from 16 cwt. 10 lbs.? 
 
 74. A prize of £2982, 14s. 2d. is divided among a captain, 
 2 lieutenants, 3 ensigns, and 120 soldiers; the captain is to 
 have 5 shares, each lieutenant 4 shares, each ensign 2 shares, 
 and each soldier one share : how much should each receive ? 
 
 75. A father left to his eldest son 4500 guineas more than 
 he left to his second son, to the second 12500 crowns more 
 than to his third son, and to the third he left 9000 guineas ; 
 find each son's portion. 
 
 76. Divide £786, 13s. 6^. among 3 persons, giving the 
 first £140, 16s. lOd. more than the second, and the second 
 £90, 18s. lOd. more than the third. 
 
 77. A merchant bought 145 gallons of whisky at iSs. 6d. 
 a gallon ; how many gallons of water must he add to it, 
 that he may gain £7, 12s. 6d., and reduce the price to 12s. 6d. 
 per gallon ? 
 
 78. £5, 19s. 2d. is to be divided among 3 classes of poor 
 people, there are 8 in the first class, 9 in the second, and 10 
 in the third; the share of the first class is to be 1^ time 
 that of the second, and the second twice the tmra ; find the 
 share of each class. 
 
 79. The weekly wages of A and B are £3, 7s. 9d. ; of A 
 and C £3, 12s. 3d. ; of B and C £3, 13s. : what are the daily 
 wages of each ? 
 
 80. Mercury revolves round the sun in 87 da. 23 ho. 15 
 min. 44 sec. ; Venus in 224 da. 16 ho. 49min. 10 sec. ; Mars 
 in 686 da. 23 ho. 30 min. 41 sec. ; Jupiter in 4332 da. 14 ho. 
 2 min. 8 sec. ; and Saturn in 10,756 da. 5 ho. 16 min. 32 sec. : 
 how many revolutions has each of these planets performed 
 in 1858 solar years? 
 
 DECIMAL COINAGE. 
 
 In anticipation of a Decimal Coinage being introduced 
 into this country, the system most likely to be adopted 
 is shown in the following 
 
DECIMAL COINAGE. 
 
 65 
 
 TABLE OP DECIMAL MONET. 
 
 1 mil (m.) = ^To'oTj = li^- 
 
 10 mils == 1 cent (c.) = £t^o = 2|d. 
 
 100 mils = 10 cents = 1 florin (fl.) = £t'o = 2s. 
 
 1000 mils = 100 cents = 10 florins = £1 = 20s. 
 
 6d. = 25m. = 2c. 5m. ; Is. = 50m. = 5c.; 2s. 6d. = 125m.= 
 
 Ifl. 2c. 5m. ; 5s. = 250m. = 2fl. 5c. ; 1 Os. =500m. = 5fl., etc. 
 
 The pound sterling, which is now divided into 960 parts, 
 would thus be divided into 1000 parts, and calculations in 
 money would be performed as in the Simple Rules, by placing 
 a point after the pounds, and making the florins occupy the 
 Jlrst place after the point, the cents the second, and the mils 
 the third place ; thus : — 
 
 £24, 2fl. 7c. 5m. would be written decimally, £24-275 
 
 £36, 7c. 
 £48, 6fl. 5m. 
 
 1. £25, 
 
 2. 57 
 8. 90 
 4. 76 
 
 5fl. 
 
 8 
 
 3 
 
 1 
 
 Express decimally, 
 
 6. £27, 
 
 6. 30 
 
 7. 17 
 
 8. 
 
 5fl. 3c. 
 9 2 
 4 
 4 
 
 9. 
 10. 
 11. 
 12. 
 
 £36-070 
 £48-605 
 
 £150, 5fl. 8c. 4m. 
 
 490 2 5 
 
 708 5 
 
 910 4 2 
 
 13. £20-450 
 
 14. 36-050 
 
 Read in £'s, florins, etc. 
 
 15. £47-825 I 17. £99-005 | 19. £210-065 
 
 16. 90-605 18. 100-725 20. 102-708 
 
 ADDITION AND SUBTRACTION. 
 
 1. £8, 2fl. 5c. 4- £7, 
 £24-133 = £24, Ifl. 3c. 3 
 
 5m. + £8, 3fl. 8m. 
 Ans. £24-133 = £24, ifl. 3c. 3m. 
 
 Ex. 2. £85, 3fl 
 
 5m. — 
 
 £58, 4fl 
 
 3c 
 
 . 6m. 
 
 Ans. £26-869. 
 
 Sol. Writ 
 cimally unde 
 proceed as in 
 and in the n 
 
 e the amounts de- 
 r each other, then 
 Simple Numbers, 
 jsult place a point 
 
 Ex. 
 
 Sum 
 
 1. £8-250 
 7-575 
 8-308 
 
 , £24-133 
 
 Ex 
 
 Dii 
 
 . 2. £85-305 
 
 58-436 
 
 af. £26-869 
 
 below thft ot 
 
 
 1. 
 £ fl. c. 
 
 5 4 3 
 
 6 7 
 
 8 6 
 
 9 5 9 
 10 7 1 
 15 
 
 m. 
 2 
 4 
 5 
 
 2 
 9 
 
 £ 
 
 14 
 
 18 
 
 24 
 
 30 
 
 45 
 
 53 
 
 fl. 
 5 
 8 
 
 
 2 
 7 
 
 2. 
 
 c. 
 
 9 
 9 
 
 4 
 2 
 
 m. 
 
 6 
 
 5 
 
 7 
 
 6 
 
 9 
 
 5 
 
 
 
 £ 
 
 75 
 67 
 50 
 39 
 30 
 24 
 
 3. 
 
 fl. c. m. 
 8 2 
 9 5 
 
 6 
 
 7 6 6 
 2 
 5 8 
 
66 
 
 £ 
 
 150 
 127 
 
 217 
 363 
 
 460 
 
 604 
 
 DECIMAL COINAGE. 
 
 £ 
 234 
 342 
 423 
 
 432 
 243 
 324 
 
 £ 
 
 100 
 140 
 104 
 110 
 101 
 104 
 
 6. 
 fl. 
 
 6 
 2 
 
 2 
 2 
 
 
 7. 
 
 
 
 8. 
 
 
 
 9. 
 
 
 
 185 
 
 4 2 
 
 5 
 
 197 
 
 4 
 
 6 
 
 567 
 
 8 
 
 2 
 
 3 
 
 67 
 
 5 
 
 9 
 
 179 
 
 3 5 
 
 7 
 
 498 
 
 9 
 
 3 
 
 5 
 
 
 10. 
 
 
 
 11. 
 
 
 
 12. 
 
 
 
 759 
 
 6 3 
 
 2 
 
 842 
 
 1 
 
 6 
 
 975 
 
 
 
 2 
 
 
 
 699 
 
 7 6 
 
 5 
 
 483 
 
 2 
 
 6 
 
 586 
 
 6 
 
 3 
 
 5 
 
 MULTIPLICATION AND DIVISION. 
 Ex. 1. £75, 5fl. 5m. X 42. Ans.£3171-210 = £3171,2fl. Ic. 
 Ex. 2. £185, 2c. 5m. — 25. Ans. £7*401 = £7, 4fl. Im. 
 
 Ex. 1. £75-505 
 
 42 
 
 151010 
 302020 
 Product, £3171-210 
 
 Ex.2, 
 
 25 J 
 
 f 5| £185-025 
 (51 37-005 
 Quotient, £7-401 
 
 Sol. Multiply or divide the amount, expressed decimally, by 
 the multiplier or divisor, and point off three figures from tiia 
 right of the result. 
 
 5. £145,5fl.2c.5m. X26,31 
 
 6. £415, 2c. 4m. X 79, 85 
 
 7. £154, 4fl. 8m. X 101,163 
 
 8. £514, 3fl. 8c. 9m. X 695, 2045 
 
 13. £359, 4fl. 5c. 5m. -H 29, 37 
 
 14. 641 2 3 2 -^61,73 
 
 15. 783 1 I 
 
 1. £75, 3fi. 5c. X 25, 45 
 
 2. £63, 7fl. 6c. 5m. X 16,63 
 
 3. £97, 6c. 8m. X 77, 96 
 
 4. £84, 7fl. 5m. X 63, 81 
 
 9. £184, 2fl. 7c. 5m. -f- 25, 45 
 
 10. 127 5 7 5 -^63,8l 
 
 11. 129 7 4 5 -^35,55 
 
 12. 126 5 8 8 -T-33,77 
 
 8 -r- 122, 131 
 16. 3083 8 8 5 -i- 365, 355 
 
 17. How much will a man's wages amount to in a year, 
 at £1, Ifl. 2c. 5m. per week ? 
 
 18. Divide £68, 3fl. 5c. 5m. among 3 men, 5 women, and 
 7 children, giving each woman twice the share of a child, 
 and each man thrice the share of a woman. 
 
 19. A man gains Ifl. 2c. 5m. in a day, and spends Ifl. per 
 day ; how many days must he work to pay a debt of £9*375 ? 
 
 THE END. 
 
 EDINBUEGH : PRINTED BY OLIVER AND BOTD. 
 
ARITHMETIC 
 
 f 
 
 FOR 
 
 ADVANCED CLASSES; 
 
 BEING A CONTINUATION OF 
 
 TROTTER'S LESSONS IN ARITHMETIC 
 FOR JUNIOR CLASSES : 
 
 CONTAINING 
 
 VULGAR AND DECIMAL FRACTIONS; SIMPLE AND COMPOUND 
 PROPORTION, WITH THEIR APPLICATION ; SIMPLE AND COM- 
 POUND INTEREST, INVOLUTION AND EVOLUTION, ETC. 
 
 By ALEXANDER TROTTER, 
 
 TEACHER OP MATHEMATICS, ETC., IN EDINBURGH, 
 
 Author of " A Key to Trotter's Complete System of Arithmetic," etc 
 
 feta mtUn. 
 
 EDINBURGH : 
 OLIVER AND BOYD, TWEEDDALE COURT., 
 
 LONDON : SIMPKIN, MARSHALL, AND CO. 
 1872. 
 
SCHOOL-BOOKS BY JAMES TROTTER, 
 
 LATE OF THE SCOTTISH NAVAL AXD MILITARY ACADEMY. 
 
 LESSONS in ARITHMETIC for Junior Classes. 6d. 
 A Complete System of ARITHMETIC, Theoretical and Practical. 3s. 
 Teotteb's Edition of HUTTON'S BOOK-KEEPING. 2s. 
 A Complete System of MENSURATION, by Ingram & Trotter. 2s. 
 Ingram and Trotter's EUCLID ; containing the Elements of Plane 
 Geometry and Trigonometry. Is. 6d. 
 
 Ingram's Concise System of MATHEMATICS. Revised by Mr 
 Trotter. 48. 6d. 
 
 Trotter's LOGARITHMS and PRACTICAL MATHEMATICS. Ss, 
 
 Ingram and Trotter's Elements of ALGEBRA. 38. 
 
 EmNBURGH : OLIVER AND BOTD, 
 TWERDDALK COURT. 
 
ADVERTISEMENT. 
 
 This work is designed for those Pupils who have thoroughly 
 mastered the Simple and Compound Kules ; and it has been 
 tlie Author's aim to adopt as simple language as possible in 
 the explanatory remarks. 
 
 Each subject is accompanied by an example fully worked 
 out and minutely explained, and has been treated as amply 
 and carefully as its importance demanded. 
 
 The Exercises, which are all new, are numerous and 
 practical ; and Answers to them are published in a separate 
 form. 
 
CONTENTS. 
 
 Page 
 
 Tables of Money, Weights, and Measures, 3 
 
 Greatest Common Measure, 5 
 
 Least Common Multiple, ib. 
 
 Vulgar Fractions, 6 
 
 Miscellaneous Exercises in Vulgar Fractions, 11 
 
 Ratios and Proportion, 13 
 
 Simple Proportion, ' 14 
 
 Compound Proportion, 21 
 
 Practice, 25 
 
 Miscellaneous Exercises, 28 
 
 Decimal Fractions, 30 
 
 Interminate Decimals, c{4 
 
 Miscellaneous Exercises on Decimals, 38 
 
 Commercial Allowances, 39 
 
 Commission and Brokerage, 40 
 
 Simple Interest, 42 
 
 Discount, 47 
 
 Insurance, 49 
 
 Stocks, 61 
 
 Equation of Payments, 53 
 
 Distributive Proportion, . 64 
 
 Simple Fellowship, ib. 
 
 Compound Fellowship, 66 
 
 Profit and Loss, 57 
 
 Exchange, 60 
 
 Duodecimals, 62 
 
 Involution, .63 
 
 Evolution, 64 
 
 Extraction of the Square Root, . •. . ib. 
 
 Cube Root, . . V 66 
 
 Compound Interest, ,...,.,,.. 68 
 
 Miscellaneous Questions, 70 
 
 Decimal Coinage, 73 
 
TABLES OF MONEY, WEIGHTS, AND MEASUEES. 
 
 MONEY. 
 
 qrs. 
 
 d. 
 
 
 
 4 
 
 1 
 
 8. 
 
 
 48 
 
 12 
 
 1 
 
 £ 
 
 960 
 
 240 
 
 20 
 
 1 
 
 TROY WEIGHT. 
 
 Grs. 
 
 Dwt. 
 
 
 
 24 
 
 1 
 
 Oz. 
 
 1 
 
 480 
 
 20 
 
 1 1 
 
 1 Lb. 
 
 5760 
 
 240 
 
 1 12 
 
 1 1 
 
 Gold, silver, and jewels are weighed 
 by Troy Weight. 
 
 APOTHECAR 
 
 lES' 
 
 WEIG] 
 
 HT. 
 
 Gr. 
 
 Scr. 
 
 
 20 
 
 1 
 
 Dr. 
 
 
 
 60 
 
 3 
 
 1 
 
 Oz. 
 
 1 
 
 480 
 
 24 
 
 8 
 
 1 
 
 1 Lb. 
 
 5760 
 
 288 
 
 96 
 
 12 
 
 1 1 
 
 Used only for medical prescriptions. 
 
 AVOIRDUPOIS WEIGHT. 
 
 Dr. 1 
 
 Oz. 
 
 
 
 
 
 161 
 
 1 
 
 Lb. 
 
 
 2561 
 
 16 
 
 1 Qr. 
 
 
 71681 
 
 448 
 
 28 
 
 1 
 
 Cwt. 
 
 
 28672 1 
 
 1792 
 
 1121 
 
 4 
 
 1 
 
 To. 
 
 573440 1 
 
 35840 22401 
 
 80 
 
 20 
 
 1 
 
 LINEAL MEASURE. 
 
 7000 grs. = 1 lb. avoir. ; 14 lb. = 
 1 stone. 
 
 This table is used for all articles, 
 except gold, silver, and jewels. 
 
 In. 1 Ft. 
 
 
 12 1 
 
 Yd. 
 
 36 3 
 
 1 Pol. 
 
 198 1 16^ 
 
 5J1 1 Fur.I 
 
 7920 660 
 
 220 1 40 1 1 Ml. 
 
 63360 5280 
 
 1760 1 320 8 1 1 
 
 4 inches = a hand ; 6 feet, or 2 
 yds. = a fathom; 3 miles = a league. 
 
 CLOTH MEASURE. 
 
 In. 1 
 
 NL 
 
 1 
 
 
 2i 1 
 
 1 
 
 Qr. 
 
 1 
 
 9 
 
 4 
 
 1 
 
 1 Yd. 
 
 36 1 
 
 16 
 
 4 
 
 1 1 
 
 3 qrs. = 1 Flemish ell : 5 qrs. = 
 1 English ell ; 6 qrs. = 1 French ell; 
 4 qrs. 1 inch, or 37 in. = 1 Scotch ell. 
 
 SQUARE OR LAND MEASURE. 
 
 Sq. in. 
 
 Sq. ft. 
 
 
 
 
 144 
 
 1 Sq.yd.l 
 
 
 1296 
 
 9 
 
 1 1 
 
 Per.| 
 
 
 39204 
 
 272i 
 
 30i| 
 
 1 Ro 
 
 1 
 
 1568160 1 10890 | 
 
 1210 1 
 
 40 1 
 
 jAc. 
 
 6272640 
 
 143560 1 
 
 4840 1 160 1 4 
 
 M 
 
 36 sq. yds. = a rood of building, and 
 100 square feet = a square of flooring. 
 
 Land is measured by a chain 66 feet 
 in length, divided into 100 links, eacli 
 = 792 inches. 10,000 square links = 
 1 square chain, and 100,000 sq. links, 
 or 10 square chains, = 1 acre. 
 
I 
 
 I 
 
 1 I 
 
 I 
 
 4 TABLES OF MONEY, WEIGHTS, AND MEASURES. 
 
 CUBIC OR SOLID MEASURE. ANGULAR MEASURE. 
 
 1728 cubic inches = 1 cubic foot, 
 and 27 cubic feet = 1 cubic yard ; 40 
 cubic feet of rough, or 50 cubic feet of 
 hewn timber, = a load ; 42 cubic feet 
 = a ton of shipping ; 5 cubic feet = 
 H barrel bulk. 
 
 MEASURE OF CAPACITY. 
 
 Pts. Qt. 1 
 
 - 
 
 
 2 
 
 1 Gal. 
 
 
 ^ 8 
 
 4 1 
 
 Pk. 
 
 
 16 
 
 8 2 
 
 1 
 
 Ba. 1 
 
 64 
 
 32 8 
 
 4 
 
 1 1 Qr. 
 
 512 1 256 1 64 
 
 32 
 
 8 1 1 
 
 3600J 60 |_ l_|_Circ^ 
 1296000 I 21600 j 360 | 1 
 
 
 TIME. 
 
 
 Min. 
 
 Ho. 1 
 
 
 60 
 
 1 1 Da. 
 
 
 1440 
 
 24 1 1 
 
 Co. Ye. 1 
 
 525600 
 
 8760 1 365 
 
 1 1 
 
 60 sees. = 1 min. ; 7 da. = 1 wk. ; 4 
 wks. = 1 CO. mo. ; 52 wks. and 1 da. 
 = 1 CO. ye.; 365J da. = 1 Julian ye.; 
 366 da. = 1 leap ye. ; 365 da. 5 ho. 48 m. 
 50 sec. = 1 solar or tropical year. 
 
 FLOUR & BREAD WEIGHT. 
 A peck-loaf = 17 lb. 6 oz. avoird. 
 A half-peck do. = 8 11 — 
 
 A quarter-loaf =4 5^ — 
 
 A peck of flour is 14-44 lb., or 14J lb. 
 nearly, and a bushel 57| lb. very 
 nearly. Five bushels =: a sack, which 
 ought to weigh 288-8 lb. avoirdupois. 
 
 HAY AND STRAW WEIGHT. 
 36 lb. avoir. = 1 truss of straw 
 56 lb. = 1 truss of old hay 
 
 60 lb. = 1 truss of new hay 
 
 36 trusses = 1 load 
 
 Hay sold between the beginning of 
 June and the end of August, of that 
 year's growth, is reckoned new. 
 
 QUARTERLY TERMS. 
 
 In England. 
 Lady-day, . March 25. 
 
 Midsummer, . June 24. 
 Michaelmas, . September 29. 
 Christmas, . December 25. 
 
 In Scotland. 
 Candlemas, . February 2. 
 Whitsunday, . May 15. 
 Lammas, . August 1. 
 
 Martinmas, . November 11, 
 
 MISCELLANEOUS TABLE. 
 
 24 sheets 
 20 quires 
 10 reams 
 12 articles 
 20 articles 
 12 dozen 
 12 gross 
 120 articles 
 500 bricks 
 1000 tiles 
 
 : 1 quire of paper 
 
 : 1 ream 
 
 : 1 bale 
 
 : 1 dozen 
 
 : 1 score 
 
 ; 1 gross 
 
 : 1 great gross 
 
 1 great hundred 
 
 1 load 
 
 1 load 
 
 500 herrings : 
 500 red do. : 
 1000 sprats 
 
 60 herrings ; 
 100 lb. avoir. : 
 
 56 lb. 
 
 64 1b. 
 256 lb. 
 112 lb. 
 19J cwt. 
 
 : 1 barrel 
 
 : 1 cade 
 
 : 1 cade 
 
 :lkeg 
 
 : 1 barrel gunpowder 
 
 : 1 firkin of butter 
 
 : 1 firkin of soap 
 
 = 1 barrel of soap 
 
 = 1 barrel of raisins 
 
 = 1 fodder of lead 
 
AKITHMETIC 
 
 THE GREATEST COMMON MEASURE. 
 
 The greatest common measure or divisor of two or more 
 numbers is the greatest number which divides them 
 without any remainder. 
 
 Ex. Find the G. C. M. of 201 and 469. Ans. 67. 
 
 Solution. Divide the greater number 201) 469 ( 2 
 (469) by the less (201), and the last divi- 402 
 
 sor (201) by the remainder (67) continu- ~67) 201 ( 3 
 
 ally imtil there is no remainder; the last 201 
 
 divisor (67) is the greatest common meas- 
 
 ure of the two numbers. 
 
 The G. C. M. of three numbers is obtained by finding that 
 of two of them, and afterwards that of the result and the 
 third number. 
 
 Find the G. C. M. of, 
 
 1. 126 & 777 
 
 2. 584, 803 
 
 3. 2449, 2573 
 
 5727 & 7802 
 5824, 13376 
 1557, 2249 
 
 7. 16531, 31659 
 a 3247, 4393 
 9. 42039, 23701 
 
 THE LEAST COMMON MULTIPLE. 
 
 The least common multiple of several numbers is the 
 least number which contains each of them an exact num- 
 ber of times. 
 
 Ex. Find the least common multiple of 4, 6, 10, 18, 
 and 30. 
 
 Sol. Arrange the numbers after each 
 other in one line ; divide by 2 as often 
 as any of the numbers will divide by 
 2, then by 3 in the same way, again 
 by 5, and so on by all the prime num- 
 bers ; the continued product of all the 
 
 divisors (2X2X3X3X5) is the least common multiple of 
 the numbers. 
 
 Find the L. C. M. of, 
 
 1. 7, 12, 14, 15, 24 I 6. 27, 32, 36, 72, 108, 144 
 
 2. 8, 16, 20, 24, 36 | 6. 12, 15, 32, 60, 64, 120 
 
 3. 4, 10, 14, 21, 28 I 7. 8, 11, 104, 52, 88, 143 
 
 4. 8, 16, 14, 10, 35 ' 8. 11, 26, 34, 52, 68, 187 
 
 
 
 
 Ans. 180. 
 
 2 
 
 4, 
 
 6, 
 
 10, 18, 30 
 
 2 
 
 2, 
 
 3, 
 
 5, 9, 15 
 
 3 
 
 1, 
 
 3, 
 
 5, 9, 15 
 
 3 
 
 1, 
 
 1, 
 
 5, 3, 5 
 
 5 
 
 1, 
 
 1, 
 
 5, 1, o 
 
 
 1, 
 
 1, 
 
 1, 1, 1 
 
6 
 
 VULGAR FRACTIONS. 
 A FRACTION consists of one or more parts of unity, and is 
 expressed by two numbers, the one placed above the other 
 with a line between them ; thus, ^- ^^^^^'^'^l' 
 
 ' ' 9 Denommator. 
 
 The lower number is called the denominator, and shows 
 into how many equal parts the unit is divided ; the upper 
 number is called the numerator, and shows how many of 
 those equal parts have been taken to make up the fraction 
 — the two together are called tlie terms of the fraction. 
 
 A fraction also indicates an unperformed division ; thufc 
 ~ signifies 14 divided by 9. 
 
 A proper fraction is one whose numerator is less than 
 its denominator, as |, |, -j^. 
 
 An improper fraction is one whose numerator is equal 
 to or greater than its denominator, as ^, |, Y. 
 
 A mixed number consists of a whole number (or inte- 
 ger) and a fraction, as 3y\, 39^. 
 
 A compound fraction is a fraction of a fraction, as 
 f off, i of If of J. 
 
 A complex fraction is one which has a fraction for its 
 
 numerator or denominator, or both, as 3, =1 =• 
 
 ^ r 9 4^ 
 
 An integer has one for its denominator, as 12 = K*. 
 
 A fraction is multiplied by multiplying its numerator or 
 by dividing its denominator, and is divided by dividing its 
 numerator or multiplying its denominator. 
 
 The value of a fraction is not altered by multiplying or 
 dividing its terms by the same number. 
 
 REDUCTION OF VULGAR FRACTIONS. 
 
 Case I. To reduce a fraction to its lowest terms. 
 
 Ex. Reduce |^| to its lowest terms. Ans. -Jf. 
 
 Sol. 1. Divide the terms of the fraction I 144^ __ 48-^4 _ 12 
 (144 and ]56) by those numbers which I 156-^3 62^4 13 
 measure them exactly (3 and 4), until no number can bo 
 found that does so, the fraction is then reduced to its lowest 
 terms (||). 
 
 Sol. 2. Find the G. C. M. (12) of the terms of the frac- 
 tion, and divide them by it for the lowest terms {\ |) of the 
 „ , 111 • 12 12 
 fraction. ^^ '. .^ = 75 as before. 
 
VULGAR FRACTIONS. 
 
 Reduce to their lowest terms, 
 
 Case II. To reduce a mixed number to an improper 
 fraction. 
 
 Ex. Reduce 5y\ to an improper fraction. Ans. -f j. 
 
 Sol. Multiply the integer (5) by I 5 e =5X11+6 __.55-H_ 61 
 the denominator (1 1), and to the I ' ' n n u 
 
 product (55) add the numerator (6), then under the sum (61) 
 place the denominator (11) for the fraction (f {). 
 
 Reduce to improper fractions, 
 4f; 6f ; 9^; 12^?; 15^^; 17^^; 25^^; 33ii; 45^V; 
 57A; 113/^; 237^VV; 69^^^; 147 VA; 178^Vt; 273V^Vt. 
 
 Case III. To reduce an improper fraction to a whole 
 »r mixed number. 
 
 Ex. Reduce 4V *o ^ mixed number. Ans. 13y\. 
 
 Sol. Divide the numerator (157) I ,5, .^„ . .« .« , 
 
 bythedenominator (12),andtothe I ^5 — 10/ — 1^ — 10^2 
 quotient (13) annex the remainder (1) with the denomina- 
 tor below it (j'5) for the fraction (13 j',). 
 
 Reduce to whole or mixed numbers. 
 
 Case IV. To reduce a compound fraction to a 
 simple one. 
 Ex. Reduce J of 1 J of $ to a simple fraction. Ans. |. 
 
 Sol. 1. Multiply all the I , ^f 1^ of * — «of « of ^— «- —^ 
 numerators together and I ^ ^^ ^^^^ 5 — 4 ot gOi g — ^^g—^ 
 all the denominators together, and reduce the resulting frac- 
 tion (yVs) to its lowest terms (|). 
 
 Sol. 2. Strike out all those factors which j 5 4 5 
 are common to the numerators and deno- J ^^ ^ ^^ o ^^ 9 
 minators, and proceed with the numbers I ^ ^ " 
 that are left, as in Sol. 1, for the fraction in its lowest terms. 
 
 Note. Mixed numbers must be reduced to improper fractiona 
 before multiplying. 
 
 a2 
 
8 VULGAR FRACTIONS. 
 
 Reduce to simple fractions, 
 5 of 4 of A; T\of|f ofj; f of I of 15; A of 3^^ of 
 lof^V; Aof7f ofl3i; ^Vofl2iof3i; vVof5|ofl3i; 
 ^\ of 12^ of A ; if of 6| of 3/^ ; 4 of 8 J of 5. 
 
 Case V. To reduce fractions having different deno- 
 minators to others of equal value having the least com- 
 mon denominator. 
 
 Ex. Reduce f of ^, f, i, 1^ to their least common 
 denominator. 
 
 Sol I ^of« - - 1«-^ 3 4 ,,_1><126,3X63 4X28 12X36 
 ■o J 1^^^-" 4 10' -^7—5^4^ 5' 7 —2X126' 4X63' 9X28 7X36 
 
 Keduce the compound to simple 
 and the mixed numbers to impro- 
 per fractions ; find the L. C. M. 
 (252) of the denominators for the required one, and divide it 
 by each of the denominators ; then multiply the quotients 
 ^126, 63, 28, and 36) by the respective numerators (1, 3, 4, 12) 
 for the required numerators. 
 
 The fractions must all be in their lowest terms before pro- 
 ceeding as directed. 
 
 Reduce to their least common denominator, 
 
 *T5 TT ^^ 2TJ "^T) TIT 
 
 01 7f5? T2? TT> S 01 -ff-j 
 
 8 4 17 19 111 
 
 aT> T3'? 77? 7F' T^"S" 
 
 13 16 6 7 '7 
 
 •j-g-j ^U) -s^ty? TT? T's^i" 
 
 126 189 112 432 
 252' 252' 252' 252 
 
 *■' Si ?' -g^' T3' TTT 
 
 94 2rwf3 11 13 
 
 ^* TT' TT 01 T¥? 2T? 7 ^^ ^B" 
 4 13 17/^f6 3 19 nf 69 17 
 
 ! 10. 
 
 Case VI. To reauce tractions irom one denomination 
 to another without altering their value. 
 
 Ex. 1. Reduce £f to the fraction of a penny, i. e. from 
 a higher to a lower name. Ans. ^-^d. 
 
 Sol. Multiply the numera- I ^5_ 5x240 ^ =— d =— d 
 forby the number of the lower I 9 9 * 9 ' 3 * 
 
 name contained in the higher (240), and reduce the fraction 
 to its lowest terms. 
 
 Ex. 2. Reduce ^ lb. to the fraction of a cwt., i, e. from 
 a lower to a higher name. Ans. -^^-^ cwt. 
 
 Sol. Multiply the denomi- I iii f _^j. _Lpwf 
 
 nator by the number of the I 9 ^l^- — 9xii2^'^^-— 252^^^' 
 lower name contained in the higher (112.) 
 
VULGAR FRACTIONS. 9 
 
 Ex. 3. Reduce £ J to the fraction of a guinea. Ans. f gu. 
 
 ., -3 3X20 3X20 5 
 
 feOL. £4 = 5 S. = ^^ gu. = ^ gu. 
 
 1. Red. I qr., fd., y\s., |cr., & 14s. 7|d. to fractions of a pound 
 
 2. >f £/y, |d., ^|s., fgu., &/i of3s.3d. // n a farthing 
 
 3. ff I lb., /y to., j\ oz., y-V (l^M & 1 cwt. 21 lb. »/ 3 cwt. 
 
 4. n ? ml., I fu., j\ yd., I ft., & 4 ft. 7 ^ in. >- >^ sl pole 
 
 5. ff £|, for., 13s. 4d., ^of 7s,6d.,& fofSh.cr. " aguinea 
 
 6. If y*g Co, ye., { I mi., f sec, & 5 h. 48 m. 50 s. >• a day 
 
 7. ». fE.E.,i?FrE.,|Fl.E.,fSc.E.,&3(ir.3nl.'/ a yard 
 
 Case VIL To find the value of a fraction in units of 
 lower names. 
 
 Ex. 1. Findthevalueof f ml. Ans. 4fu.17p.4yd.10in. 
 
 Here, 5 ml. fu. po. &c. -^ 9 = 4 fu. 17 po. 4 yd. 10 in. 
 
 Sol. Divide the numerator, as so many of the given 
 name, by the denomuiator, as in Compound Division. 
 
 Ex. 2. Find the value of f of 7s. 6d, Ans. 5s. 
 
 Sol. 7s. 6d. X 2 = 15s. and 15s. -h 3 = 5s. 
 
 Find the values of, 
 1- ^tV fs., |d., A cr., ^%gii., and | of 16s. 8d. 
 
 2. ^^ cwt., if qr., f lb., I ml., i^ yd., f of 2 ml. 50 yds. 
 
 3. *E.E., .{-^Fl.E., fac, fro., Js.per., -}f of 4ac. 3ro. 
 
 4. Txto.jAac, T-«y0f3qr. 3b., |ml., /-j- lb.tr., ^-^of 18s.9id. 
 
 5. » of 5s.6id., I of t\ of 3f gu., if co. ye., -,\ Jul. ye. 
 
 6. Joff ofS^cr., jf of|iofl8jbu., fofaS.ye,, f of2i|of4j-'' 
 
 ADDITION OF VULGAR FRACTIONS. 
 
 Ex.1. 5 + |of4|+A=| + | + ,^ = ^iy^±^ 
 
 Sol. Reduce the fractions to their least common deno- 
 minator by Case V., then add the numerators, and below the 
 sum (509) place the denominator (315). 
 
 Ex. 2. £| + /;^s. + *d. = 7s. 6d. + 2id. + Jd. J 
 
 = 7s.8fd.|. 
 
 Sol. Find the values of the fractions by Case VII., and 
 add as in Compound Addition. 
 
10 
 
 3.3i 
 
 VULGAR FRACTIONS. 
 
 9 T^ T^ 
 _L 6 I T 
 
 T6 T^ T2 
 
 5. 4i + 5 
 
 6.7^ 
 
 "6 
 
 13. 
 
 7 _i_ 6 
 
 T-^ nr -^^ 
 8-3f + 74 + 6f + 9f 
 
 10. 6^of/^+l|+^3^ofl 
 
 11. l«ofi|+fof/^+lU 
 
 12. 2^of4| + ^\of|+|of| 
 
 13. £f + |s. + |d. 
 
 15. 
 16. 
 17. 
 
 18. 
 
 ^ cwt. + f qr. + 41 lb. 
 ^\ton+^\cwt.+ T%lb. 
 T^oac+TT^o. + Sfper. 
 
 19. £f + * gu. + f cr. + 1 of 8s. lOid. 
 
 20. ^3^ qr. + f bu. + -j^ pk. + ^^ of 9 qr. 4 bu. 
 21- tV ye. + ^\ da. + ^V ho. + ^^V of 85 da. 1 ho. 
 
 SUBTRACTION OF VULGAR FRACTIONS. 
 
 Ex. 1. I of 2 - - = |-i| = ^«A = ^7^ 
 
 Sol. Prepare the fractions as in Addition, and subtract the 
 numerators. 
 
 ■t 3 1 
 
 ^' T TT 
 
 3. 14f— 6i 
 
 6. 6- 
 
 6.15- 
 
 T 
 
 -7A 
 
 8.42 — 2441 
 
 13. 8f oflf-^AoflyV 
 
 14. 4-,VofH — 2iof I 
 
 9. 10^-2^ 
 
 10. f of4^— lofJI 
 
 11. ^«^ofH-T\of|| 
 
 12. 7iof4f-6iofA 
 15. 134of H — ^ofl^ 
 
 55 
 
 Sol. Find the values of the fractions by Case VII., and 
 subtract them as in Compound Subtraction. 
 
 17. 
 18. 
 19. 
 20. 
 
 -4qr. 
 
 Tfgu- 
 
 TuCWt, 
 
 ^\ lb. — I oz. tr. 
 
 21. A ml. — 17^\ po. 
 ^E. E. 
 
 i§Fr.E.-^Vyd. 
 .j^ ac. — t of 2 ro. 
 
 25. TVofigye. — 4of^iye. 
 
 MULTIPLICATION OF VULGAR FRACTIONS. 
 
 Ex. T\XilfX4i = H?^g = |; orvVXi|fX4^ 
 = |X|Xi = f. 
 
 Sol. 1. Multiply all the numerators (4 X 165x41) to- 
 gether for the numerator (27060), and all the denominators 
 
VULGAR FRACTIONS. 
 
 11 
 
 (11 X 164 X 25) together for the denominator (45100) ; then 
 reduce the fraction (||i|§) to its lowest terms (|). 
 
 Sol. 2. Strike out all the factors that are common to the 
 numerators and denominators, and proceed with those num- 
 bers that are left as in Sol. 1. 
 
 7. 54 X I of 6| 
 
 8. 98 X I of ^\ 
 
 9-TVof^\X T\of6| 
 10. 8^of 14f X 7§of6vV 
 ii-(12i + 6|)X(4i-2f) 
 12. (21 3_14^V)X (6^3^+71) 
 
 } ll^d., Is. 9|d., & 2s. 6|d. p. yd. 
 14. // 174ilb.&212^Vlb.@10id.,ls.7TVd.,&3s.4id.p.lb. 
 
 1. 
 
 f 
 
 X 
 
 f 
 
 X 
 
 1 
 
 
 2, 
 
 t\ 
 
 X 
 
 1 
 
 X 
 
 f 
 
 
 3. 
 
 4- 
 
 X 
 
 6 
 
 "8 
 
 X 
 
 7 
 
 1X5 
 
 
 4. 
 
 H 
 
 X 
 
 A 
 
 X 
 
 4 
 
 
 5. 
 
 27 
 
 X 
 
 2 
 
 of 
 
 6 
 
 
 6. 
 
 37 X 
 
 tS 
 
 of 
 
 3 3 
 T6 
 
 
 L3. 
 
 Val 
 
 H 
 
 yd 
 
 .&16f 
 
 yd 
 
 DIVISION OF VULGAK FRACTIONS. 
 
 T?Y -♦ nf 5 -1- 1 3 1 O _L. 1 3 1 O V 1 4 2 O 
 
 shx. T or ^ -r- x:f — ¥t ^^ t^? — 21 X tt — -g-^- 
 SoL. Invert the divisor (if), and proceed as in Multiplication. 
 
 of 4 
 
 T6 . 
 
 25-^ 
 37-^ 
 
 off 
 of^l 
 
 7. 42 -^- 
 
 8.56^ Vofil 
 
 9. ■ '^ " 
 10. 
 
 nf 2 7 
 
 of if 
 
 63 
 
 s of '— 
 
 7 01 23- 
 
 2T\of|4 
 
 ii-(6f + 7i)^(7i-2|) 
 I2.(8t-4i)-f-(4j + 2|) 
 
 l6|,21f,24A,26xV,&32H 
 14. G72cwt. 3qr. 14|lb.-Mlf , 12|, 15|, 18/^, 23/,, & 27^^ 
 
 13. £375, 6s. lOJ^d. ■ 
 
 14#, 
 
 MISCELLANEOUS EXERCISES IN VULGAK FRACTIONS. 
 
 1. Find the sum, difference, product, and quotient of 
 ^\of6f andf of|f 
 
 2. A can do a piece of work in 8 days which B can 
 do in 9 days ; what part will they do together in 1 day ? 
 
 3. What number added to 4 of 5^ gives 14|? 
 
 4. What part of 3f is | of f ? 
 
 5. What number is that ^ of which is equal to 30 ? 
 
 6. A and B can do a piece of work in 8 days which 
 A alone can do in 12 days ; what part of it can each do 
 alone in one day ? 
 
12 VULGAR FRACTIONS. 
 
 7. A gentleman having ^ of a ship, worth £3115, pur- 
 chases another person's share which is ^ of f of it ; what 
 part has he now, and what is its value ? 
 
 8. Wliat number divided by ^\ of 7^ gives 240 ? 
 
 9. How many chests of tea, each containing 124f lbs., 
 can be filled from 73 cwt. 2 qrs. 1^ lb. ? 
 
 10. What number is that j*-,- of which is equal to 25 ? 
 
 11. What part of 5 guineas is f of £3 ? 
 
 12. A farmer went to market with £2| ; he received 
 there £73^\, £89^\, and £49/^: with what sum did he 
 return ? 
 
 13. What number multiplied by J of 7| gives | of 15f ? 
 
 14. Divide £4125 among 4 men, 6 women, and 12 chil- 
 dren, giving each woman | of a man's share, and each 
 child -f of a woman's share. 
 
 15. Two persons, by trading, gained a certain sum, the 
 first lodged f of the capital, and received £200 as his 
 share of the gain ; what was the whole gain, and the 
 second's share ? 
 
 16. What numl 
 taken there remains 35 ? 
 
 17. Two places are 72 miles distant from each other : 
 A starts from the one at the rate of 12f mis. an hour, 
 and at the same time B starts from the other, to meet 
 A, at the rate of 18j miles in 2 hours ; when and where 
 will they meet ? 
 
 18. A gentleman's income is j\ of || of £7560, and he 
 spends | of f of it ; how much does he lay up ? 
 
 19. A person spends ^ of his money + £2, and has 
 left :^ of it -f- £3 ; what sum had he at first ? 
 
 20. What number is that from which ^ of it being 
 taken there remains 40 ? ' 
 
 21. I of the trees in an orchard are pear trees, Jf are 
 apple trees, and there are 50 cherry trees ; what is the 
 number of trees ? 
 
 22. A man's present age is 65 years, 5 years since his 
 son's age was f of his ; what is the son's present age ? 
 
 23. A cistern can be filled by two pipes in 24 and 25 
 minutes respectively, and can be emptied by a third in 
 32 min. ; what part of it will be filled in 12 min., the 
 three pipes being all open ? 
 
VULGAR FRACTIONS. 13 
 
 24. A person has f of a ship worth £4200, and he sells 
 ^ of his share ; what part has he left, and what is its 
 value ? 
 
 25. A and B can do a piece of work in 6 days, A and 
 C the same in 8 days, and B and C in 12 days ; what 
 part could the three together perform in 5 days ? 
 
 26. A ship and its cargo are together worth £23750, 
 and the cargo is 5^ times more valuable than the ship ; 
 find the value of each. 
 
 27. Simplify (14I + 6VV — 2^V) X ^f-S^V 
 
 28. A father left ^% of his estate to one son, and the 
 remainder to another ; the difference of their fortunes 
 was £750 : what was the estate worth ? 
 
 29. Divide £2000 among A, B, and C, giving A | of 
 the whole, B | of A's share, and C the rest ; find also 
 what fraction of the whole C receives. 
 
 30. What number multiplied by } of J, and the pro- 
 duct divided by ^-^j^ of 5i, will give for the quotient -j't 
 of 64 of 4? 
 
 RATIOS AND PROPORTION. 
 
 In comparing two numbers of the same kind, their ratio 
 or relation to one another is found by dividing the first ' 
 by the second ; thus, the ratio of 4 to 2, generally writ- 
 ten 4 : 2, is 4-^2 = 2; of 3 mis. to 6 mis. is 3-^-6 = 1. 
 
 The first number is called the antecedent, and the 
 second the consequent ; the two together are called the 
 terms of the ratio. 
 
 Proportion consists in the equality of ratios; thus, 
 since 4:2 = 8:4, the numbers 4, 2, 8, and 4, consti- 
 tute a proportion : they are generally written 4 : 2 : : 8 : 4, 
 and are read as 4 is to 2 so is 8 to 4. 
 
 In every proportion the product of the 1st and 4th 
 terms (or of the extremes as they are called) is equal to 
 the product of the 2d and 3d terms (or of the means) ; 
 thus in the proportion 4 : 2 : : 8 : 4 we have 4 X 4=2 X 8. 
 Hence the first three terms of a proportion being given, 
 the 4th is found by dividing the product of the 2d and 
 3d terms by the 1st. 
 
£144 
 
 14 
 
 SIMPLE PROPORTION or the RULE of THREE. 
 
 When three terms of a proportion are given, the object 
 of this rule is to find its 4th or last term. 
 
 Of the three given numbers, two are always of the 
 same kind, and the remaining one is of the same kind as 
 that which is required. 
 
 Ex. 1. If 16 men earn £32 in a week; what sum will 
 72 men earn in the same time ? Ans. £144. 
 
 Sol. 1. Place that term which is of Men 16 : 72 : : £32 
 the same kind as the answer is to be, 
 for the third or right-hand term (£32). 
 
 2. Consider from the nature of the 
 question whether the answer is to be 
 greater or less than the term written down : if greater (as 
 in this Ex.), place the greater of the two remaining terms 
 (72) in the middle, and the other on the left (16) ; but if less, 
 place the less of the two like terms in the middle, and the 
 other upon the left. 
 
 3. When none of the terms is compound (as in this Ex.), 
 multiply the 2d and 3d terms together (72 X 32), and divide 
 the product (2304) by the 1st or left hand- term (16) for the 
 answer, in the same name as the 3d or right-hand term (£'s). 
 
 1. If 25 yds. of velvet cost £30; what should 760 yds. 
 of the same cost ? 
 
 2. If 14 cwt. of sugar cost £42 ; what should be paid 
 for 207 cwt. ? 
 
 3. A train runs at the rate of 73 mis. in 3 hours; in 
 how many hours will it run 438 mis. ? 
 
 4. A person spends £500 yearly ; how much will he 
 spend in 146 days ? 
 
 5. If 7 men do a piece of work in 36 days ; in how 
 many days will 9 men do the same ? 
 
 6. What cost 162 copies of a book, when 171 copies 
 cost £19? 
 
 Ex. 2. If 6 cwt. 3 qrs. of tea cost £170, 2s. ; what 
 should 27 cwt. 3 qrs. of the same cost ? Ans. £699, 6s. 
 
 Sol. State the question as before. Reduce the 3d term to 
 the lowest name in it (shil.), and the 1st and 2d terms to the 
 lowest name in either (qrs.) ; then multiply the 2d and 3d 
 
SIMPLE PROPORTION. 15 
 
 6 cwt. 3 qr. : 27 cwt. 3 qr. : : £170, 2s. 
 _4 _4 __20 
 
 27qrs. Ill qrs. 3402s. 
 
 3402 
 
 27 )377622 
 2,0 )1398,6 s. 
 £699, 6s. 
 
 terms togethef (111 
 X 3402), and di- 
 vide the product 
 (377622) by the 1st 
 term (27) for the 
 answer, in that 
 name to which the 
 3d term was re- 
 duced (shil.). 
 
 7. What cost 4 yds. 3 qrs. 2nls. of cloth, when 15 yds. 
 2 qrs. cost £8, 3s. 4|d. ? 
 
 8. If 13 cwt. 14 lbs. of coffee cost £131, 13s. 9d. ; how 
 much may be bought for £13, 3s. 4Jd. ? 
 
 9. If a person walks 14 mis. 2fu. 28 po. in 4 ho. 6min. 
 40 sec. ; how far will he walk in 9 ho. 3 min. 20 sec. ? 
 
 10. How many yds. of linen at 3s. 6d. a-yd. should b( 
 given for 136 yds. of muslin at 2s. 7^d. a-yd. ? 
 
 11. If 4 yds. of cloth cost 84s. 4d. ; what will 27 yds. 
 2 qrs. cost? 
 
 12. Find the value of 2 qrs. 3 pks. of wheat, when 
 36 qrs. 2 bu. 2 pks. cost £76, 5s. lid. 
 
 Ex. 3. If 14 lbs. of tobacco cost 73s. 6d. ; what cost 
 10 lbs. of the same ? Ans. £2, 12s. 6d. 
 
 Obs. When the first and ^;4 lb. : ^0 lb. : : 73s. 6d. 
 either of the other terms can i ^ - ^.^ . 
 
 be divided without remain- j P ^ ^9^a. 
 
 der by the same number, the j 126 
 
 quotients may be used in 5 
 
 place ofthe original numbers. | £2, 12s. 6d. = 630d. 
 
 13. A courier travels 176 miles in 4 days; how far 
 will he travel in 15 days? 
 
 14. How much sugar may be bought for £95, at the 
 rate of 28 lbs. for 14s. 3d. ? 
 
 15. A man's wages are £37, 2s. 6d. a -year ; what 
 should he receive for 219 days' service? 
 
 16. If the 8d. loaf weigh 4 lbs. 5i oz. ; what should the 
 shilling loaf weigh ? 
 
 17. How many pairs of stockings, at 14s. 6d. per doz, 
 pairs, may be bought for £30, 19s. 10 Jd. ? 
 
 18. Find the value of 1 cwt. of sugar, when 3 cwt. 
 14 lbs. cost £10, 18s. 9d. 
 
 b2 
 
16 SIMPLE PROPORTION. 
 
 19. What cost 5 pieces of silver, each 3 lbs. 4 cz. 
 12 dwt., at 5s. 9d. per oz. ? 
 
 20. If the quartern loaf costs lOjd. when wheat is at 
 £3, 10s. per qr. ; what should it cost when wheat is at 
 £2, 3s. 4d. per qr. ? 
 
 21. A bankrupt's effects an;iount to £3528, and he 
 compounds with his creditors for 12s. 3d. per £1 ; what 
 is the amount of his debts ? 
 
 22. If 16 men consume £10 worth of beef when the 
 price is 7-^d. per lb. ; what value of beef will they 
 consume in the same time when the price is lO^d. 
 per lb. ?* 
 
 23. Sound moves at the rate of 1142 ft. in a second, 
 and the report of a gun is heard 14| sec. after seeing the 
 flash ; how far distant is the gun ? 
 
 24. How many paces of a man, each 2i ft., are equal 
 to 150 steps of a horse, each 2f ft. ? 
 
 25. A bankrupt's debts amount to £7428, and he com- 
 pounds with his creditors for 10s. 9|d. per £1 ; find the 
 amount of his effects. 
 
 26. Find the value of 8 cheeses, each 26 J lbs., at T^d. 
 per lb. 
 
 27. At what time between 6 and 7 o'clock are the 
 hour and minute hands of a watch exactly together? 
 Sol. (11 : 12 : : 6 hours.) 
 
 28. Bought 17 yds. 2 qrs. of cloth for £16, 2s. 3id. ; 
 what should 4 yds. 3 qrs. be sold for to gain £2, 5s. 2|d. 
 on the whole ? 
 
 29. If 36 gallons of whisky, worth 17s. 6d. a-gallon, be 
 mixed with 4 gallons of water ; what should be the price 
 of a gallon of the mixture ? 
 
 30. A person pays £65, 6d. for income-tax, at the rate 
 of Is. 4d. per £1 ; what is his income? 
 
 31. Required the circumference of a circle whose di- 
 ameter is 22035 mis., the ratio of the diameter to 
 the circumference of a circle being as 113 is to 355. 
 Sol. (113 : 355 : : 22035 mis.) 
 
 32. A pound troy of standard gold is coined into £46, 
 14s. 6d. ; find the weight of a sovereign. 
 
 * When the same term is twice mentioned in a question, that 
 term must he altogether excluded. 
 
SIMPLE PROPORTION. 17 
 
 33. The ratio of standard to pure gold being 22 to 24; 
 what is the value of an ounce of pure gold ? 
 
 34. A garrison of 3300 men have provisions for 12 
 months; how long would the same provisions serve 
 4950 men ? 
 
 35. A 16 gun-battery discharges 1760 cwt. of shot in a 
 certain time ; how much will an 18 gun-battery discharge 
 in the same time ? 
 
 36. The chain of QQ ft. for measuring land is divided 
 into 100 links ; what is the length of a wall measuring 
 1760 links? 
 
 37. What is the commission on £477, 2s. 6d., at £27^ 
 per £100? 
 
 38. A pound troy of standard silver is coined into 66s. ; 
 find the weight of half-a- crown, and of a florin. 
 
 39. The ratio of standard to pure silver is 37 to 40 ; 
 what is the value of a lb. of pure silver? 
 
 40. From a garrison of 2000 men with provisions for 
 9 months, 500 are sent out ; how long will the provi- 
 sions serve the remaining men ? 
 
 41. If 250 men dig a trench in 5 da. 5 ho., working 12 
 hours a-day ; in how many days would they do tlie same, 
 working 1 1 hours a-day ? 
 
 42. If 49 men do a piece of work in 3f days ; in how 
 many days will 48 men do the same ? 
 
 43. A garrison being besieged, has 49 days' provi- 
 sions, at the rate of 15 oz. a-day for each man ; how 
 long will they be able to hold out if each receives lOJ oz. 
 a-day ? 
 
 44. Required the charge for 12125 cubic feet of gas- 
 at 5s. lOd. per 1000 cubic feet. 
 
 45. The rent of a farm of 350 ac. 3 ro. 20 per. is £1710, 
 10s. 3|d. ; what should be the rent of another of equal 
 quality, containing 525 ac. 1 ro. 20 per. ? 
 
 46. If £14, 8s. be the interest on £360 for a year ; wliat 
 sum will gain £33, 12s. in the same time and at the 
 same rate per cent. ? 
 
 47. A garrison of 2500 men, with provisions for 7 
 months at the rate of 21 oz. a-day for each, is reinforced 
 by 1000 men ; how many ounces a-day must each be 
 allowed that the provisions may last that time ? and if 
 
 c 
 
18 SIMPLE PROPORTION. 
 
 each receives the full allowance, hov/ long will the pro- 
 visions serve? 
 
 48. Find the value of 5 bars of steel, each weighing 
 4 cwt. 3 qrs. 14 lbs., at £12, 14s. 4d. for 10 cwt. 3 qrs. 
 21 lbs. 
 
 49. In what time would 6 battalions of foot, each 375 ft. 
 in length, march through a town If mile long, at the 
 rate of 75 paces of 2| ft. per minute? 
 
 50. A piece of work can be done by 45 men in 13 days ; 
 now at the end of 6 days, 10 men leave : in how many 
 days will the remaining men finish the work ? 
 
 51. What is the price of 6f Fr. ells, at £66, lis. for 
 72|Eng. ells? 
 
 52. What is the price of 7 pieces of cloth, each 16§ 
 yds., at £3, 4s. 9d. for 3|- Scotch ells? 
 
 53. A bankrupt's debts amount to £4020, and his assets 
 to £3266, 5s. ; how much will this afford his creditors 
 per £, and how much will A lose, whose claim is 
 £560, 13s. ? 
 
 54. A gentleman's income is £3867, 15s. per annum; 
 his expenses amount to £1050, and he wishes to save 
 £500 : how much may he spend between Whitsunday 
 and Martinmas ? 
 
 55. How many yards at 4s. l^d. are equal in value to 
 1231 yards at 12s. 7id. per yd. ? 
 
 56. If 4 to. 5 cwt. 14 lbs. of lead cost £50, 17s. 6d. ; what 
 should be given for 20 to. 11 cwt. 49 lbs. of the same ? 
 
 57. A cubic foot of chalk weighs 2784 oz., and a cubic 
 foot of basalt 2860 oz. ; how many cubic feet of the 
 former are equal in weight to 7830 cubic feet of the 
 latter? 
 
 58. A column of chalk weighs 20 cwt. 2 qrs. 24 lbs. ; re- 
 quired the weight of a column of basalt of the same 
 dimensions. 
 
 59. How much wheat can be bought for £101, 5s. when 
 7 qr. 4 bu. 3 pks. cost £20, 10s. 0|d. ? 
 
 60. What should be paid for 102 qrs. 3 bu. 2 pks. of 
 oats, at the rate of £5, 4s. ll^d. for 4 qrs. 2 bu. 2 pks. ? 
 
 61. How much water must be mixed with 250 gallons 
 of "whisky, at 14s. 6d. per gal. to reduce the price tc 
 12s. 6d. per gal.? 
 
SIMPLE PROPORTION. 19 
 
 62. How much water must be mixed with whisky at 
 15s. a-gal. to fill a cask of 360 gals., so that a gallon of 
 the mixture may be worth 13s. 4d. ? 
 
 63. If the rent of 4J acres be £7, 13s. ; wliat will be the 
 rent of 5^ acres ? 
 
 64. An express train runs 58 mis. in 1 h. 30 m. with 
 two stoppages of 3 minutes each ; in what time will it 
 run 435 miles with 5 stoppages of 4 minutes each ? 
 
 65. What quantity of linen at 2s. 6d. a-yard should be 
 exchanged for 5 dozen pairs of shoes at lis. a-pair? 
 
 66. A and B barter, A has oats at 24s. per qr., which 
 he rates at 27s. 6d. to B for sugar at 75s. per cwt. ; at 
 Avhat should B rate his sugar to be even with A, and 
 how many cwts. should he give for 175 qrs. of oats? 
 
 67. If 78 qrs. 5 bu. of barley be given for 53 qrs. 1 bu. 
 of wheat at 64s. 9d. per qr. ; what is the barley valued 
 at per qr. ? 
 
 68. A grocer mixes 56 lbs. of tea at 4s. per lb. with 
 44 lbs. at 5s. ; how should he sell 11 lbs. of the mixture 
 to gain £5, Is. lOd. on the whole? 
 
 69. At what time after 2 o'clock are the hour and min- 
 ute hands of a watch exactly together ? 
 
 70. Find the diameter of the earth, whose circumfer- 
 ence is 24850 miles nearly. 
 
 71. B gives to C 12 gallons of brandy at 37s. 6d. per 
 gal. and £14, 12s. 6d., and receives from him tea at 4s. 
 6d. per lb. and 7 cwt. 2 qrs. of sugar at £3, 5s. per cwt. ; 
 what quantity of tea did B receive ? 
 
 72. Find the weight of 600000 sovereigns, 1869 sove- 
 reigns weighing 40 lbs. troy. 
 
 73. Lent a friend £455 for 6 months ; how long should 
 he lend me £630 to return the favour ? 
 
 74. If f cwt. cost £5i ; what should | cwt. cost ? 
 
 75. If ^\ of a ship be worth £420 ; what should | of it 
 cost? 
 
 76. What velocity will a falling body have at the end 
 of 7i sec, if it acquires a velocity of*168|- ft. in 5i 
 sec? 
 
 77. A hare starts 140 yards before a greyhound, but 
 while the hare runs 5 yds. the dog runs 7 ; how far 
 must the do^r run to catch the hare ? 
 
20 SIMPLE PROPORTION. 
 
 78. If -/y of an estate be worth £500 ; what is the vaUie 
 of f of it? 
 
 79. If 30 horses be maintained for 5 montlis on a cer- 
 tain value of oats when the price is 22s. 6d. per qr. ; 
 how many horses may be fed for the same sum and time 
 when oats are at 25s. per qr. ? 
 
 80. A person, after paying income-tax at Is. 4d. per £, 
 has remaining £665 ; required his income. 
 
 81. How long would a cannon-ball with a velocity of 
 2000 ft. per second take in passing from the earth to 
 the moon, a distance of 237630 miles ? 
 
 82. The distance of Jupiter from the sun is 494513000 
 mis. ; what is the length of its orbit, supposing it circular ? 
 
 83. The same planet performs its revolution round the 
 sun in 4332-| days ; what is his mean motion in 365^: 
 days? 
 
 84. Jf a tower 150 ft. 4 in. high cast a shadow of 181 ft. 
 1 in. : what length of a shadow wiU a pole 38 ft. 6 m. 
 high cast at the same time ? 
 
 85. How many revolutions will a coach-wheel 3^ ft. ii? 
 diameter make in 4 miles ? 
 
 86. The weight of an 18-pounder iron gun being 41 
 cwt. 2 qrs., and the weight of a 12-pounder 33 cwt. 2 qrs. ; 
 how many 12-pounders will be equal in weight to 469 
 18-pounders? 
 
 87. What should be paid for 15 cwt. 1 qr. 14J lbs. of 
 lead, when 14 cwt. 3 qrs. 16 lbs. cost £17, 7s. 6d. ? 
 
 88. A person whose annual income is £650, spends 
 £15, 2s. 6d. a-week for the first 20 weeks ; what should 
 his daily expenses be during the rest of the year, to save 
 
 89. Bought 7 pieces of cloth, each containing 61 yds., 
 for £424, 6s. 7^d. ; what should 241 yds. of the same be 
 sold for to gain £5, 6s. 9d. on the whole? 
 
 90. A can do a piece of work in 9 days which B can 
 do in 12 days ; in how many days would they be able 
 to finish the work, working together? 
 
 91. A cistern has two spouts, by one of which it can 
 be filled in 3 months, and tfy the other it can be emp- 
 tied in 8 months ; in what tune will it be full, supposing 
 it empty and both spouts running? 
 
SIMPLE PROPORTION. 21 
 
 92. A can do a piece of work in 6 days, which B can 
 do in 8 days ; after A has been working 2 days, B comes 
 to help him ; in what time will they finish the work to- 
 gether ? 
 
 93. A starts from a certain place at the rate of 5 miles 
 an hour ; after 2 hours, B starts from the same place at 
 the rate of 6^ miles an hour ; when will B overtake A, 
 and how far will each have travelled ? 
 
 94. A grocer uses a weight of 15|oz. instead of the pound 
 avoirdupois ; how much does he cheat his customers by 
 selling 365 such pounds ? 
 
 96. A cistern, containing 399 gallons, is emptied in a 
 certain time by a pipe which discharges 4| gals, per 
 minute, and another is emptied in the same time by a 
 pipe which discharges 7-§- gals, per minute ; how many 
 gallons does the last cistern contain? 
 
 96. A wine merchant uses a measure containing 1224 
 cub. in. instead of 131^ c. in. ; of how many gallons, each 
 277 J c. in., does he defraud the public by selling 739 J 
 such measures ? 
 
 COMPOUND PROPORTION. 
 When a question requires for its solution two or more 
 statements of Simple Proportion, the method of finding 
 the answer by one operation is called Compound Pro- 
 portion. 
 
 Ex. •!. If 30 men eat £9 worth of bread in 12 days, 
 when the price of the loaf is 8d. ; what value will 64 men 
 eat in 10 days, when the loaf is at 6d. ? Ans. £12. 
 
 Sol. 1. Place upon the right 
 hand that term which is of the 
 same kind as the answer is to be 
 (£9). 
 
 2. Take from the question two 
 terms that are like one another 
 (30 men and 64 men) and state 
 til em, without any reference to the 
 
 Men, 30 : 64 : : £9 
 Days, 12 : 10 
 Price, 8 : 6 
 
 2880 : 3840 : : £9 
 9 
 
 2880 )34560 
 
 £12 worth 
 other similar terms, as in Simple Proportion ; in the same 
 way, take other two similar terms (12 da. and 10 da.), and 
 state them as in Simple Proportion below the last pair, and 
 proceed thus till all the terms are stated. 
 
22 COMPOUND PROPORTION. 
 
 3. Multiply all the left-hand terms together, and also the 
 middle terms, then work out the resulting Proportion 
 (2880 : 3840 : : £9) as in Simple Proportion for the an- 
 swer (£12). 
 
 When some of the terms are Compound, they must be re- 
 duced as in Simple Proportion ; the work may be greatly 
 abridged by cancelling. 
 
 Ex. 2. If 14 persons spend £5, 5s. in 10 days ; how 
 long will £42 serve 16 persons? Ans. 70 da. 
 
 Sol. State the 
 question as in Ex. 
 1, and reduce £5, 
 OS. and £42 to sh. 
 Arrange the mid- 
 dle and the right- 
 hand terms, with 
 the sign of Multi- 
 plication between 
 
 £ 5, OS. £42 
 
 105s. : 840s. : : 10 da. 
 
 Persons 16 : 14 
 
 8 7 
 $0XUX^O 1X7X10 
 
 ^0X10 
 
 70 da. 
 
 them above a line, and the left-hand terms below it ; then 
 cancel the upper and under numbers as much as possible, as 
 in fractions, and divide the product of the remaining numbers 
 above the line by the product of those below for the answer. 
 
 1. If 45 men cut down 120 acres of grass in 7 days ; 
 how many acres will 84 men cut down in 10 days ? 
 
 2. If 300 soldiers consume 4 barrels of flour in 10 
 days; how many soldiers will 12 barrels serve for 15 
 days? 
 
 3. If 48 yds. of cloth, 4 quarters wide, cost £24, 12s. ; 
 what should be paid for 36 yds. of the same, 6 quarters 
 wide ? 
 
 4. What is the interest on £383, 5s. for 325 days at 4^ 
 per cent, per annum ? 
 
 5. If 30 men consume £7 worth of bread in 10 days, 
 when the price of the loaf is 8d. ; what value of bread 
 will 40 men consume in 15 days, when the loaf is at 7id. ? 
 
 6. If 30 men can do a piece of work in 12 days of 10 
 hours each ; in how many days of 8 hours each will 45 
 men do a piece of work 6 times as large ? 
 
 7. If 63 cwt. be carried 42 mis. for £3, 10s., when tho 
 rate of carriage is ^d. per mile per cwt. ; what distance 
 should 142 cwt. be carried for £8, 17s. 6d., when the 
 rate is Id. per mile per cwt. ? 
 
COMPOUND PROPORTION. 23 
 
 8. At 2^ per cent, per annum £375 was lent, and it 
 now amounts to £431, 5s. ; how long has it been lent ? 
 
 9. The pound weight of standard gold is coined into £46, 
 14s. 6d. (22 carats in 24 being pure gold) ; what is the 
 value of 3 ounces of pure gold ? 
 
 10. If 3 men or 5 boys do a piece of work in 8 days of 
 10 hours each ; in how many days of 9 hours each 
 would 4 men and 10 boys do a piece of work 3 times as 
 large ? 
 
 11. If 40 masons build a wall 56 yds. long in 10 days 
 of lOj hours each ; how many hours a-day must 60 ma- 
 sons work to build a wall 120 yds. long in 20 days? 
 
 12. If 120 men can dig a trench 150 yds. long, 4 yds. 
 wide, and 2 deep, in 7^ days of 10 hours each ; what 
 length of a trench, 5 yds. wide and 3 deep, will 200 men 
 dig in 15 days of 12 hours each? 
 
 13. If 14 horses plough 112 acres in 40 days ; how 
 many horses would plough 64 acres in 16 days ? 
 
 14. If 30 men earn £80, 14s. in 15 days ; how many 
 men will earn £107, 12s. in 12 days ? 
 
 15. A traveller completes a journey of 240 miles in 3 
 days of 12^ hours ; in how many days will he complete 
 a journey of 360 miles, travelling 9 hours a-day? 
 
 16. If the 8d. loaf weighs 3 lbs. 4 oz. when wheat is at 
 64s. per qr. ; what should the shilling loaf weigh when 
 wheat is at 72s. per qr. ? 
 
 17. Required the avoirdupois weight of 600000000 
 sovereigns, there being 1869 sovereigns in 40 lbs. troy, 
 and 7000 grains in a pound avoirdupois. 
 
 18. A certain value of bread is sufficient to serve 3200 
 men for 44 days when the loaf is at 9d., allowing each 
 man 16 oz. a-day ; how many men will 7 times the value 
 serve for 112 days, at 20 ounces each per day, when the 
 loaf is at lid.? 
 
 19. If 135000 bricks, 8 in. long, 3^ in. broad, and 2f in. 
 thick, be required to build the walls of a magazine ; how 
 many bricks, 14 in. long, 4 in. broad^ and 3 in. thick, 
 would be sufficient for the same ? 
 
 20. If 7 compositors set up a volun^e of 12 sheets in 21 
 days of 12 hours each ; how many would be required to 
 set up 3 volumes of 10 sheets in 35 days of 9 hours each? 
 
21 COMPOUND PROPORTION. 
 
 21. 35 masons build 48 yds. of a wall which is to be 
 192 yds. long in 12 days of 12 hours each ; how many 
 additional masons will be required to finish the wall in 
 18 days of 10 hours each? 
 
 22. If 15 men build a wall, 80 ft. long, 3§ ft. thick, and 
 9 ft. high, in 27 days of 10 hours each ; in how many 
 days of 12 hours each will 25 men build a wall 100 ft. 
 long, 2 J ft. thick, and 8 ft. high? 
 
 23. A garrison of 4050 men, with provisions for 5 
 months at the rate of 32 oz. a-day for each, is reinforced 
 by 750 men, and cannot be relieved for 8 months ; how 
 many oz. a-day must each man be allowed that the pro- 
 visions may last that time ? 
 
 24. The cost of papering a room with paper 3 qrs. wide, 
 at 3f d. a-yard, is £2, 3s. 9d. ; what would be the cost if 
 the paper were 1^ yd. wide, and the price 4|d. a-yard? 
 
 25. A block of marble, 5 ft long, 4 wide, and 1 ft. 3 in. 
 thick, weighs 39 cwt. 2 qrs. 8 lbs. 13 oz. ; what is the 
 weight of another block, 8 ft. long, Ah wide, and 2 ft. 4 in. 
 thick? 
 
 26. In what time will the interest of £750, r2s. 6d. be 
 sufficient to pay a debt of £112, lis. 10^ d. at 4 per cent. 
 per annum ? 
 
 27. Find the interest of £1418, Os. 6d. for 375 days, at 
 3^ per cent, per annum. 
 
 28. If the 6d. loaf weighs 3 lb. 4^ oz. when the wheat 
 is at 56s. a-quarter ; what is the price of wheat per qr. 
 when the 8d. loaf weighs 3 lb. 13| oz. ? 
 
 29. If 18 men working 9 hours a-day, or 36 boys work- 
 ing 6 hours a-day, can do a piece of work in 8 days ; in 
 how many days would 10 men and 24 boys do a piece 
 of work 5 times as large, all working 8 hours a-day ? 
 
 30. A contractor engages to construct 3 J mis. of a road 
 in 90 days, and for this purpose he employs 120 men, 
 who work 8 hours a-day, but after 60 days, he finds they 
 have only accomplished 2 mis. of the road ; how many 
 additional men must he employ to finish the work in 
 the appointed time, the men working 9 hours a-day ? 
 
J] 
 
 25 
 
 PRACTICE -^^^sss^ 
 
 Is an expeditious method of finding the values of goods 
 by means of aliquot parts. 
 
 A less number is said to be an aliquot part of a greater 
 when the less is contained an exact number of times in the 
 greater ; thus 3 is an aliquot part of 24, which contains it 
 exactly 8 times ; so also is 2 s. 3d. of 18s., which contains it 
 exactly 8 times. 
 
 TABLE OF ALIQUOT PARTS. 
 
 lOs. = £i 
 
 lid. = i^of 6d. = is. 
 
 6s. 8d.= £i. 
 
 Id. = £^i^ = ^\s. 
 
 5s. — loflOs.— £i 
 
 |d. =iof6d. = ^Vs. 
 
 4s. = £i 
 
 7 1 , 
 
 3s. 4d.— ^ of 10s. — £i 
 
 id. = £^1^ = ^Vs- 
 
 2s.6d.= iofl0s. =£i 
 
 AVOIRDUPOIS WEIGHT. 
 
 2s. —i of 10s. — £Vo 
 
 10cwt.= i ton 
 
 ls.8d.= iof6s.8d.=£V^ 
 
 5 cwt. = J ton 
 
 Is. 4d.= £^V 
 
 4 cwt. = \ ton 
 
 Is. 3d.— J of 10s. — £Ve 
 
 2 cwt. = -^-Q ton 
 
 Is. =- £^V 
 
 2 qr. = i. cwt 
 
 6d. = is. =£^^^ 
 
 161b. = 1 cwt 
 
 4d. = |s. 
 
 14 lb. = ^ qr. = ^ cwt 
 
 3d. = is. 
 
 71b. =^qr. = TVcwt 
 
 2d. = is. 
 
 41b. = 1 qr. 
 
 This table should be extended by the pupil. 
 
 Case I. When the price is an aliquot part of £1, Is., or Id. 
 Ex. Find the price of 2744 yds. at 4d. and 3s. 4d. per yd. 
 4d. = is.) 2744s. = val. at Is. 
 2,0) 914s. 8d. val. at 4d. 
 Va.at4d.=£45, 14s.8d. 
 
 Sol. 1. Since 4d.=r^s. the 
 value at 4d. = ^ of the va. 
 at 1 s. ; now 2744 yd. at Is. 
 =2744s., hence ^ of 2744s. 
 
 = 914s. 8d., or £45, 14s. 8d. is the value at 4d. 
 
 Sol. 2. Since 3s. 
 4d. =£^, the va. at 
 3s. 4d. = I of the va. 
 
 3s. 4d. = £i)£2744va. at £1 
 
 £457, 6s.8d. va. at3s.4d. 
 
 at £1 ; now the va. at £1 is £2744, hence \ of £2744 = £457; 
 6s.8d. =va. at 3s.4d. 
 
 Find the values of, 
 1. 7459 oz. at id., fd., Id., Ijd., 2d., 3d., 4d.,&6d.per oz. 
 
 c2 
 
26 
 
 PRACTICE. 
 
 2. 1786 yds. at Is., Is. 3d., ls.4d., Is. 8d., 2s., 2s. 6d., 
 3s. 4d., and 6s. 8d. per yd. 
 
 3. 3457 lbs. at 10s., 5s., 4s., 3s. 4d., Is. 8d., Is. 4d., 6d., 
 and 4d. per lb. 
 
 Case II. When the price is not an aliquot part of 
 £1, Is., or Id. 
 
 Ex. Find the value of 575 lbs. at 3s. 9d. per lb. 
 
 2s. 6d. =£i)£ 575 va. at £ 1 
 
 £71, 17s. 6d.va.at2s.6d. 
 ls.3d.=:riof 2s.6 d. 35, 18s. 9d . >> Is. 3d. 
 
 3s. 9d. 
 
 Sol. 3s.9d.= 
 2s.6d. + ls.3d.; 
 now the va. at 
 2s. 6d. by Case I. 
 
 is £71, 17s. 6d., £107, 16s. 3d. 
 
 and since Is. 3d. = ^ of 2s. 6d., the va. at Is. 3d. = i of the 
 va. at 2s. 6d. = ^ of £71, 17s. 6d., or £35, 18s. 9d. The sum 
 of the values at 2s. 6d. and Is. 3d. = the value at 3s. 9d. 
 
 Note. When there are £'s in the price, multiply the quantity 
 by them, and take aliquot parts for the s. and d. 
 
 Find the values of, 
 
 4. 375 at 4s. 4d., 4s. 8d., 5s.6d., 6s.3d., 7s. 4d., 8s. 4d., 
 10s. lOd., and 13s. 4d. each. 
 
 5. 692 at 12s. 4id., 13s. 9id., 14s. 4d., 15s. 7id., 
 18s. lOd., 19s. 5d., 19s. 7id., and 19s. lOd. 
 
 6. 1476 at Hd., 2id., 3f d., 4id., 6|d., 7id., 8id. & lOid. 
 
 7. 297 at £1, 14s. 8d., £1, 18s. lOd., £2, 5s. 7d., £3, 15s. 
 lUd., £5,17s.l0d., £6,16s.6d., £7,lls.9d.&£9,18s.4id. 
 
 8. 379 at £2, 2s. 2d., £3, 3s. 3d., £7, 7s. 7d., £11, lis. 
 
 Case III. When the price consists of £ and s. only. 
 
 Ex. Find the value of 493 cwt. at 39s. per cwt. 
 
 Sol. Multiply the quantity (493) by 493 
 half the number of shillings (19|) ; then 19 J 
 
 double the right-hand figure of the pro- ^^7^ /?q/.i r. 
 
 duct (3^) for shillings (7s.), and the ybid^_£Jbi, /s. 
 rest C961) are £'s. 
 
 Find the values of, 
 
 9. 1476 at 2s., 3s., 7s., 9s., lis., 13s., 17s., 19s., 29s., 
 43s., and 47s. 
 
 10. 1729 at 16s., 18s., 21s., 37s., 95s., £5, 5s., £5, lis., 
 £16,4s., and£17, lis. 
 
PRACTICE. 27 
 
 Case IV. When the quantity contains a fraction. 
 Ex. Find the value of 579| yds. at 21s. 3d. per yd. 
 Sol. 1. Is. 3d. = £j\ ) £579 value at £1 
 
 36, 3s. 9d. va. at Is. 3d. 
 I of 21s. 3d. = 15s. ll^d . 
 
 Val. of 5791 yds. = £615, 19s. 8id. 
 
 Sol. 2. 579| X 4 
 
 Is. 3d. = £j\ ) £2319 value at £1 
 
 144, 18s. 9d . va. at Is. 3d. 
 
 4 ) £ 2463, 18s. 9 d. va. of 4 X 579| 
 
 £615, 19s. 8jd. va. as before. 
 
 Find the values of, 
 
 11. 476| and 549| at 14s. 8d., 15s. 5d., 17s. 8d., & 19s. 6d. 
 
 12. 375^ and 742^ at 13s. 9d., 12s. 8d., 14s.lld., & 17s.6d. 
 
 13. 1146f&1763/Tat26s.4d.,37s.9d.,46s.7id.,&76s.4id. 
 
 14. 2986f and 4863,-V, at £4, 17s. 5d., £6, 14s. 7id., 
 £7, 2s. 2id., and £10, lis. 9d. 
 
 Case V. When the quantity is compound, and the 
 price of one of the highest name is given. 
 
 Ex. Find the price of 4 cwt. 3 qrs. 14 lbs. at £3, 16s. 
 7|d. per cwt. 
 
 2qr. = ^cwt.)£3 16 
 
 Sol. Find the va- 
 lue of the quantity 
 of the highest name 
 given, then take ali- 
 quot parts for the 
 lower names, and 
 add. Thus, 2 qr. = 
 ^ cwt., va. of 2 qr. = 
 i of £3, 16s. 7id. ; 
 1 qr. = ^ of 2 qr., va. of 1 qr. 
 
 15 6 
 
 1 18 
 
 lqr.=^of2qr. 19 
 
 141b.=iqr. 9 
 
 7^ va. of 1 cwt. 
 
 6 va. of 4 cwt. 
 3i '' 2qr. 
 Ifi'- Iqr. 
 6||" 141b. 
 
 £18 13 
 
 6JJva.of4cwt. 
 3 qr. 14 lb. 
 
 ^of£1,18s. 8|d.; and 141b. 
 ='iqr.,"va. of 14 lb. = | of 19s. Ifd.^. The sum of the 
 separate values gives the whole value. 
 
 Find the values of, 
 
 15. 3 cwt. 3 qrs. and 6 cwt. 2 qrs. 21 lbs. at £4, 5s. 4d. 
 and £4, 7s. 6d. per cwt. 
 
 16. 7 cwt. 1 qr. 16 lbs. and 21 cwt. 2 qrs. 18 lbs. at £5 
 16s. 8d. and £6, 17s. 8d. per cwt. 
 
"« PRACTICE. 
 
 17. 12 lbs. 3 oz. 15 dwt. and 27 lbs. 5 oz. 6 dwt. at 
 £3, 3s. 4d. and £5, 16s. 8d. per lb. 
 
 18. 17 yd. 3 qr. 2 nl. and 37 yd. 2 qr. 3 nl. at £1, 3s. 6d. 
 and £1, 17s. 6d. per yd. 
 
 19. 27 ac. 3 ro. 12 per. and 47 ac. 2 ro. 25 per. at £4, 
 lis. 8d. and £5, 15s. per acre. 
 
 20. 33 qr. 3 bu. 3 pk. and 67 qr. 1 bu. 2 pk. at £2, 2s. 
 4d. and £2, 7s. 4d. per qr. 
 
 21. 14 bu. 3 pk. 1 gal. and 17 bu. 2 pk. 1 gal. at £2, 4s. 
 and £2, 12s. per qr. 
 
 22. 45 ac. 3 ro. 24 per. and 67 ac. 1 ro. 14 per. at £5, 
 13s. 4d. and £6, 8s. 4d. per ac. 
 
 MISCELLANEOUS EXERCISES. 
 
 1. Find tlie price of 116 cwt. of sugar at £3, 14s. 8d. 
 and £4, lis. 9d. per cwt. 
 
 2. Kequired the value of 1147| yds. of cloth at £1, 2s. 
 7id. and£l,4s. 8id. per yd. 
 
 3. 'What should be given for 18 cwt. 3 qr. 21 lbs. 
 and 27 cwt. 2 qr. 21^ lbs. of tea, at £25, 7s. 6d. and 
 £27, 19s. 8d. per cwt. ? 
 
 4. A bankrupt's debts amount to £1250, and he com- 
 pounds with his creditors for lis. 10|d. per £1 ; find his 
 effects. 
 
 5. How much sterling money is equal to 1000 francs, 
 each 9fd. sterling? 
 
 6. Find the cost of digging a ditch, the solid content 
 of which is 6753 cubic yds., at Is. 8|d. per cubic yd. 
 
 7. The daily pay of a foot-soldier is Is. Id. ; how much 
 does it take to pay a regiment of 750 men for a year at 
 that rate ? 
 
 8. The annual cost of the Police of Paris amounts to 
 5335295 francs of 9|d. each ; express this in sterling 
 money. 
 
 9. How much sterling money is equal to 2000 rupees, 
 each2s. l^d.? 
 
 10. Required the income-tax on £975, 17s. 6d. at Is. 
 4d. per £1. 
 
 11. The annual rent of a parish is £36750, and a tax is 
 
PRACTICE. . 29 
 
 assessed for the poor at 2s. IJd. per £ ; how much will 
 it amount to ? 
 
 12. In 1856, the expenses of the British Postal Service 
 were £1660229, and the net revenue was £1207725; 
 express each of these in francs and rupees of Is. lOJd. 
 
 13. Sold 273 qrs. 5 bu. of wheat at £2, 15s. per qr. ; 
 159 qrs. 3 bu. of barley at 42s. 8d. per qr. ; and 79 qrs. 
 6 bu. of oats at 22s. 7d. per qr, ; find what sum was 
 received in all. 
 
 14. Find the value of 14 cwt. 3 qrs. 16 lbs. of tobacco at 
 £23, 7s. lOd. per cwt. 
 
 15. A farm, containing 675 ac. 3 ro. 24 per., is let at 
 £l, 17s. 6d. per acre; what is the whole rent? 
 
 16. Edinburgh, May 15th, 1871. James Drummond, 
 Esq., bought of Robert Hunter, 163| lbs. tea at 3s. 9d. 
 per lb., 167i lbs. sugar at 7id., 147i lbs. coflfee at Is. 8d., 
 1 1 cheeses, each 56 lbs., at 8Jd. per lb. ; what is the whole 
 value ? 
 
 17. Leith, April 17th, 187 1 . Alexander Clark bought of 
 Scott and Co., 179J doz. sherry at 27s. 6d., 185J doz. 
 port at 36s., 163 gals, aqua at 17s. 6d., 17 gals, brandy 
 at 36s. 6d., and 21 doz. claret at 47s. 6d. ; what is the 
 whole value ? 
 
 18. The number of sovereigns coined in 1855 was 
 8448482, each weighing 5 dwt. 3y\ grs. ; required the 
 whole weight. 
 
 19. The number of shillings coined in 1855 was 
 1368499, each weighing 3 dwt. 15y\ grs. ; required the 
 whole weight. 
 
 20- What is the value of 3 casks ot molasses, each 7 cwt. 
 3qr. 3iib.,at 12s. 7|d. per cwt., and duty 4s. 2d. per cwt.? 
 
 21. A gentleman has 3 farms ; the first contains 450 
 ac. 3 ro. 24 per., and is let at £1, 13s. 4d. per ac. ; the 
 second contains 564 ac. 1 ro. 36 per., and is let at £1, 16s. 
 per ac. ; and the third contains 635 ac. 2 ro. 16 per., and 
 is let at £2, Is. 8d, per ac. ; the taxes which he pays 
 upon each are respectively 5s., 6s. 8d., and 3s. 4d. per 
 ac. : what is the full rent of all his farms, the amount or 
 taxes which he pays, and his net income ? 
 
 22. A bankrupt owes £7580, and he can pay 15s. 7id. 
 per £ ; what are his effects worth ? 
 
30 
 
 DFXIMAL FRACTIONS. 
 A FRACTION which has unity with one or more ciphers 
 after it for its denominator is called a Decimal fraction ; 
 as, -j%, T^^TJ- Such fractions are expressed without 
 their denominators by pointing off, from the right of the 
 numerators, as many figures as there are ciphers in the 
 denominators; thus, -^^ ^§§, g-%Vtr ^^^ written '4, 1'69, 
 •412. "^^^len the number of figures in the numerators is 
 less than the number of ciphers, the deficiency is made 
 up by prefixing ciphers to the numerators ; thus, -j^^ 
 = -04, TTi%%V^ = -00251. 
 
 Ciphers on the right of a decimal do not alter the 
 value; thus, -040 = ^^g^, = ^^^ = -04. 
 
 The fii'st figure after the point indicates tenths ; the 
 second figure, hundredths ; the third, thousandths, and 
 so on ; that is, in decimals, as in integers, the value in- 
 creases in a tenfold ratio from right to left. Decimals 
 are therefore operated upon in the same way as integers, 
 due attention being paid to the placing of the point. 
 
 80 ) 7-0000 
 
 «^o=-0875 
 
 REDUCTION OF DECIMALS. 
 
 Case I. To reduce a vulgar fraction to a decimal. 
 
 Ex. Reduce ■^''■^ to a decimal. Ans. -0875. 
 
 So L. Divide the numerator (7 ) by the denom- 
 inator (80), annexing ciphers to the numerator 
 until the division terminates or repeats ; then 
 point off as many figures from the right of the quotient (875) 
 as there were ciphers annexed (4), and make up the defi- 
 ciency (if any) in the quotient by prefixing ciphers to it. 
 
 When the division terminates, the result is called a 
 Finite decimal ; if not, it is called a Repeating or Cir- 
 culating decimal, according as one or several figures 
 recur, and a dot is placed above the repeater, or above 
 the first and last figures of the circulate ; as, -|, = '6 ; 
 1= -142857 (seep. 34). 
 
 Reduce to decimals, 
 
 1 1 3 i 13 27 231 19 511 17 23 197 n-nA 1001 
 O 1 19 173 153 11 183 214 363 279 87_ 
 
 '^- ¥7? TaT' 6^5? TTT-^J 2T5) T3T5) SJ-^T^ TdTTJ -g^TsJ T3'6 25- 
 
 «14 7 6 25 6 36 54 121 143 15 .?,111 
 
 *• T! ^J -ST? TJ T2 6' 115") 2lT^> TTbOJ TTeXy? ^¥7^J -^^'4^ ^ T 6 4^' 
 
DECIMAL FRACTIONS. 31 
 
 Case II. To reduce a finite decimal to a vulgar fraction. 
 Ex. Reduce '0375 to a vulgar fraction. Ans. -g^, 
 
 Sol. Write the given decimal (-0375) as the | Tofeao = /o 
 numerator of the fraction, and for the denominator write 
 unity ^ with as many ciphers after it as there are figures in 
 the decimal (4) ; then reduce the fraction dlg^o) t^ ^^ \ow- 
 est terms (g^^). 
 
 Reduce to vulgar fractions, 
 
 1.-5; -25; -75; -625; -3125; -03125; •18725r096875; -000575 
 2. -48; -364; -4248; -0672; -4152; -04096; -03136; '00048 
 3. -525; 6-0425; -00675; 8-0864; -0001875; 1-04264; 2-18575 
 
 Case III. To reduce a compound quantity to the 
 decimal of a higher name. 
 
 Ex. Reduce 4 cwt. 3 qr. 21 lb., or 553 lb., to the dec- 
 imal of a ton. Ans. -246875 ton. 
 
 Sol. Reduce the given | 5531b. = ^V?^ to- = •246875 ton. 
 quantity (553 lb.) to the fraction of the required name (by 
 Case YI., p. 8), and again (by Case I. of dec.) reduce the 
 fraction (/2V5) to a decimal (-246875). 
 
 1. Reduce 2s. 6d., 3s. 9d., 53. 6d., 12s. 8id., 15s 9f d., 
 and lO^d., to the decimal of £1. 
 
 2. Reduce 3 qr. 211b., 2 cwt. 141b., 4 cwt. 17^^., 
 141b., 2 qr. 141b., and 981b., to the dec. of 1 ton. 
 
 3. Reduce 2 ml. 7fu., 4 ml. 16 po., 37 po. 5^ yd., 7fu. 
 34 po., 8 ml. 16 po., and 374 yd., to the dec. of 9 ml. 
 
 4. Reduce 2 ac. 3 ro., 3 ac. 24 per., 2 ro. >21 yd., 17 per. 
 151 yd., 1 ac. 363 yd., and 363 yd., to the dec. of 3 ac. 
 
 5. Reduce 4 oz. 1 dwt., 19 dwt. 15 gr., 21 gr., 11 oz. 
 15 gr., 10 oz. 10 dwt., and 1 dwt., to the dec. of 1 lb. tr. 
 
 6. Reduce 14s. 7d., 16s. lid., 3 cr., 4 half-cr., f of 
 14s. 5id., and 3^d., to the dec. of 1 guinea. 
 
 7. Reduce £14, 5s. lOd., and £16, 17s. 6d., to the dec. 
 of 20 guineas. 
 
 Case IV. To find the value of a dec. in lower names. 
 Ex. Find the value of 1-375 ac. Ans. 1 ac. 1 ro. 20 per. 
 
 Sol. Multiply the given decimal (-375) 
 by the number of the next lower name 
 contained in that given (4), and point off, 
 from the right hand of the product, as 
 
 1-375 ac. X 4 
 1-500 ro. X 40 
 20-000 per. 
 
.?2 DECIMAL FRACTIONS. 
 
 many figures as are in the decimal (3) ; again, mnltiply tho 
 decimal part of the last product (-500) by the number of the 
 next lower name contained in this last name (40), and point 
 off as before ; proceed in the same way as far as necessary. 
 The figures on the left of the points are integers of the re- 
 spective names. 
 
 Fii>d the values of, 
 
 1. £-4625; -37258.; -6875 gu.; '3425 or.; £-7725; -9258. 
 
 2. -3775 cwt.; -4275 ton; -68725 or.; -3975 cwt. ; 
 •4375 ton; •4651b. 
 
 3. -8975 ml. ; -3875 ac. ; -496725 da. ; -8975 co. ye. ; 
 •1875 bu. ; -3875 ro. 
 
 4. -4725 Eng. E. ; -45875 yd. ; -2875° ; -9875 Ju. ye. ; 
 £8-6775; 9*725 gu. 
 
 5. -242242 da.; £-8794^ 8-746 ton; 10-12125 ac. ; 
 11-6874 ml.; 14-72 yd. 
 
 Case V. To reduce shillings and pence to the deci- 
 mal of £1 mentally. 
 
 Ex. 1. Reduce 4s. 10|d. to the dec. of £1 mentally. 
 
 Ans. £-24375. 
 
 Sol. Divide the shillings by 2 for the first figure of the 
 decimal (-2) ; the farthings in the pence and farthings (42), 
 increased by their 24th part (l^f or If), gives the next two 
 figures (43) ; then to the third figure annex the remainder 
 (f ), reduced to a decimal (75), for the value (£-24375). 
 
 Ex. 2. Reduce 15s. 8id. to the decimal of £1. 
 
 Ans. £'784/^, or £-784375. 
 When the shillings are odd, 50 must be added to the far- 
 things, increased as above. 
 
 Reduce to the decimal of £1 mentally, 
 
 1. 7s. 6d. ; 10s. 7id. ; 14s. 8id. ; 15s. 9d. ; 19s. 8id. ; 
 12s. 7id; 18s. 9id. 
 
 2. lis. 8d.; 128. 4d.; 13s. 5d. ; 14s. lljd. ; 16s. 8ad.; 
 £1, 17s. 9d.; £3, 18s. 7d. 
 
 Case VI. To value the decimal of £1 mentally. 
 Ex. Value £-6354 mentally. Ans. 12s. S^d. 
 
 Sol. Divide the first two figures (63) of the dec. by 5 for 
 shillings (12) ; to the remainder, if any, annex the thin! 
 
DECIMAL FRACTIONS. 
 
 33 
 
 figure (5), and tins number (35) diminished by its 25tli part 
 (1) gives farthings (34), which must be reduced to pence (8^d.) 
 Note. Since three places of the decimal only are required, 
 call the third figure one more than it is, when the fourth is 5 or 
 upwards, otherwise reject it. 
 
 Find mentally the values of, 
 £•972; £-496; £'896; £1-8914; 
 •873; -785; -999; 6-4377; 
 
 1. £-525; 
 
 2. -675; 
 
 £11-7364 
 
 22-8976 
 
 Sum 
 Diff. 
 
 7-96752 
 
 -0478 
 8-01532 
 7-91972 
 
 ADDITION AND SUBTEACTION OF FINITE DECIMALS. 
 
 Ex. Fmd the sum and difference of 7-96752 and -0478. 
 
 Sol. Arrange the numbers so that the 
 decimal points may be directly under each 
 other, and proceed as in integers ; then 
 place the point in the result directly under 
 the other points. 
 
 Find the sum of, 
 
 1. -25, 4-675, -00475, 84, 96-23725 
 
 2. -0046, 217, -284, -0478, 3-44756 
 
 3. -728921, -00043, 211-2, 86-114875 
 
 4. -00867, 1-432, 247, -00083, -674 
 
 5. 9-732, -048076, -1234, 6-7289, -214, -7 
 
 6. -6498, -37293, 311-4, 21-72, -00875 
 
 7. -046, 36-479, 2-101, -111, -04789 
 
 8. -3596, -24798, -35, 37, -00705 
 
 9. £375, 16s. 6d., £331,14s.9d., £375, 18s.9|d., £157,7s.8id., 
 
 £97 4s. 6d. 5s. 9d. 
 10.47-98625— 13-97846; 7-0423— -4789; 28-23546— 16^479258 
 11.29-46537—21-57698; 8-2458— -0034; -6728934— -00628575 
 12.1-4386- -004289; -04657- '00827 ; -4798231- -46991482 
 13. 17 cwt. 2 qr. 14 lb.— 14 cwt. 3 qr. 21 lb. ; 29 qr. 5 bu. 2 pk. 
 
 — 23 qr. 7 bu. 3 pk. 
 
 MULTIPLICATION OF FINITE DECIMALS. 
 
 Ex. Multiply 4-7025 by -0025. Ans. -01175625. 
 
 Sol. Multiply the factors together, as in in- 
 tegers, disregarding the point ; then, from the 
 right hand of the product, point off as many 
 figures as there are decimal places in both fac- 
 tors (8), making up the deficiency (if any) by 
 prefixing ciphers (1) to the product. 
 
 4-7025 
 
 ♦0025 
 
 235125 
 
 9405 
 
 •01175625 
 
 d2 
 
34 DECIMAL FRACTIONS. 
 
 Note. A decimal is multiplied by 10, 100, 1000, &c. by re- 
 moving the point one, two^ three, «&:c. places to the right; an, 
 2-134 X 10000 = 21340. 
 
 1.4^6275x4-63, 5-75, -046, -824, 86-4, -005, 1000, 10001 
 2. •00796x37-8, 42-89, 7-824, -046, -3724, 1-738, 100, 10101 
 3.27-8372x8-434,96-429,-00429,-7426,3-14152,-001,1001 
 4. Val.27yd. 3qr . 2nl., at 2/6, 4/9|,23/4^,27/10|,31 /I li p.yd. 
 
 DIVISION OF FINITE DECIMALS. 
 Ex. Divide 3-146 by 42-8. Ans. -073505 nearly. 
 
 Sol. Make the decimal places in 42800 )3146-000000 
 both numbers alike by annexing ci- -073505 
 
 phers (2) to that which has the least 
 number ; then divide as in integers, and to the remainder 
 (if any) annex ciphers to carry on the division : the number 
 of ciphers last annexed (6) is the number of decimal places 
 in the answer (-073505). 
 
 Note. A decimal is divided by 10, 100, 1000, &c. by removing 
 the point one, two, three, &c. places towards the left; as, 2-134 -f- 
 100 = -02134. 
 
 1. 382-8825-7-55, 1-36, 31-5,-325, -1309, -00119, 2-75, 81-9, 100 
 
 2. 24-22728-r-l-15, 85-5, -805, -0368, 103-5, 369-6, -01539, 1000 
 3. -0483923^-20-35,475-6, 8-584,-03157,-002552,l-221, -0019721 
 4. £4779, 17s. 8jd.-M7-5, 4-375, 281-25, 687-5, -03125, -1875 
 
 INTERMINATE DECIMALS. 
 
 In reducing vulgar fractions to decimals, when one or 
 more figures of the quotient recur, the result is called 
 an Interminate decimal. 
 
 Decimals consisting of one or more figures which re- 
 cur, are called pure repeating or circulating decimals ; 
 as, -3, -142857. 
 
 Decimals consisting of a non-recurring and a recurring 
 part are called mixed repeating or circulating decimals ; 
 as, '46, '3796 : the non-recurring parts (4 and 37) are 
 generally called the finite parts of the decimals (-46 and 
 '37960 
 
INTERMINATE DECIMALS. 35 
 
 REDUCTION OF INTEEMINATE DECIMALS. 
 
 Case I. To reduce a pure repeater or circulate to a 
 vulgar fraction. 
 
 Ex. Reduce '75 to a vulgar fraction. Ans. ^| or -§f. 
 
 Sol. Write the given decimal for the numerator, and be- 
 low it, for the denominator, place as many nines (2) as there 
 are decimal places; then reduce the fraction (||) to its 
 lowest terms (y). 
 
 Reduce to vulgar fractions, 
 1.-3, -6, -4, -9, -27, -36, -396, -594, -185, -259, -063, -0072 
 2. -571428, -153846, -190476, -171, -428571, -095238 
 
 Case II. To reduce a mixed recurring decimal to a 
 vulgar fraction. 
 Ex. Reduce '0476 to a vulgar fraction. 
 
 -MII&. -g-goo -5900' 2^T5 
 
 Sol. From the given decimal (-0476), considered as an 
 integer, subtract the finite part (04) for the numerator, be- 
 low which, for the denominator, place as many nines as there 
 are figures in the circulating part (2), with as many ciphers 
 annexed to them as there are figures in the finite part (2) ; 
 then reduce the fraction (/9V0) to its lowest terms l^^^^^^). 
 
 Reduce to vulgar fractions, 
 
 1. -472, -583, -16, -027, -QliS, -4891, -6381, -729693 
 
 2. -146, -2359, -0026, -06563, -11818, -4585, -68472 
 
 Case III. To make circulates similar. 
 
 Ex. Make -03, -775, and -76034 similar. 
 
 Sol. Extend each decimal as many places 
 beyond the longest finite part (2), as is indi- 
 cated by the L. C. M. of the number of places in 
 the several circles (6). 
 
 Make the following circulates similar. 
 
 •03333333 
 -77575757 
 •76034034 
 
 1. -143, ^037, -014 
 
 2. -3742, -0089, ^476 
 
 3. -1769, -2456, 'im 
 
 4. -402, '179, •0423 
 
 5. -117, -1146, -0894 
 
 6. -2486, -1175, -0624 
 
 7. 1^729, •2684, -0046, 2-478 
 
 8. 4-3, 8-729, •4673, -OOl 
 
 9. -00101, -26770, -1421, 3-428 
 
 E 
 
36 
 
 INTERMINATE DECIMALS. 
 
 ADDITION AND SUBTRACTION OF INTERMINATE 
 
 DECIMALS. 
 Ex. 1. Find the sum and difference of 37-143 and 29-8736 
 
 Sol. Since there are only repeaters given, 
 extend them one place beyond the longest 
 finite part, and carry or borrow at 9 on the 
 right hand; the right-hand figure of the 
 result is a repeater or 0. 
 
 37-1433 
 29-8736 
 
 Sum 67-017 
 DifF. 7-2696 
 
 Ex. 2. Find the sum and difference of 71-857 and 
 43-97642. 
 
 Sol. Make the circulates similar, 
 
 and add the carriage (if any) from the 
 left-hand column of the circles to the 
 right-hand figure of the under circle, 
 before adding or subtracting. 
 
 71-85757575 
 
 43-97642642 
 
 Sum 115-83400218 
 
 Diff. 27-88114933 
 After the right-hand figure of the result has been obtained, 
 proceed as in Finite decimals. 
 
 Find the sum of, 
 
 1. 1-6, 23-052, -583, 6-3, -05i I 3. -7, -245, -006, -043, -i 
 
 2.7-8, 8-964, -729i, 14-0561 4. -72, -345, -854, '00625 
 
 5. 9-76, 8-427, -0864, -75, 8-4572 
 
 6. -1341, -672, -1487, -05, 6-4576 
 
 7. 11-i, 1-63, -9625, -03, 7-1167 
 
 O 2 5 3 4 6 or\f\ 3 
 
 9. £12, 14s. 5d., £27, 16s. 7id., £33, 16s. 6^d., £17, 
 
 lis. 8d., and lOfd. 
 10.29-146— 13-17, 16-72—4-6583, 57-6854-14-976851 
 11.17-36—3-143, 21-867—7-863, 41-6872-19-478623 
 12. 17 ml. 3 f. 4 yds.— 6 ml. 39 po. 5 yds., 18 cwt. 3 qr. 
 
 161b.— 7 cwt. 181b. 
 
 MULTIPLICATION OF INTERMINATE DECIMALS. 
 Ex. Multiply 42-375 by -037. 
 Sol. When the multiplicand is a repeater, 
 and the multiplier a finite decimal, multiply as 
 in integers, but add 1 to the right-hand figure 
 of the product for every 9 in it; then extend 
 the several products the same length and add 
 them. 
 
 42-375 
 •037 
 
 296628 
 1271266 
 1-567895 
 
INTERMINATE DECIMALS. 
 
 37 
 
 7-14672 
 '69 
 
 6432054 
 42880360 
 
 Ex. 2. Multiply 7-14672 by -69. 
 
 Sol. When the multiplicand is a circulate and 
 the multiplier a finite decimal, multiply as in 
 integers, and add the carriage from the left of 
 the circle to the right-hand figure of the circle ; 
 then extend the several products the same length 
 and add them. 4-9312414 
 
 When the multiplier is interminate, or when both are in- 
 terminate, reduce the multiplier to a vulgar fraction, then 
 multiply by its numerator and divide by its denominator. In 
 dividing, instead of ciphers, the repeating or circulating 
 figures must be annexed in their order to carry on the 
 division: thus, 
 
 6-285714 X -3 = 5-2857142 X ^ = 1-761904. 
 
 1.5-7963 X 4-8, 5-76, 8-942, 7-63, 11-5, -0042, -176, -0087 
 
 2.8-1426 X 7-3, 6-84, 9-428, 3-76, 1-51, -43, -0074, -4875 
 
 8. 6-8726 X -4, 6-6, 7-2, -043, -069, -0428, '0072, -1456 
 
 4.7-8763 X -6, -63, -171, -069, -487, 3-i48, 6-709, 8-472 
 
 DIVISION OF INTERMINATE DECIMALS. 
 Ex. 1. Divide 26-80583 and 21-18729 by 8. 
 
 Sol. When the dividend only is inter- 
 minate, divide as in finite decimals, and in 
 carrying on the quotient, instead of ciphers, 
 annex the repeating or circulating figures 
 in their order, until a repeater or circulate 
 is obtained in the quotient. 
 
 8 )26-80583333 
 3-35072916 
 
 8)21-18729729 
 1-64841216 
 
 Ex. 2. Divide 6-7283 by G'6. Here 6'6z=z6^=^z=y> 
 
 Sol. When the divisor or both are inter- 
 minate, reduce the divisor (6-6) to a vulgar 
 fraction (6 §), then multiply by its denomi- 
 nator (3), and divide by its numerator (20) 
 for the quotient, which may be carried on 
 as in Ex. 1. 
 
 1. 7-416-^-125, 187-5. 43-75, -52, -427, -729 
 
 2. -2307692 -^ -65, 4-16, -975, -0208, 4-*63, 7-83 
 8. 14-i42857 -r- '84, -583, 68-4, 7-23, 81-6, 9-63 
 
 6-7283 
 3 
 
 20 )20-18498 
 
 1-009249 
 
38 
 
 MISCELLANEOUS EXERCISES ON DECIMAL FRACTIONS. 
 
 1. Find the values of £-31416; -142857 ton; -12645 
 ml. ; -846283 lb. troy; -1728 yd. ; and '78646 day. 
 
 2. From the sum of 7-6, 8-24, 9*1583, subtract 4-72, 
 and multiply the remainder by 21-24. 
 
 3. Find the value -875 of 17s. 6d. + -143 guinea — 
 -725 of 8s. 6d. 
 
 4. Express 1456*725 cub. ft. in French steres, each . 
 35*31658 cubic feet. 
 
 5. Find by decimals the value of 14 cwt. 3 qrs. 14 lbs. 
 of coffee at £9, 6s. 8d. per cwt. 
 
 6. The ratio of the diameter of a circle to its circum- 
 ference is 1 : 3*14159 ; required the mean equatorial cir- 
 cumference of the earth, the diameter being 7925*626 mis. 
 
 7. Find the diameter of the planet Jupiter, its circum- 
 erence being 273318*33 miles. 
 
 8. Reduce £4, 13s. 4d. to the dec. of £5, 12s. 6d. 
 
 9. The gold eagle of the United States weighs 270 
 grains, 21*875 carats fine; what is its value in sterling 
 money, 46*725 sovereigns weighing a lb. troy, 22 carats 
 fine? 
 
 10. A and B can do apiece of work in 4*8 days, A and 
 C the same in 4*4 days, and B and C in 5*45 days ; find 
 by decimals in what time the three together could do it, 
 and also separately. 
 
 11. Find the value of -1875 ton + -375 qr. + -8751b., 
 and reduce the result to the decimal of 3 cwt. 3 qrs. 
 
 12. The whole area of France is 131017513*33242 acres; 
 find the area in hectares, each 2*473614 acres. 
 
 13. Multiply -06723 by -00401, and divide 301*5 by 
 -00045. ^ 
 
 14. A French metre is 3*2808992 imperial feet ; how 
 many imperial feet are there in a quadrant of the me- 
 ridian, or in 100000565*268 metres ? 
 
 15. What is the hourly motion of the earth, whose 
 distance from the sun is 95 millions of miles and period 
 of revolution 365 days ? 
 
 16. An ounce of tea costs 2-8125d. ; what should be 
 paid for 6 583 lbs. of the same? 
 
EXERCISES ON DECIMAL FRACTIONS. 39 
 
 17. Find the value of 14-8745 ml. — 3*427 mile. 
 
 18. £4, 6-625S. X 27-45 and 993-714285-^234-2. 
 
 19. Keduce -025 of 4 ml. 3 fu. 19-264 pole to the dec, 
 of 2 ml. 5 fu. 
 
 20. Keduce 2-275 of 4i gu. to the dec. of £20, 9s. 6d. 
 
 21. Find the values of -073 of 8s. 6d. and -785 of 15s.9d. 
 
 22. Reduce '2 of |- of 4 cwt. 3 qrs.23 lbs. to the dec. of 
 31cwt. 2qrs. 24 lbs. 
 
 23. Divide £1050, 3|d. among 5 men, 8 women, and 16 
 boys, giving each woman -5 of I of a man's share, and 
 each boy -5 of 1-25 of a woman's share. 
 
 24. Divide £1125 among A, B, and C, giving A 4- of 
 2-625 of the whole— £45; B 1-025 of what A receives 
 -|- £75, and C the remainder. 
 
 COMMERCIAL ALLOWANCES. 
 
 The Gross weight of goods is their whole weight, including 
 the weight of the cask, barrel, &c., which contains them. 
 
 Tare is the weight of the cask, barrel, &c., which con- 
 tains the goods, or it is an allowance made for it. 
 
 That which remains after deducting the tare is called 
 the Tare Suttle. 
 
 Tret is an allowance of ^V? or 4 lbs. on every 104 lbs. 
 of the Tare Suttle for waste. — Draft is also an allowance 
 sometimes made, and is deducted before the Tare. 
 
 The Net weight is what remains after all the allow- 
 ances have been deducted. 
 
 Questions under this head may be solved by Practice. 
 
 Ex. Find the net weight of 5 hhds. sugar, each 10 
 cwt. 3 qrs. 4 lbs., allowing tare 14 lbs. per cwt., tret 4 
 lbs. per 104 lbs., and draft 4 lbs. per hhd. 
 
 10 cwt. 3 qr. 4 lb. gross weight of each hhd. 
 4 draft on 1 hhd. 
 
 10 
 
 3 
 
 0X5 
 
 141b.= icwt.)53 
 
 3 
 
 
 
 6 
 
 2 
 
 24^ tare. 
 
 4lb.p.l04lb.=^'^)47 
 
 
 
 3i tare suttle. 
 
 1 
 
 3 
 
 6H tret. 
 
 45 24 1 7 net weight. 
 
40 COMMERCIAL ALLOWANCES. 
 
 Find the net weight of, 
 
 1. 48 cwt. 3 qr. 14 lb., tare 16 lb. per cwt. & tret as usual. 
 
 2. 79 cwt. 2 qr. 21 lb., tare 7 lb. // // // 
 
 3. 147 cwt. 1 qr. 7 lb., tare 81b. // // // 
 
 4. 984 cwt. 3 qr. 16 lb., tare 14 lb. // // ^ 
 
 5. 748 cwt. 2 qr. 12 lb., tare 12 lb. // // // 
 
 6. 896 cwt. 1 qr. 241b., tare 18 lb. // // // 
 
 7. 4 chests of tea, each 12 cwt. 3 qrs. 14 lbs., allowing 
 tare 15 lbs. per cwt., tret as usual, and draft 3 lbs. per 
 chest. 
 
 8. 7 casks of sugar, each 14 cwt. 2 qrs. 18 lbs., allowing 
 tare 14 lbs. per cwt., tret as usual, and draft 4 lbs. per 
 cask, and the value of the net weight at 6id. per lb. 
 
 9. 3 hhds. tobacco ; the first, 8 cwt. 3 qrs. 14 lbs., tare 
 3 qrs. 7 lbs. ; the second, 9 cwt. 2 qrs. 7 lbs., tare 2 qrs. 
 19 lbs. ; and the third, 10 cwt. 1 qr. 16 lbs., tare 3 qrs. 
 7 lbs., allowing draft 7 lbs. per hhd., and tret as usual. 
 
 10. Bought 2709 lbs. of coffee, and was allowed 1 lb. 
 gratis to the score; what did I pay for it at 16id. per lb.? 
 
 11. How much pure silver in a mass weighing 42 lbs., 
 allowing 15 dwt. of alloy in each lb. of the mass? 
 
 12. Purchased 4 bags of rice, each 265 lbs., and was 
 allowed 3 lbs. gratis to every 50 lbs. ; what did it cost 
 at 3id. per lb. ? 
 
 COMMISSION AND BROKERAGE. 
 
 Commission is an allowance of so much per cent, paid 
 to one person for transacting the business of another. 
 Brokerage is a smaller allowance of the same nature. 
 
 Ex. 1. Find the commission on £475, 12s. 6d., at 
 £li per cent. Ans. £7, 2s. S^d. 
 
 Sol. Multiplythesum(£475,12s.6d.) | £475 12 6 
 
 by the rate per cent. (1^), and divide 1^ 
 
 the product (£713, 8s. 9d.) by 100. 100)713 8 9 
 
 ^ Com. £7 2 "81 
 
 When the rate is guineas, add :^\ of the sum to itself, 
 then multiply by tlie rate as £'s, and divide by 100 
 when the rate is shillings, &c., take aliquot parts of £1, 
 and divide by 100. 
 
Sol. 1. 5^0) £322 10 
 
 16 2 
 
 338 12 
 
 
 6 
 6 
 
 1,00)8,46 11 
 Com. at 2^ p. c, £8 9 
 
 3 
 
 3f 
 
 COMMISSION AND BROKEKAGE. 41 
 
 Ex. 2. Find the commission on £322, 10s., at 2^ gu. 
 and 8s. 9d. per cent. 
 
 Sol. 2. 5s.r=£|) £322 10 
 
 80 12 6 
 2s.6d.=:^of5s.= 40 6 3 
 ls.3d.=iof2s.6d.=20_3__l| 
 
 100 )141 1 10^ 
 
 Com.at8s.9d.p.c.,£l 8 2^:} 
 
 1. Find the com. on £148, 2s. 6d., at 2,^, 3, 3i, and 
 3| per cent. 
 
 2. Find the brok. on £152, 10s., at ^, f, -j*^, andl^p.cent. 
 
 3. Find the com. on £500, at 2s. 3d., 3s. 9d., 4s. 3d., 
 and 16s. 9d. per cent. 
 
 4. Find the brok. on £4216, 5s., at 3s., 2s. 6d., 3s. 4d., 
 and 4s. per cent. 
 
 5. Find the com. on £2850, at 1|. gu.. If gu., l-^ gu., 
 and 2^ gu. per cent. 
 
 6. Find the brok. on £375, 17s. 6d., at 3s. 9d., 5s. 3d., 
 lis. 3d., and 13s. 4d. per cent. 
 
 7. An agent sells for his employer goods to the amount 
 of £1260, 17s. 6d. ; the expenses attending the sale amount 
 to £14, 2s. 6d. : what is his commission at 3^ per cent. ? 
 
 8. A banker discounts bills to the amount of £1252, 
 10s. ; what is his commission at ^ per cent. ? 
 
 9. An agent charges 3| per cent, for commission and 
 risk of bad debts ; his sales during the year amount to 
 £9275, 15s., and his losses to £150 : required his net 
 income. 
 
 10. A broker is authorized to purchase £1120, 10s. of 
 3 per cent, stock ; what is his brokerage at \ per cent. ? 
 
 11. An agent's annual sales amount to £12783, 13s. 4d. ; 
 his bad debts, valued at 12s. 6d. per £1, amount to £360, 
 and his losses to £150 : what is his income, if he is al- 
 lowed 5 per cent, for commission and guarantee ? 
 
 12. A factor collects the half-yearly rents of 3 farms ; 
 the annual rent of the 1st is £1250 ; of the 2d, £775 ; and 
 of the 3d, £840; the charge for repairs on each is f, 1^, 
 and 2 per cent. : what sum will he remit to the landlord, 
 his factorage being 3} per cent, upon the rental ? 
 
42 
 
 INTEREST. 
 Interest is the money paid for the loan of money. 
 
 The money lent is called the principal^ and the sura 
 of the principal and its interest is called the amount. 
 
 Interest is divided into simple and compound. 
 
 SIMPLE^ INTEREST. 
 
 Case I. To find the interest for any number of years. 
 
 Ex. Required the interest of £375, 2s. 6d. for 4 years, 
 at 3i per cent. Ans. £50, 0%. 4d. 
 
 Sol. Multiply the principal by £375 2 6 
 
 the rate per cent. (3J), and by the 
 number of years (4) ; and divide the 
 product (£5001, 13s. 4d.) by 100. 
 
 £1250 8 
 
 I 
 
 100) £50,01 13 
 Int. £50 
 
 3 
 4 
 4 
 
 4 
 
 Note. For months take parts of a year, or multiply by them 
 and divide by 12. 
 
 1. Find the interest of £1345, 10s. for 1 year, at 5, 
 5|, 5^, 4^, 4|, and 3| per cent. 
 
 2. Find the amount of £575, 13s. 4d. for 1 year, at 2^, 
 3, 3J, 4i, 5, and 5f per cent. 
 
 3. Find the interest of £1200, 13s. 4d. for 5 years and 
 G years, at 2i, 3J, and 4i per cent. 
 
 4. Find the amount of £150, 17s. 6d. for 6f yrs. and 
 7^ yrs., at 2i, 3, and 5 per cent. 
 
 5. Required the interest of £1244, 15s. for 5 ye. 7 mo. 
 and 4 ye. 5 mo., at 3i, 4, and 5f per cent. 
 
 6. Borrowed £750, at 2J per cent. ; what sum will be 
 required to discharge the loan at the end of 5 ye. 8 mo. ? 
 
 Case II. To find the interest for any number of days. 
 Ex. Find the interest of £675, 10s. for 195 days, at 
 
 4 per cent. 
 
 Sol. Multiply the princi- 
 pal by twice the rate per 
 cent. (8), and by the number 
 of days (195) ; and divide 
 the product by 73000 (i. e. 
 2 X 365 X 100). 
 
 Ans. £14, 8s. 8id. |f f 
 £675 10 
 
 8 
 
 5404 
 
 
 195 
 
 73,000) £1053780 
 £14 
 
 _0 _ 
 
INTEREST. 43 
 
 7. Required the interest of £677, 10s. 7icl. for 198 
 (lays and 364 days, at 2^, 3^, and 4i per cent. 
 
 8. Find the amount of £1436, 14s. 7id. for 1 ye. 95 da. 
 and 2 ye. 5 da., at 2^, 3^, and 4 J per cent. 
 
 To divide by 73000. 
 
 Taking Ex. 2— To the pounds ^) £1053780 
 
 of the dividend add ^ of itself, yV) 351260 
 
 j'^ of this third, and ^^^ of the t*^) 35126 
 
 last; then point off 5 figures 3513 
 
 of a decimal from the right £14^ gs. 8^d. = £14-43679 
 hand of the sum. This gives 
 
 the interest too much, by about Jd., for every £10 of 
 interest. 
 
 9. Required the interest of £483, 12s. 6d. from Mid- 
 summer to Christmas, and from Christmas to Midsum- 
 mer, at 2^, 4, and 5 per cent. 
 
 10. Lodged in the bank £748, 5s. on March 1st, find 
 the amount of this on Dec. 31st, interest at 2i per cent. 
 
 11. Borrowed £1051, 4s. on April 4th ; ^ at 3^, and the 
 rest at 3^ per cent. ; what sum should be returned on 
 Nov. 11th? 
 
 12. Find the interest of £210, 12s. 8id. for 275 days, 
 at 4J and 4^ per cent. ; and of £445, 18s. 2d. for 252 
 days, at 2^ and 3i per cent. 
 
 13. Find the amount of £4482, 4s. from Feb. 23d to 
 June 13th, at 3-^, 4-f, and 5^ per cent. 
 
 14. What is the interest of £1005, 17s. 7d. from Jan. 
 1st to May 16th, and from April 7th to Dec. 15th, at 
 3|, 3^, and" 4^ per cent. ? 
 
 15. Borrowed £340, 19s. 5d. on Lammas-day at 4 per 
 cent., and £361, 7s. at 4-i- per cent, on Michaelmas-day ; 
 what sum will discharge the whole loan on Whitsunday 
 following ? 
 
 Case III. To find the interest when a debt is dis- 
 charged by partial payments at short intervals of time. 
 
 Ex. Borrowed £750 on Jan. 1st, of which £200 was 
 paid on March 4th, £250 on May 15th, and the balance on 
 August 1st ; what was then due, interest at 2^ per cent. ? 
 
 Ans. £307, 10«. 
 
44 INTEREST. 
 
 Obs. J rom Jan. 
 1 st to March 
 4th is 62 days, 
 Mar. 4th to May 
 15th is 72 days, 
 and from May 
 15th to Aug. 1st 
 is 78 days. 
 
 The balances 
 are multiplied 
 by the respective 
 days. 
 
 Jan. 1. Borrowed £750X62=46500 
 Mar. 4. Paid 200 
 
 Balance 550X72=39600 
 May 15. Paid 250 
 
 Balance 300X78=23400 
 £109500 
 
 (Mult, by 2^X2=) 5 
 
 Divide by 78000) £547500 
 
 £7, 10s. 
 
 Balance as above 300 
 
 Aug. 1. Amount due £307, 10s. 
 
 16. A bill of £960 was due Jan. 4th, of which £300 
 was paid on April 9th, £260 on July 11th, £200 on 
 Nov. 11th, and the balance on Dec. 31st ; what was then 
 due, interest at 3 per cent. ? 
 
 17. Lodged in the bank £1500 on May 13th, and drew 
 £300 on July 11th, £400 on Oct. 1st, £350 on Dec. 14th, 
 £200 on March 29th, and the balance, along with the 
 interest, on June 9th ; what was then drawn, interest at 
 2J per cent. ? 
 
 18. Borrowed £1050 on March 9th, of which ^ was 
 paid on June 14th, £200 on Sept. 23d, -f of the remain- 
 der on Nov. 29th, and the balance on Feb. 11th; what 
 was then paid, interest at 3^ per cent. ? 
 
 19. Lent, Jan. 15th, £1320, and received -25 of it on 
 March 31st, £400 on June 18th, -5 of the remainder on 
 Aug. 19th, £100 on Dec. 30th, and the balance on March 
 1st ; what was then received, interest at 3| per cent. ? 
 
 Case IV. To calculate interest on Accounts-Current. 
 
 An Account-Current is a statement of the mercantile 
 transactions of two persons when immediate payments 
 are not made. It is written on two pages marked Dr. 
 and Cr. ; the Dr. or left-hand side containing all sums 
 paid by the person furnishing the account ; the Cr. or 
 right-hand side those 2:>a^c? to him. 
 
 Ex. Required the interest on the following Account- 
 Current between March 2d and Nov. 11th, interest at 
 3i per cent. 
 
INTEREST. 
 
 45 
 
 Dr. Wilson & Co. in Account-Current with Murray & Co. Or, 
 
 Mar. 2. To Cash, £550 
 
 June 30. " Do. .320 
 
 Sept. 15. >^ Do. .470 
 
 Nov. 11. » Int. . 1 16 2| 
 
 £ 1341 16 2f 
 
 Nov. 11. ToBal. £166 16 2i 
 
 Dr. da. Prod. 
 
 Mar. 2. £550X254=139700 
 
 June 30. 320X134= 42880 
 
 Sept. 15. 470X 57= 26790 
 
 209370 
 
 April 14. ByCash, £400 
 May 17. >' Do. .350 
 July 31. >' Do. . 425 
 Nov. 11. /' Bal. . 166 16 2| 
 £1341 16 2| 
 
 Cr. da. Prod.* 
 
 April 14. £400X211= 84400 
 
 May 17. 350X178= 62300 
 
 July 31. 425X103= 43775 
 
 190475 
 
 1 90475 
 £ 18895 X 7 
 73000) £132265 
 Interest =£1, 16s. 2|d. 
 
 Sol. Multiply each sum by the number of days between 
 the date opposite to it and the last date (Nov. 11). Add the 
 Dr. and Cr. products separately, and multiply the sum of 
 each by twice its respective rate per cent. ; subtract their 
 products, and divide by 73000 for the interest which is entered 
 on the Dr. or Cr. side of the Account, " To or By Interest ;" 
 as the Dr. or Cr. products, after multiplying by twice the 
 rates, is the greater. Then add each side of the Account, 
 and write the difference on the less side, with the words 
 *' To or By Balance." 
 
 20. Find the interest, at 3 per cent., on the following 
 Account-Current from March 2d to Oct. 28th, 1871. 
 
 Dr. J. Brown in Account-Current with A. Anderson, Cr, 
 
 To Cash, . 
 . Do.. . 
 » Do.. . 
 
 £750 
 . 240 
 . 560 
 
 April 17. By Cash, . 
 
 . £640 
 
 May 30. " Do. . 
 
 . .550 
 
 July 18. - Do. . 
 
 . .310 
 
 Mar. 2. 
 June 3. 
 
 Aug. 30. 
 
 21. Required the interest on the following Account- 
 Current, at 4 per cent., to April 8th, 1871 
 
 Dr. R. Scott in Account- Current with Thos. Younger, Cr. 
 
 April 14. To Goods, . . £650 
 Aug. 12. » Cash, ... 400 
 Dec. 15. /' Do 700 
 
 June 11. By Goods, . . £740 
 Oct. 19. '/ Cash, .... 625 
 Feb. 14. // Do 300 
 
4G INTEREST. 
 
 22. Eequired the interest on the following Account- 
 Current to Oct. 15th, allowing Smith 3J per cent., and 
 Weddell 3J per cent. 
 
 Dr. Jas. Smith in Account-Current with Henry Weddell, Cr, 
 
 June 3. To Cash, . 
 
 . £700 
 
 Aug. 1. By Cash, . 
 
 . £1050 
 
 Oct. 7. " Do. . . 
 
 . .500 
 
 Dec. 12. n Do.. . 
 
 . . 600 
 
 Jan. 9. " Do. . . 
 
 . . 650 
 
 Mar. 15. » Do.. . 
 
 . . 450 
 
 May 29. f Do. . . 
 
 . . 420 
 
 July 30. '/ Do. . . 
 
 . . 160 
 
 23. Required the principal and interest on the follow- 
 ing Account-Current to Nov. 29th, allowing Harrison 
 4 per cent., and Cochrane 4 J per cent. 
 Dr. H.Harrison in Account-Current with John Cochrane, Cr. 
 
 Sept. 11. By Cash, . . £750 
 
 Jan. 1. '/ Do 360 
 
 May 9. '' Do 250 
 
 Sept. 20. " Do 540 
 
 July 4. To Cash, . . £600 
 
 Nov. 11. " Do 240 
 
 Mar. 2. - Do 400 
 
 July 12. /' Do 300 
 
 24. Required the principal and interest on the follow- 
 ing Account-Current to Jan. 12th, allowing Henderson 
 2^ per cent., and Clark 2i per cent. 
 Dr. Henderson & Son in Account-Current with Jn. Clark, Cr. 
 
 Aug. 2. To Cash, . . £840 
 Dec. 11. " Goods, . . 800 
 April 9. " Cash, ... 700 
 Aug. 14. " Goods, . . 840 
 
 Oct. 17. By Cash, . . . £960 
 
 Feb. 3. // Do 750 
 
 Jmie 9. " Do 900 
 
 Nov. 1. " Goods, ... 600 
 
 The following examples are solved by Simple and Com- 
 pound Proportion : 
 
 25. In what time will the interest of £725, 16s. 8d. at 
 2.^ per cent, pay a debt of £81, 13s. Ud.? 
 
 26. How long must £532, 5s. lOd. be lent to amount to 
 £548, 4s. 4d. at 3 per cent, per annum ? 
 
 27. What sum will amount to £476, 9s. 5id. in 224 
 days, at 3| per cent, per annum ? 
 
 28. In what time will £1825 amount to £1840, 18s. 6d. 
 at 3J per cent. ? 
 
 29. In what time will any sum of money double itself at 
 2 J, 2f , 3, 3^, 3|, and 4 per cent. ? and in what time would 
 any sum of money treole itself at each of these rates ? 
 
 30. At what rates per cent, will any sum of money double 
 itself in 7^, 10, 11^, 12^ 15, 16, 20, and 25 years? 
 
 31. How long must £1125 be lent to amount to £1188. 
 15s. at 4 per cent. ? 
 
DISCOUNT. 
 Discount is an allowance granted for discharging a 
 debt before the period allowed for payment has expired. 
 
 The p7^esent value of a debt due at the end of a certain 
 time is that sum tlie amount of which for the given 
 time is equal to the sum due at the end of that time : 
 Thus, the present value of £105, due 2 years hence, at 
 2a per cent., is £100; for the amount of £100, for 2 
 years, at 2^ per cent., is £105 ; and the discount allowed 
 for present payment is £105 — £100 = £5. 
 
 Ex. Find the present value of £913, 10s., due 6 months 
 hence, at 3 per cent., and also the discount. 
 
 Ans. £900 and £13, 10s. 
 
 Sol. The interest on £100 for 6 months, at 3 per cent., is 
 3 X A = £1 i, and the amount of £100 for that time is £101 ,. 
 Then, by Proportion, 101^ : 100 : : £913, 10s. : £900 present 
 value, and £913, 10s. — £900 = £13, 10s. is the discount, or 
 by Proportion £101^ : £1^ : : £913, 10s.: £13, 10s., discount 
 as before. 
 
 1. What is the present value of £1158, lis. 6d., due 4 
 months hence, at 2^- per cent. ? 
 
 2. Wliat is the discount upon £345, Is. lO^d., due in 9 
 months, at 3 per cent. ? 
 
 3. What sum will amount to £285, 4s. 4d. in 3 years, 
 at 3 per cent. ? 
 
 4. A debt of £188, 12s. Sjd. is to be paid; £47, 16s. 
 4d. in 2 months, £89, 8s. G^d. in 3 months, and the rest 
 in 4 months ; wliat discount should be allowed for pre- 
 sent payment of the whole, interest at 4 per cent. ? 
 
 5. Required the present value of £527, lOs. 4d., due 219 
 days hence, at 3j per cent. 
 
 6. What is the difference between the interest of £608, 
 10s. 6d. for 146 days, and the discount upon it due in 
 146 days, interest at 2i per cent. ? 
 
 7. Bought goods to the amount of £2400 ; ^ due 1 month 
 lience, ^ due 2 months hence, i due 4 months hence, and 
 the rest due 6 months hence ; what sum will be sufficient 
 to pay the whole now, interest at 3 per cent. ? 
 
 8. Required the discount on £373, 16s. IJd,, due 3, 4, 
 and 6 months hence, at 4 per cent. 
 
48 discoujST. 
 
 9. 1 am offered a discount of £40 for present payment 
 of £640 worth of goods to be paid 3 months hence ; at 
 what rate per cent, is the offer made? 
 
 10. The present value of £436, 5s. 4id. due a certain 
 time hence, is £420, 10s. ; required the time, interest 
 at 2i per cent. 
 
 In discounting Bills, bankers find the interest on the 
 amount for the time which the bill has to run for the 
 discount ; the difference between this discount and the 
 amount is called the net j)roceeds. 
 
 In this country three days, called Days of Grace^ more 
 than the term of the bill are allowed. 
 
 Ex. Find the net proceeds of a bill of £572, 10s., dated 
 April 8th, at 3 months, and discounted June 3d, at 3i 
 per cent. 
 
 Here, 3 months from April £572, 10s. 
 
 8th is July 8th, and adding 3 38 
 
 'lays of grace, the bill is due on 
 
 July 11th; again from June 
 3d to July nth is 38 days. 
 Then the interest on the 
 amount (£572, 10s.) for 38 
 days, at 3^ per cent., viz. 
 £2, Is. 9d., is the discount, 
 and the net proceeds is found 
 by subtracting £2, Is. 9d. from £572, 10s. 
 
 The interest is calculated to the nearest penny. 
 
 21755, Os. 
 
 73,000)£ 152285, Qs. 
 
 Discount = £2, Is. 9d 
 Amount = £572, 10s. Od. 
 
 Net proceeds =£570, 8s. 3d. 
 
 L £572, 10s. 
 the nearest penny. 
 
 Find the net proceeds of the following biUs : 
 
 Amount. 
 
 Date. 
 
 Term. 
 
 Discounted. 
 
 Rate. 
 
 11. £672, 12s. 
 
 Jan. 4. 
 
 4 mo. 
 
 Mar. 5. 
 
 2^ per cent. 
 
 12. 743,11s. 
 
 Feb. 9. 
 
 6 // 
 
 May 11. 
 
 3 // z^' 
 
 13. 897.15s. 
 
 Mar. 11. 
 
 5 // 
 
 June 14. 
 
 31 // // 
 
 14. 983, 4s. 
 
 May 12. 
 
 7 // 
 
 Aug. 17. 
 
 3|: // // 
 
 15. 1260, 14s. 
 
 June 15. 
 
 3 V 
 
 July 26. 
 
 4 // // 
 
 16. 1340, 17s. 
 
 Oct. 14. 
 
 5 // 
 
 Dec. 26. 
 
 4i // // 
 
 17. 1572, 8s. 
 
 Apr. 10. 
 
 8 // 
 
 Sept. 30. 
 
 4| // ^ 
 
 18. 2183, 16s. 
 
 Dec. 30. 
 
 7 // 
 
 Mar. 1. 
 
 2| // // 
 
 Discounts on merchants' bills are generally calculated the 
 same way as m Commission. 
 
49 
 
 INSURANCE 
 
 Is a contract by which an individual or company, in con- 
 sideration of a certain allowance called premium, agrees 
 to repay the owners of the goods, or other property in- 
 sured, any loss or damage which they may have sus- 
 tained to the amount stated in the written agreement or 
 Policy of Insurance. 
 
 The policy of insurance in this country must be written 
 on Stamped Paper, the amount of which is called Policy-duty, 
 and is always charged upon exact hundreds ; thus, if the sum 
 insured be £510 or £570, the duty is charged on £600. 
 
 The calculations are made the same way as in Commis- 
 sion and Brokerage. 
 
 Ex. 1. Find the insurance on £310 at 3s. 6d. per cent., 
 and policy-duty 2s. 6d. per cent. 
 
 3s. 6d. per cent, on £310 = £0, 10s. lO.^d. 
 
 2s. 6d. " » on 400 = 10 
 Sum required for insuring £310 = £1, Os. 10|d. 
 
 1. What must be paid for insuring £920 at 3s. 6d., 4s., 
 OS. 6d., 6s. 3d., 12s. 3d., and 13s. 4d. per cent.? 
 
 2. What is the premium for insuring property to the 
 amount of £3530 at 2i, 3i, 4^, 5^^^ H gu- and 3^ gu. 
 per cent. ? 
 
 3. What must be paid for insuring £4350 at £4^, £2, 
 2s. lOd., £3, Is. 6d., 2igu., 3^ gu., 3| gu. per cent., and 
 policy 3s. per cent. ? 
 
 4. What is the expense of insuring £12500 on the ship 
 Isabella from Leith to Calcutta, at 2i gu. per cent., policy 
 2s. 6d. per cent., and commission \ per cent. ? 
 
 5. Insured £12520 on a ship at 5 gu. per cent., and 
 policy 3s. per cent. ; she received damage to the extent 
 of £3250 ; what sum will be recovered, allowing If per 
 cent, discount on the loss ? * 
 
 6. Insured £14350 on the ship Ohio from Leith to New 
 Orleans at 4^ gu. per cent., policy-duty 2s. 6d. per cent., 
 and commission i per cent. ; she received damage tc 
 
 * To find the sum recovered, from the amount of the damage, 
 subtract the premium and other charges. 
 
50 INSURANCE. 
 
 the amount of £2580 ; hoAv much will be recovered, al- 
 lowing 2^ per cent, discount on the damage ? 
 
 7. Insured £6750 on a ship at 7^ gu. per cent., £10050 
 on the cargo at 3| gu. per cent, and £500, the net 
 freight at 5 gu. per cent. ; the policy-duty was | per 
 cent, and commission i per cent. ; required the whole 
 expense of insurance. 
 
 Ex. 2. What sum must be insured to recover £7700 
 at 2^ gu. per cent., policy 5s. per cent., and commission 
 17s. 6d. per cent., in case of total loss? 
 
 Sol. From I £100— (£2,12s.6d.+5s.+17s.6d.)=£96,5s. 
 £100 subtract | and £96, 5s. : £100 : : £7700 : : £8000 sum. 
 the rate and other charges; then state, as the remainder 
 (£96, 5s.) is to £100, so is the given sum (£7700) to the sum 
 to be insured (£8000). 
 
 How much must be insured to recover in case of total 
 loss, 
 
 8. £2365 at 5gu. per cent., and policy 3s. per cent.? 
 
 9. £4459 at If gu. per cent., and policy 5s. per cent.? 
 
 10. £1384, 10s. on a single voyage at 6|- gu. per cent., 
 policy 5s. per cent., and commission f per cent. ? 
 
 11. What must be insured on a ship worth £6750, and 
 the value of the cargo £15954, to cover the whole value; 
 premium 8 gu. per cent., policy 5s. per cent., and com- 
 mission ^ per cent. ; 3^ per cent, to be returned if the 
 ship sailed with convoy, which she did ? 
 
 Ex. 3. How much must be insured on a voyage out 
 and home to cover £9120, 5s. at 3| gu. per cent., policy 
 5s. per cent., and commission -^^ per cent. ? 
 
 Here £100— (£3, 18s.9d.-f 5s.+6s.3d.) = £95,10s.; hence 
 by Comp. Proportion / £95^ : £1 00 : : £9120, 5s. : £10000 sum. 
 I 95^: 100 
 
 How much must be insured on a voyage out and home 
 to cover, 
 
 12. £223729 at 4igu. p. c, pol. 5s. p. c, & com. 8s. 6d. p. c. ? 
 
 13. £145924 // 3|-gu. // ^ 3s. // // lOs. 
 
 14. £580326 // 5^gu. // '^ 5s. /^ // 13s.6d. '// 
 i5.£157323// 7^gu. // // 6s. // // 5s.6d. // 
 
INSURANCE. 51 
 
 16. Insured 250 hlicls. sugar, at £24 per lihd., from Ja- 
 maica to Leitli, at 10 gu. per cent. ; policy-duty 5s. per 
 cent., and commission | per cent. ; to return 5 per cent, 
 if the ship sailed with convoy and arrived, which she did . 
 on her arrival, however, it was found that 200 hhds. only 
 were shipped : required the sum due to the insurers. 
 
 Note. The insurers charge ^ per cent, on the value of the 
 goods not shipped, in returning the premium upon them. 
 
 17. Insured 350 chests of tea, at £12, 10s. per chest, 
 from Canton to Leith, at 9i gu. per cent. ; policy-duty 
 5s. per cent., and commission 5s. lOd. per cent. ; to re- 
 turn 4 per cent, if the ship sailed with convoy and arrived, 
 which she did : on her arrival it was found that only 300 
 chests were shipped, and these were so much damaged 
 that they sold only for £11, 10s. per chest; whereas, 
 had they been undamaged, they would have brought 
 £13, 16s. : how much is due by the underwriters ? 
 
 STOCKS. 
 Stock is the name given to the money borrowed by 
 government to defray the expenses of the nation ; it is 
 also the term applied to the capital of any bank, rail- 
 way, or trading company. 
 
 AVhen £100 of stock is sold for £100 sterling, the price of 
 stock is said to be at par ; the price of stock, however, is 
 continually fluctuating. When we see the 3 per cents, 
 quoted at 93, it signifies that £93 sterling is the selling price 
 of £100 stock, and that £3 is the annual dividend on £100 
 stock, or £93 sterling. 
 
 Stock is bought and sold through the agency of brokers, 
 who charge usually i per cent, on the amount of the 
 stock for their trouble. 
 
 The following examples illustrate the several cases 
 which are met with in stocks : 
 
 Ex. 1. How much 3 per cent, stock at 93 can be purchased 
 for £3131, 7s. 9d.? 
 
 Here £93 : £3131, 7s. 9d. : : £100 : £3367, Is. 8d. stock. 
 
 Ex. 2. How much will be received by selling £2150 Bank 
 stock (7 per cent.) at £220^, and brokerage ^ per cent. ? 
 
 Here £220^ — | = £220 sum received for £100 stock. 
 Hence £100 : £2150 : : £220 : £4730 sum received. 
 
52 STOCKS. 
 
 Ex. 3. What rate per cent, is derived from the 3 per cents, 
 at £96? £96 : £100 sterling : : £3 : £3i per cent. 
 
 Ex. 4. How much must be invested in Russian 5 per cents. 
 at 104i to produce an annual income of £300, allowing ^ per 
 cent, for brokerage? Here 104^ + 5 = 104|. Hence 
 £5 : £300 : : £104| : £6262, 10s. sum to be invested. 
 Ex. 5. At what rate should money be invested in the 4 per 
 cents, to yield 3^ per cent, interest? 
 
 Sol. 3^ : 4 : : £100 : £114f per cent. 
 
 1. How mucli stock can be purchased for £68728, Os. 
 O^d. in the 3 per cents, at 91^, 91 J. 92, 92 1, 93, 93-», 
 93i, and 93j per cent. ? 
 
 2. How much sterling money will be required to pur- 
 chase £5750, 3 per cent, stock at 92|, 92^, 92i, 93, 93^, 
 and 93^ per cent., including brokerage ^ per cent.? 
 (Here £100 stock will cost | more tlian the prices given.) 
 
 3. Find the yearly income derived from investing £6012, 
 7s. O^d. in the 4 per cents, at 84, 84i, 85, 85^, 88, and 92^. 
 
 4. What rate per cent, is derived from the Russian 4^ 
 per cents, at 95, 95j, 95i, 96, 96f , and 99 ? 
 
 5. How much sterling must be invested in the 4 per 
 jcnts. at 83^ to produce an annual income of £252, 10s.? 
 
 6. At what rate should money be invested in Bank 
 stock to produce 3^, 3f , 4, 4i, 4^, and 5 per cent. ? 
 
 7. What is the price of India stock (lOi per cent.), when 
 £4752 can purchase £1728 stock? 
 
 8. What is the price of the 3 per cents., when £3412, 
 lOs. invested in them produces £105 per annum? 
 
 9. If £8932 be invested in the 3j per cents, at 101^, 
 and sold out at 102| ; what difference will it make in my 
 income to reinvest the proceeds in Bank stock at 220? 
 
 10. When the 3 per cents, are at 93, India stock at 
 230, and Bank stock at 208 ; which is the preferable 
 investment, including brokerage -| per cent. ? 
 
 11. Invested £3196 in the 3 per cents, at 94, and was 
 obliged to sell at 92-| ; what was the whole loss ? 
 
 12. Invested £5194 in Danish 3 per cents, at 53, and 
 sold out so as to gain £294 ; at what price was it sold ? 
 
 13. Invested £3570 in Bank stock at 212|, and sold 
 out at 228^ ; what is gained, allowing -| per cent, for 
 brokera<2fe ? 
 
STOCKS. 5.3 
 
 14. How mucli is derived annually by investing £5590 
 in India stock at 215 per cent. ? 
 
 15. A has £2400 in 3 per cents. ; how much must he 
 invest in 3^ per cents, at 84 to have an income of £350 V 
 
 16. At what rate must money be invested in Russian 
 4i per cents, to yield 3| per cent. ? 
 
 17. If £2261 be invested in 3 per cents, at 84, and sold 
 out at 85 J ; what difference will it make in my income 
 to reinvest the proceeds in Dutch 4 per cents, at 95? 
 
 18. How much 3 per cents, at 99 f must be sold out to 
 pay a debt of £931 ? 
 
 19. A father leaves his son ^ of his fortune in 3 per 
 cent, stock, i in the 3| per cents., and the remainder 
 £2100, in 4 per cent, stock ; what is his annual income ? 
 
 20. Invested £3683 in Russian 4 J- per cents, at 95}, and 
 sold out so as to gain £43-5 ; at what price was it sold ? 
 
 EQUATION OF PAYMENTS 
 
 Is the method of finding the time when two or more 
 debts due at different periods may be discharged at one 
 payment without loss to either party. 
 
 Ex. Find the time for discharging at one payment 
 £300 due in 3 mo., £200 in 4i mo., and £400 due in 6 mo. 
 
 Sol. Multiply each sum by its 3 X 300 = 900 
 respective time (3 X 300, &c.) ; then 4^- X 200 = 900 
 divide the sum of the products 6 X 400 = 2400 
 (4200) by the sum of the debts (900). 9^00 ) 4200 
 
 Ans. 4§ mo. 
 Find the time for discharging at one payment, 
 
 1. £40 due in 3 mo., £45 in 4 mo., and £55 in 6 mo. 
 
 2. £110 due in 72 da., £140 in 84 da., £200 in 96 da., 
 and £240 in 108 days. 
 
 s. £300 due in 210 da., £420 in 340, £500 in 365 da. 
 
 4. A debt, -i of which is due in 6 mo., | in 7 mo., ^ in 
 9 mo., and the remainder in 10 months. 
 
 5. A debt, i of which is due on Christmas-day, ^ on 
 Whitsunday, -J on Nov. 11, and the rest on Jam 1. 
 
 6. A debt, -^ of which is due on March 14th, and \ on 
 the 14tli of each succeeding month. 
 
54 EQUATION OF PAYMENTS. 
 
 The following exercises may be solved in a similar mamier: 
 What is the average price per qr. of, 
 • 7. 40 qrs. wheat at 60s. 6d. per quarter, 20 qrs. at 65s., 
 30 qrs. at 75s. 6d., and 60 qrs. at 80s. ? 
 
 8. 12 qrs. barley at 42s. per qr., 18 at 45s., 20 at 
 39s., 24 at 36s. 6d., 30 at 45s., and 36 qrs. at 43s. 4d. ? 
 
 9. 10 qrs. oats at 25s. per qr., 20 qrs. at 23s. 6d., 25 
 qrs. at 26s., 30 qrs. at 26s. 6d., and 45 qrs. at 27s. ? 
 
 10. A wine-merchant mixes 5 gals, sherry at 28s. per 
 gal., Avith 8 gals, at 30s. 9d., 10 at 36s., 12 at 42s. 8d., 
 and 16 at 42s. 6d. ; what is the average price per gal. ? 
 
 11. A grocer mixes 12 lbs. tea at 3s. 4d. with 42 lbs. 
 at 3s. 8d., 25 lbs. at 4s., 28 lbs. at 4s. 3d., and 30 lbs. at 
 4s. 6d. ; what should the selling price per lb. of the mix- 
 ture be to gain £4, lis. 4d. upon the whole ? 
 
 12. 8 oz. of gold, 24 carats fine, are melted with 16 oz. 
 23 carats fine, 18 oz. 21-| carats fine, and 20 oz. 18 carats 
 fine ; what i^ the average fineness of the mixture per oz. ? 
 
 DISTRIBUTIVE PROPORTION 
 
 Is the method of dividing a number into parts propor- 
 tional to as many given numbers. This rule is employed 
 to divide the gain or loss of a company in proportion to 
 the shares or stocks of eacli partner, and is then termed 
 Felloivship or Partnership^ which is either Simple or 
 Compound: Simple Fellowship, -when each partner's gain 
 is proportional to his stock only ; Compound Fellowship, 
 when each partner's gain is proportional to his stock 
 and the time of its being employed. 
 
 SIMPLE FELLOWSHIP. 
 
 Ex. Three merchants, A, B, and C, in company, gain 
 £420; A\s stock is £500, B's £400, and C's £300: re- 
 quired eacli man's share of the gain. 
 
 Sol. Add the ^^00 + £400 + £300 = £1200 
 
 stocks; then state ^1200 : £500 : : £420 : £175 A's share. 
 asthesum(£1200) 1200: 400:: 420: 140 B's >• 
 IS to each part- 1200 : 300 : : 420 : 105 C's .> 
 ner's stock, so is Whole gain, £420 
 
 the gain (£420) to each partner's gain. 
 
DISTRIBUTIVE PROPORTION. 55 
 
 1. Divide 7020 into 3 parts proportional (1) to tlie niim- . 
 bers 55, 65, and 75, and (2) to the numbers 3, 4, and 5. 
 
 2. Three merchants, X, Y, and Z, gain by trade £225 ; 
 X's stock is £425, Y's £350, and Z's £225 : find each 
 man's share of the gain. 
 
 3. A bankrupt owes £1470 ; A's claim is £350, 17s. 
 od., B's £415, 8s. 9d., C's £420, 16s. 3d., and D's the 
 rest ; his effects amount to £980: what will each receive? 
 
 4. Divide 4428 into 3 parts proportional (1) to the num- 
 bers 2, 3, and 7, and (2) to the fractions a, i, and i. 
 
 5. A tax of £2997 is to be raised from 4 towns ; the 
 number of inhabitants in each is respectively 2100, 2400, 
 3000, and 3600 : how much should each town pay ? 
 
 6. Three graziers, L, M, and N, rent a park for £104, 
 7s. 6d. ; L puts in 12 oxen and 8 horses, M 8 oxen and 
 12 horses, and N 10 oxen and 10 horses ; how much 
 ought each to pay, if 2 oxen eat as much as 3 horses ? 
 
 7. Gunpowder consists of 74-8 parts of nitre, 13*3 of 
 charcoal, and 11*9 of sulphur ; how much of each will be 
 required to make 214 cwt. 32 lbs. of gunpowder? 
 
 8. Gun-metal consists of 100 parts of copper and 11 of 
 tin ; how much of each of these is there in a brass-gun 
 which weighs 19 cwt. 3 qrs. 8 lbs. ? 
 
 9. Divide £1620, 15s. among D, F, and E, giving D 6 
 as often as F 5, and E 4 as often as F 5. 
 
 10. A pound troy of sterling silver consists of 37 parts 
 of pure silver and 3 parts of alloy, and is coined into 
 66s. ; how much of each is in 231s. ? 
 
 11. A pound troy of sterling gold consists of 22 carats 
 of pure gold and 2 carats of alloy, and is coined into 
 £46-725 : what quantity of each is there in £700, 17s. 6d. ? 
 
 12. 37 ac. 3 ro. 2 per. of ground is to be divided among 
 three persons. A, B, and C, in proportion to their estates ; 
 A's being worth £560 a-year, B's £640, and C's £700 : 
 what part should each receive ? 
 
 13. Four companies of 60, 56, 52, and 36 men, require to 
 furnish 51 men daily for a particular duty, in proportion 
 to their strength ; how many must each furnish ? 
 
 14. A gentleman hired a carriage for 40 miles for £5, 
 5s. ; at the 10th milestone he admits 3 others, and at the 
 15th milestone other two : what should each pay? 
 
56 DISTRIBUTIVE PROPORTION. 
 
 COMPOUND FELLOWSHIP. 
 Ex. A and B enter into partnership ; A contributes 
 £500 for 5 months, and B £630 for 10 months ; they 
 gained £572 : what share of the gain should each receive? 
 Sol. Mult, eachpart- 500 X 5 = 2500 
 
 ner's stock by the 630 X 10 = 6300 
 
 time it continues, Sum of prod. =. ggQQ 
 
 then State as the gSOO : 2500 : : £572 : £162, 10s. = A. 
 sum of the products 8800 : 6300 : : 572 : 409, 10s. = 13. 
 
 and 6300), so is the whole gain (572) to each partner's gain. 
 
 15. L and M enter into partnership ; L advances £525 
 for 6 months, and M £375 for 8 months ; they gain 
 £221, 8s. : what is the share of each? 
 
 16. A, B, and C, engage in trade ; A's stock of £1200 
 continues for 8 months, B's of £1575 for 10 months, 
 and C's of £1455 for 12 months ; they gain £998, 18s. : 
 what is each man's share ? 
 
 17. X, Y, and Z, rent a grass-park for £39, 19s. ; X put8 
 in 12 oxen for 4 months, Y 15 for 6 months, and Z 18 foi 
 8 months : what part of the rent should each pay? 
 
 18. E, F, and G, enter into company; E advances 
 £1200 at the first, after 3 mo. F advances £1400, and 
 after 5 mo. G advances £1600; the whole gain during 
 12 mo. was £573 : required each man's share. 
 
 19. A and B engage in trade for 12 months ; A advan- 
 ces at first £1200, and after 7 mo. withdraws £500 ; and 
 B advances at first £800, and after 5 mo. £400 more ; 
 they gain £2004, 15s. : how much of it belongs to each ? 
 
 20. The wages of A and B for 4 weeks amount to £12, 
 19s. ; A works 9 hours a-day for f of the time, and 10.^ 
 ho. a-day for the rest of the time ; while B is idle one 
 day a-week, and works 11 ho. a-day the rest of the week : 
 how much of the wages should each receive ? 
 
 21. A, B, and C, rent a grass-park for 14 months at a 
 rent of £97 ; A put in 20 oxen, and paid £30 ; B put in 
 25 oxen, and paid £40 ; and C put in 36 oxen, and paid 
 the remainder : how long should each hold the park ? 
 
 Note. Each party's proportional is here found by dividing the 
 sum which he paid by the number of oxen he put into the park ,* 
 thus, A's proper, is here 30 -^ 20 = 1^, &c. 
 
DISTRIBUTIVE PROFORTIOX. 57 
 
 22. Four graziers rented a field for 9 mo. at a rent of 
 £80 ; A pat in 120 sheep, and paid £14 ; B 30 oxen, and 
 paid £24; C 180 sheep, and paid £18 ; and D 36 oxen^ 
 and paid the remainder : liow long should each man re- 
 tain the field, if 5 sheep eat as much as an ox ? 
 
 23. A common, consisting of 506 ac. 23 per., is to be 
 divided among 4 persons. A, B, C, and D, whose estates 
 on which their claims are founded are respectively 
 £8000, £7500, £6400, and £6000 yearly, while the value 
 of the land allotted to each is 64s., 60s., 50s., and 48s. per 
 acre : what quantity of the land should each receive ? 
 
 24. Tlie gain of three merchants was £802, 10s., of which 
 A's share was £360, B's £262, 10s., and C\s the remain- 
 der ; now A's stock of £4000 continued 6 mo., B's 5 mo., 
 and C's 4 mo. : what was the stock of each ? 
 
 PKOFIT AND LOSS 
 Is that branch of Arithmetic which treats of the gains 
 and losses of merchants, and which enables them to fix 
 the prices of their goods so as to gain or lose so much 
 per cent, upon them. 
 
 The price at which goods are bought is called the 
 prime cost, tlmt at which they are sold the selling pt^ice ; 
 when the selling price is greater than the prime cost^ 
 the difference is called gain, otherwise it is called loss. 
 
 The calculations are made by means of the Compound 
 Rules, Practice and Simple & Compound Proportion. 
 
 Ex. 1. Bought tea at £21 per cwt., and sold it at 4s. lO^d. 
 per lb. ; what was the gain or loss per cwt. and per lb. ? 
 
 Obs. The S. P. being 
 greater than the P. C. 
 per cwt., the difference 
 (£6, 6s.) is the gain per 
 cwt., from which the 
 
 S. P. of 112 lbs. at 4/101 — £27,6s. 
 Prime cost of do. =21 
 
 Gain per cwt. = £6, 6s. 
 £6, 6s. H- 112 = 1/1^ gain per lb. 
 gain per lb. is found by dividing by 112. 
 
 Ex. 2. Bought tea at 3/9 per lb. ; at what price should it 
 be sold per lb. to gain 10 per cent.? Obs. £100 worth is 
 sold for £110; hence £100 : £110 : : 3/9 : 4/1^ S. P. per lb. 
 
 Ex. 3. Bought tea at 3/9 per lb., and sold it at 4/1^ ; what 
 was the gain per cent. ? Obs. 4/1 1 — 3/9=4^d. is the gain on 
 8/9; hence 3/9 : 4id. : : £100 : £10 the gam per cent. 
 
58 PROFIT AND LOSS. 
 
 Ex. 4. Gained 10 per cent, bv selling tea at 4/1^ per lb. ; 
 what was the P. C. per lb. ? Sol. £110 : £100 : : 4/1^ : 3/9 
 P. C. per lb. 
 
 Ex. 5. Bought sugar at 37/6 per cwt. ; at what price should 
 it be sold to lose 8 per cent. ? Obs. £100 worth is sold for 
 £92 ; hence £100 : £92 : : 37/6 : 34/6 S. P. per cwt. 
 
 Ex. 6. Gained 7^ per cent, by selling coffee at 1/9^ per lb. ; 
 what is gained or lost per cent, by selling it at 1/10 per lb. ? 
 Sol. 1/9| : 1/10 : : 107^ : 110, & 1 10— 100=£10 per cent. gain. 
 
 Ex. 7. Bought goods at 15/3 and 4 months' credit, interest 
 at 5 per cent. ; at what rate should they be sold to gain 6 
 per cent., and allow a discount of 4 per cent. ? 
 For the 4 months' cred. 101§ : 100 : : 183d. : 16/6| S. P. 
 " the gain ... 100 : 106 
 
 " the discount . . 96 : 100 
 
 1. Bought 3 cwt. 3 qrs. 14 lbs. of tea at 3s. 9d. per lb. and 
 sold it at £23, lis. 4d. per cwt. ; what was the gain per lb., 
 per cwt., and on the whole? 
 
 2. Bought 4 casks sugar, each 3 cwt. 2 qrs. 21 lbs., at od. per 
 lb. ; what should the whole be sold for to gain 14s. per cwt ? 
 
 3. Sold 143 yds. at 10s. 3d. per yd. and gained £13, 8s. l^d. ; 
 what was the P. C. of 1 yd. and of the whole ? 
 
 4. Bought muslin at Is. 4^d. per yd. ; how should it be soh 
 to gain 7^ per cent. ? 
 
 5. Bought soap at 4|d. per lb., and sold it at 5|d. ; how many 
 lbs. must be sold to gain 13s. 9d. ? 
 
 6. Sold 326 dozen wine at 31s. 6d. per doz. and gained 
 £24, 9s. ; what was the P. C. of 1 doz. and of the whole ? 
 
 7. How much per cent, is gained by selling Is. worth of 
 goods for Is. l^d. ? 
 
 8. Bought goods at £3, 6s. 8d. ; how should they be rated to 
 gain 4 p. cent., and allow the purchaser a discount of 5 p. cent.? 
 
 9. Bought sago at 70s. per cwt., and sold it at 73s. 6d. ; 
 what was the gain per cent. ? 
 
 10. Gained 3^ per cent, by selling 126 yds. of cambric for 
 £48, 16s. 6d. ; what was the P. C. per yd. and of the whole? 
 
 11. Bought linen at 3s. 2d. per English ell, and sold it at 
 the same per yd. ; what was the gain or loss per cent. ? 
 
 12. At what price should a yard of gingham which cost 
 Is. 5d. a-yard, be sold to gain 15s. 8|d. on 151 yds.? 
 
 13. Lost 4* per cent, by selling goods at £72, lis. 3d.; 
 what was their prime cost ? 
 
 14. Gained 10 per cent, by selling coffee at £10, 10s. lOd. 
 per cwt. ; what was the prime cost per cwt. and per ton? 
 
PROFIT AND LOSS. 59 
 
 15 Bought 4 cwt. 3 qrs. 21 lbs. of raisins at 98s. per owt. ; 
 how much per cent, was gained by selling the whole for 
 £28, 2s. lO^d., the expenses of the sale being 16s. 5|d.? 
 
 16. Grained 3^ per cent, by selling tea at 5s. 3d. per lb. ; 
 what was gained or lost per cent, by selling it at 5s. per lb. ? 
 
 17. The prime cost of a book is 6s. 8d., the expense of sell- 
 ing is 3 per cent., and the gain is 12 per cent. ; what is the 
 selling price of 40 copies of the book ? 
 
 18. Lost 3 J per cent, by selling butter at 16s. 3|d. per stone ; 
 what was gained or lost per cent, by selling it at 1 s. 4d. per lb.? 
 
 19.. By selling 5 apples for 2d., 3 per cent, is gained; what 
 is gained or lost per cent, by selling 18 for 6d. ? 
 
 20. How much per cent, is 2s. 6d. profit per £1 ? 
 
 21. Bought 50 reams of paper at 18s. 6d. per ream; 3 per 
 cent, was lost in selling : what was the whole loss ? 
 
 22. A merchant bought 252 gallons of wine at 35s. 6d., but 
 J of it being damaged, he sells it at a loss of 2^ per cent. ; 
 how must he rate the remainder per dozen to gain 5 per cent, 
 on the whole ? 
 
 23. Bought 4 casks of brandy, each 126 gallons, at 5s. 3d. 
 a -bottle : now each cask leaked a gallon ; how should the re- 
 inainder be rated per gallon to gain 10 per cent, and allow a 
 discount of 4 per cent. ? 
 
 24. Bought a horse for £40, and sold it for £45, and 3 mo. 
 credit, interest at 5 per cent. ; required the gain. 
 
 25. Purchased 108 yds. of cloth at 18s. 9d. a-yd., but being 
 damaged, I am willing to lose 5 per cent, in selling it ; for how 
 much must a yard and also the whole be sold ? 
 
 26. A buys goods to the amount of £2025, and sells them 
 to B for £2250, who in turn disposes of them to C at a profit 
 of 4 per cent. ; how much per cent, above their prime cost 
 did C pay for them ? 
 
 27. Bought 350 qrs. of wheat at £2, 12s. 6d. per qr., and 
 sold f of them at a profit of 7^ per cent., and the rest at a 
 loss of 2^ per cent. ; what was gained upon the whole? 
 
 28. Purchased 4350 yds. of linen at 2s. 7^d. per yd., and 
 field i of the whole at 2s. 8^d., | at 2s. 9d., and the remain- 
 der at 10 per cent, profit; requu-ed the price of the remain- 
 der per yd., and the gain upon the whole. 
 
 29. By selling an article for £43, 10s. I lost 3 J per cent., 
 and recovered the loss by selling another for £19, 10s. ; what 
 was the gain per cent, on the second article ? 
 
 30. Bought sugar at 70s. per cwt. ; how must I sell it per 
 cwt. to gain 5 per cent., and allow the purchaser a discount 
 of 4 per cent, and 4 months' credit, interest at 6 per cent. ? 
 
60 
 
 EXCHANGE 
 
 Is the method of valuing the money of one country in 
 that of another, according to a certain rate. 
 
 The intrinsic value of the money of one country com- 
 pared with that of another is called the Par of Exchange, 
 and is determined by the weight and fineness of their coins. 
 
 The Com'se of Exchange at any time is the value of a 
 fixed sum of the money of one country estimated in that 
 of another : from various circumstances this is contin- 
 ually fluctuating. In some countries, money is distin- 
 guished into Banco and Currency, or into Specie and 
 Paper money, — the former being more valuable than 
 the latter by a certain rate per cent., which is called 
 agio, discount or premium. 
 
 TABLES OF FOREIGN MONEYS. 
 
 France. — 100 centimes=10 decimes=l franc=9^d. ster. 
 nearly. Par of exch. with London in gold, 25 francs 22 cents 
 for £1 ster. ; in silver, 25 francs 57 cents for £1 ster. 
 
 Holland and Belgium.— 100 cents = 20 stivers = 1 florir 
 = Is. 8d, Par of exch. with London, 12 fl. 9 cents for £1. 
 
 Hamburg. — 192 pfennings — 16 schillings = 1 mark. 
 3 marks or 48 schillings = 1 rixdoUar of exchange. 
 Par of exch. with London, 13 marks 10^ sch. for £1 ster. 
 Money is here divided into banco and currency ; the agio 
 fluctuates between 20 and 25 per cent. Accounts are kept 
 in currency, and exchanges are made in banco. 
 
 Portugal. — 1000 reas = l milrea=:57p. ster.; 400 reas 
 = 1 crusado, and 1000000 reas = 1 conto = £239, lis. 8d. 
 ster. The discount on paper money is about 24 per cent. ; ex- 
 change money is ^ in paper. 
 
 Russia. — 100 copecs=: 1 silver ruble = 37 Jd. ster 
 1 paper ruble = 10| ster. nearly. 
 
 Turkey. — 40 paras = 1 piastres 2 |d. ster. Par of exch. 
 with London, 100 piastres for £1 ster. 
 
 North America and West Indies. — £100 ster. at par == 
 £llli currency, or £100currency= £90 ster. In Jamaica, 
 £1661 currency = £100 ster. 
 
 United States. — 100 cents=10 dimes=1 dol.=4s. 6d. ster. 
 The par of exch. with London was originally 4| dol. for £1 
 Bter. ; this value being now too small, a variable premium 
 of 9 or 10 per cent, is added to the par value. 
 
EXCHANGE. 61 
 
 East Indies. — 192 pice = 16 annas = 1 sicca rupee = 2 s. 
 ster. nearly. 116 current rupees =100 sicca rupees; 
 100000 rupees = a lac, and 10 million rupees =: a crore. 
 
 The Calculations of Exchange are made by means of 
 Proportion or Practice. 
 
 Ex. How much sterling money is equal to 750 copecs, 
 exchange at 3s. 2id. per ruble ? 
 Sol. 100 copecs : 750 copecs : : 3s. 2^d : £1, 4s. Ofd. ster. 
 
 1. How much sterling money in 11619 francs 30 cents, 
 and in 21126 fr., exch. at 25 fr. 20 cents, and at 25 fr. 15 
 cents per £1 ster. ? 
 
 2. In £420, 17s. 6d. and £580, 13s. 4d., how much French 
 money, exch. at 25 fr. 20 cts., and 25 fr. 16 cts. per £1 ster. ? 
 
 3. How much sterling money in 2145 marcs 15 sch. and in 
 5845 marcs 2 sch., exch. at 13 marcs 10 sch. and 13 marcs 
 8 sch. per £1 ster. ? 
 
 4. In 456325 reas, and in 874625 reas, how much sterling, 
 exch. at 56d. and at 57|d. per milrea ? 
 
 5. In £212, 17s. 6d. and in £318, 2s. 6d., how much money 
 of Holland, exch. at 12 fl. 8 cts. and at 12 fl. 9 cts. per £1 ster.? 
 
 6. How much Turkish money in £124, 5s. and in £340, 7s. 
 6d., exch. at 100 piastres, and at 103^ piastres per £1 ster.? 
 
 7. How much sterlhig money in 100 rubles 50 copecs, and 
 in 1825 rubles 25 copecs, exch. at lOd. and 10|d. per ruble? 
 
 8. How much Hamburg currency in £360, and in £756, 13s. 
 4d., exch. at 13 marcs 8 sch. banco per £1 ster., agio 20 per 
 cent., and at 13mar. 1 sch. banco per £1 ster., agio 2 5 p. cent.? 
 
 9. How much sterling in 435 rupees 9 annas, and in 750 
 rup. 5 an. 8 pice, exch. at 2s. and 2s. 4d. per rupee? 
 
 10. How much United States cun-ency in £250, 12s. 6d., 
 and in £742, 17s. 6d., exch. at 4| dollars per £1 ster., pre- 
 mium 8 and 10 per cent. ? 
 
 rr: How much sterling in £364, and in £1008 Canadian 
 currency, exch. at 112 and 112^ per cent.? 
 
 12. How many current rupees in £376, 5s. and in £980, 
 exch. at 2s. and 2s. O^d. per sicca rupee? 
 
 13. How many rupees in 3452 dollars 80 cents, and in 5179 
 dol. 20 cents, exch. at -415 dol. and '416 dol. per rupee? 
 
 14. How much Hamburg currency in 706 francs 70 cents, 
 and in 869 francs 50 cents, exch. at 100 marcs banco for 185 
 francs, agio 20 and 25 per cent. ? 
 
 15. In 11880 milreas current, and in 10560 milreas current, 
 how much ster. at 56d. per milrea, agio on paper money 20 per 
 cent., and at 57}d. per mil., agio on paper money 24 p. cent.? 
 
62 
 
 DUODECIMALS 
 Is a method employed for multiplying feet and inches, 
 &c. by feet and inches, &c. 
 
 A foot is divided into 12 inches, an inch into 12 parts or 
 primes, and a prime into 12 seconds. 
 
 Ex. Multiply 6 ft. 3 in. 4 pts. by 7 ft. 2 in. 5 pts. 
 
 Sol. Arrange the numbers so that 
 ft. may be below ft., in. below in., &c. 
 Multiply by the ft. (7) in the multi- 
 plier as in Compound Multiplica- 
 tion ; in the same way, multiply by 
 the inches (2), but write the pro- 
 duct one place nearer to the right 
 hand ; again, multiply by the parts (5), and write the pro- 
 duct one place nearer to the right hand than the last ; then 
 add the separate products, carrying at 12. 
 
 The answer is 45 s. ft., 2 twelfths of a s. ft., six 144ths 
 of a s. ft. {i. e. 6 s. in.), and eight 144ths of a s. in. ; now 2 
 twelfths = twenty-four 144ths ; hence the answer may be 
 written 45 s. ft. (24 + 6 y^^) s. in. = 45 s. f. 30 y?^ s. in. 
 
 6 ft. 3 in. 4 pts. 
 
 7 2 5 
 
 
 43 11 4 
 
 12 6 8 
 31 4 
 
 8 
 
 45 2 6 8 
 
 
 ft. 
 
 in. 
 
 pt. 
 
 
 ft. 
 
 in. 
 
 pt. 
 
 ft. 
 
 in. 
 
 pt. 
 
 ft. in. 
 
 pt. 
 
 1. 
 
 7 
 
 4 
 
 6 
 
 X 
 
 4 
 
 6 
 
 
 
 5 
 
 7 
 
 
 
 6 4 
 
 
 
 2. 
 
 10 
 
 5 
 
 3 
 
 X 
 
 3 
 
 5 
 
 
 
 4 
 
 3 
 
 
 
 10 5 
 
 
 
 3. 
 
 11 
 
 6 
 
 9 
 
 X 
 
 2 
 
 2 
 
 4 
 
 3 
 
 4 
 
 8 
 
 6 11 
 
 9 
 
 4. 
 
 12 
 
 8 
 
 4 
 
 X 
 
 3 
 
 6 
 
 9 
 
 7 
 
 3 
 
 6 
 
 9 10 
 
 3 
 
 5. 
 
 15 
 
 9 
 
 10 
 
 X 
 
 2 
 
 6 
 
 3 
 
 3 
 
 9 
 
 6 
 
 8 9 
 
 4 
 
 6. 
 
 16 
 
 11 
 
 2 
 
 X 
 
 3 
 
 9 
 
 6 
 
 6 
 
 8 
 
 9 
 
 10 11 
 
 3 
 
 7. 
 
 18 
 
 9 
 
 8 
 
 X 
 
 4 
 
 7 
 
 6 
 
 7 
 
 9 
 
 3 
 
 12 11 
 
 9 
 
 8. 
 
 21 
 
 10 
 
 7 
 
 X 
 
 6 
 
 3 
 
 5 
 
 9 
 
 5 
 
 4 
 
 11 3 
 
 6 
 
 9. 
 
 48 
 
 4 
 
 9 
 
 X 
 
 7 
 
 10 
 
 11 
 
 10 
 
 10 
 
 5 
 
 11 8 
 
 9 
 
 10. 
 
 56 
 
 3 
 
 6 
 
 X 
 
 14 
 
 6 
 
 4 
 
 15 
 
 9 
 
 2 
 
 17 6 
 
 6 
 
 11. 
 
 78 
 
 6 
 
 4 
 
 X 
 
 21 
 
 4 
 
 6 
 
 25 
 
 7 
 
 9 
 
 32 8 
 
 4 
 
 12. 
 
 99 
 
 11 
 
 8 
 
 X 
 
 36 
 
 10 
 
 3 
 
 49 
 
 11 
 
 9 
 
 54 7 
 
 6 
 
 Note. The area of a board is found by multiplying the length 
 by the breadth, and the cubic content by multiplying the length, 
 breadth, and thickness together. 
 
 13. Find the area of a board 4 feet 7 in. broad and 18 feet 
 
 9 in. long. 
 
 U. Find the area of a floor 12ft. 6 in. 4 pts. by 18 ft. 6m. 3pts. 
 
 15. Find the area of a wall 17 ft. 4 in. 6 pts. long and 
 
 10 ft. 6 in. high. 
 
 16. Find the content of a cistern 7 ft. 4 in. long, 6 ft. 6 in. 
 
DUODECIMALS. 63 
 
 deep, and 3 ft. 9 in. wide, and the number of gallons it would 
 contain, each 277J c. in. 
 
 17. Find the cubic content of a block of marble 3 ft. 4 in. 
 long, 2 ft. 10 in. wide, and 1 ft. 8 in. thick. 
 
 18. What is the length of a floor containing 44 s. yd. 96 s. 
 in., whose breadth is 17 ft. 6 in. ? 
 
 19. What length of carpet f wide will cover a floor 22 ft. 
 G in. long and 18 ft. 4 in. broad? 
 
 20. How much paper will be required to cover the walls of 
 a room 27 ft. 8 in. long, 20 ft. 3 in. broad, and 12 ft. 6 in. 
 high? 
 
 21. How many gallons of water must be run off from a 
 cistern 8 ft. 6 in. long, 4 ft. 3 in. broad, and 6 ft. 8 in. deep, 
 to make the surface sink a foot ? 
 
 22. The paving of a court-yard cost £13, 4s. at 5s. 6d. per 
 sq. yard ; how broad is it, its length being 36 ft. ? 
 
 INVOLUTION. 
 
 When a number is multiplied by itself any number of 
 times, the process is called Involution, or the raising 
 of Powers. 
 
 The original number is called the root^ and the products 
 powers of the root. Powers are often indicated by writing 
 the number once, and a small figure (called the index or ex- 
 ponent of the power) a little to the right above the number, 
 denoting how many times the number is to be taken as a 
 factor. Thus, 
 
 5 2=5x5 = 25, is the second power or square of 5. 
 
 53 =5 X 5x5=1 25, is the third power or cube of 5. 
 
 5 7 = 5X5X5X5X5X5X5=78125, is the 7th power of 5. 
 r ^ \K 3X3X3X3X3 243 ,, ^ „,, - _ 
 
 (A)'= 11X11X11X11X1 1 = 161051 = t^^ ^^*^ P^^^^ ^^ I'l- 
 
 It may be noticed that 5^=53 X 5*= 125 X 625 = 78125 
 as above, i. e. the sum of the indices of powers of the same 
 number, is the index of their product. 
 
 1. Find the cubes of 21, 33, 44, 67,89,11-9, l-25,& 1-075. 
 
 2. Raise 24«, 75^, l-05«, 2-15«, •025r and 1-025^ ^-^=£=25^ 
 3.Raise(f)«, (|)«, i^sy, {^%y, GV)^ and(^)^: .^:^ 
 
 4. The side of a square is 11 feet; finS its- area. (ll<*=::r 
 area in s. feet.) X* ' [ i 
 
 5. The side of a cube is 8 feet; find its content. {S^S' " ^ 
 content in c. feet.) c^sr ^ 
 
64 INVOLUTION. 
 
 6. The side of a square court-yard is 22 ft. 6 in. ; what is 
 its area ? 
 
 7. The side of a cubic cistern is 6 ft. 3 in. ; what is its 
 content ? 
 
 8. A cubic foot of quartz weighs 2640 oz. ; required the 
 weight of a piece 4^ in. in the side. 
 
 9. A cub. ft. of chalk weighs 2784 oz. ; find the weight of 
 a column 4 ft. 6 in. in the side. 
 
 10. A cub. ft. of water weighs 1000 oz. ; what weight of 
 water does a cubic cistern contain, whose side is 4 ft. ? 
 
 11. How many dice, i in. in the side, can be cut from a 
 cubic piece of ivory 6 in. in the side ? 
 
 12. How many squares, 3 in. in the side, can be cut from 
 a square piece of pasteboard, whose side is 1 ft. 6 in. ? 
 
 EVOLUTION 
 
 Is the method of extracting the root of a given power. 
 The square root is the method of extracting the second 
 root of a given number, or of finding a number which, 
 when raised to the second power, produces the given 
 number; thus, the square root of 169 = 13, for IS'* = 
 
 The cube root is the method of extracting the third 
 root of a given number, or of finding a number which, 
 when raised to the third power, produces the given num- 
 ber]^ thus, the cube root of 1331 is 11, for 11 ^ = 1331 ; 
 
 The sign V placed before a number indicates that the 
 square root of the number is to be taken ; %/ placed before 
 a number indicates that the cube root of the number is to 
 be taken. 
 
 EXTRACTION OF THE SQUARE ROOT. 
 
 Ex.1. Extract the square root of 9177-64. Ans. 95-8. 
 
 91,77,-64(95-8 root. 
 81 
 185 1077 
 5 925 
 
 Sol. 1. Divide the given num- 
 ber into periods of two figures 
 each, beginning at the units^ 
 figure. 
 
 2. Find the greatest square 
 number in the first period (81), 
 place its root (9) on the right 
 
 1908 15264 
 15264 
 
 of the given number, and subtract its square (81) from the 
 
EVOLUTION. 65 
 
 first period (91) ; then to the remainder (10) annex the next 
 period (77) for a resolvend (1077). 
 
 3. Write the double of the figure in the root for a partial 
 divisor (18), and find how often it is contained in the resolv- 
 end (1077), omitting its right-hand figure (7); place the 
 number of times (5) after the last figure of the root, and after 
 the partial divisor (18), for a complete divisor (185); then 
 multiply the complete divisor (185) by the figure last placed 
 in the root (5), and subtract the product (925) from the re- 
 solvend (1077) : to the remainder (152) annex the next period 
 (64) for a new resolvend (15264). 
 
 4. To the last complete divisor (185) add its right-hand 
 figure (5) for a new partial divisor, and so proceed until all 
 the periods are brought down. 
 
 Note. When there is a remainder, after bringing down the 
 last period, the root may be carried on decimally, by annexing 
 periods of two ciphers each to the remainder. 
 
 The square root of a fraction is found by taking the square 
 roots of its terms, if they are exact squares ; if not, the frac- 
 tion must be reduced to its equivalent decimal and its square 
 root taken. 
 
 Extract the square roots of, 
 1. 5184, 6889,9801, 14884, 17161, 22201, 297025,&958441 
 2.1100401,1279161,3786916,4008004,14356521,60481729 
 3. 9862-4761, 99-980001,56-725, 597-184, 674-85,&948-625 
 4.127-3,2479-6, 118-63, 2459-147, 4-8, 5-4245, & 121-45 
 
 Note. The repeating figures of the decimals must be annexed 
 in their order, in periods of two figures each. 
 
 5.2, 3, 5, 7, 11, 12, 13, 17. and 19, each to 6 places of dec. 
 6-tVt, t%V nh 3^1, Hff, Hi, 14^, 17Vt, and 24f. 
 7. 102030201, 10020210201, and 9018027018009. 
 
 Ex. 2. Find a mean proportional between 9 and 25. 
 
 Ans. 15. 
 
 Sol. V9 X 25 = V225 = 15, for 9 : 15 : : 15 : 25. 
 8. Find a mean proportional between 7 and 28, 15 and 
 135, 24 and 96, 18 and 288, 44 and 396, 19 and 46. 
 
 Note 1. The side of a square equal to any given area is the 
 square root of that area. 
 
 2. Circles are to each other as the squares of their diameters. 
 
 3. In a right-angled triangle, the square of the hypothenuse, 
 or side opposite the right angle, is equal to the sum of the squares 
 of the other two sides. 
 
GQ EVOLUTION. 
 
 9. Find the side of a square to contain 756 s. yds. 
 
 10. A gentleman's estate contains 4851 ac. 1 per., and ho 
 wishes another of equal area in the form of a square ; required 
 its side. 
 
 11. An army of 58564 men is to be formed into a square ; 
 how many men will the front contain ? 
 
 12. The diameter of a circular pond is 540 ft. ; what is the 
 diameter of another 5 times as large ? 
 
 13. Two ships sail from the same port, the one due east 
 180 mis., and the other due south 230 mis. ; what is the dis- 
 tance between them ? 
 
 14. A wall is 83 ft. high ; what length of line will reach 
 from the top to a point 67 feet from its base ? 
 
 15. The wages of a certain number of men amounted to 
 £561, 2s. 6d. at 2s. 6d. per day ; they wrought as many days 
 as there were men employed ; what was the number of men ? 
 
 16. A ladder 84 ft. long reaches from the edge of a ditch, 
 40 ft. wide, to the top of a wall on the opposite side of the 
 ditch; what is the height of the wall? 
 
 17. A room is 48 ft. long, 36 ft. broad, and 16 ft. high ; what 
 is the length of each of the diagonals, and also the diagonal 
 of the contained space ? 
 
 18. What is the length and breadth of a parallelogram 4 
 times as long as it is broad, whose area is 3 ac. ? 
 
 19. 79524 trees 16 ft. distant are planted in a square plan- 
 tation ; what is the length of the side ? 
 
 20. A room as broad as it is high, and 32 ft. 6 in. long, 
 contains 8937 c. ft. 1 254 c. in. ; find the height. 
 
 21. Arrange 24964 soldiers so that the number of men in 
 rank may be 4 times the number in file. 
 
 22. The paving of a square enclosure cost £36, 9d. at 9d. 
 per square yard ; find the length of its side. 
 
 EXTRACTION OF THE CUBE EOOT. 
 
 Ex. Extract the cube root of 12-812904. Ans. 2*34. 
 
 Sol. 1. Divide the 
 given number into pe- 
 riods of 3 figures each, 
 beginning at the units^ 
 figure. 
 
 2. Find the greatest 
 cube number in the first 
 period (8), place its root 
 (2) towards the right of 
 the given number, and 
 subtract its cube (8) from the first period (12); then to 
 
 2"-X 300 
 
 12-812,904 (2-34 
 
 1200 
 
 8 4 
 
 189) 
 
 4812 63X3 
 
 1389 y 
 
 4167 6 
 
 9) 
 
 645904 694 X ^ 
 
 158700 
 
 645904 
 
 2776 
 
 
 161476 
 
EVOLUTION. 67 
 
 the remainder (4) annex the next period (812) for a resolvend 
 (4812). 
 
 3. Write 300 times the square (4) of the figure in the root 
 for a partial divisor (1200), and find how often it is contained 
 in the resolvend (4812), then place the number of times (3) 
 to the right of the figure in the root. Again to the former 
 part of the root (2) add its double (4), to the sum (6) annex 
 the trial figure (3), and multiply this number (63) by it (3) ; 
 then add the product (189) to the partial divisor (1200) for 
 a complete divisor (1389). Multiply this number (1389) 
 by the figure last placed in the root (3), subtract the pro- 
 duct (4167) from the resolvend (4812), and to the remainder 
 (645) annex the next period (904) for a new resolvend 
 (645904). 
 
 4. Place the square of the last figure in the root (9) below 
 the last complete divisor (1389), add it (9) and the two lines 
 above it (189 and 1389) together, and to the sum (1587) 
 annex two ciphers for a new partial divisor (158700). 
 
 5. With this partial divisor find another figure (4), and 
 place it in the root. To the number on the right (63), which 
 was multiplied by the last figure of the root (3), add the 
 double of that figure (6), annex to the sum (69) the new 
 trial figure (4), then multiply the number thus found (694) 
 by the trial figure (4), and add the product (2776) to the 
 partial divisor (158700) for a complete divisor (161476), and 
 so proceed till all the periods are brought down. 
 
 Note. When there is a remainder, after bringing down the 
 last period, the root may be carried on decimally by annexing 
 periods of three ciphers each to the remainder. 
 
 The cube root of a fraction is found by taking the cube 
 roots of its terms when they are exact cubes ; if not, the 
 fraction must be reduced to its equivalent decimal and its 
 cube root taken. 
 
 Extract the cube roots of, 
 
 1. 76765625, 143877824, 260917119, 485587656. 
 
 2. 997002999, 25128-011089, 143795466-919, 865-250742889. 
 
 3. 14-75, 118-62, 1-47825, 7-6, 8-36, 94-8, to 6 places of dec. 
 
 4. 2, 4, 6, 7, 9, 12, 13, 16, to 6 places of decimals. 
 
 5. 1030607060301, 27054306369020601. 
 
 «• Uh mh HU, H, 51, -000000405224. 
 
 Note. Similar solids are to each other as the cubes of their 
 like dimensions. 
 
68 EVOLUTION. 
 
 7. The side of a cubic vessel is 10 in. ; what should be the 
 side of another to contain ^ as much ? 
 
 8. A block of granite is 6 ft. long, 6 ft. broad, and 4 ft. 
 thick ; what are the dimensions of another 3 times as heavy? 
 
 9. A stone is 8^ ft. long, 7 ft. broad, and 5 ft. thick ; what 
 are the dimensions of another 9 times as large, and the side 
 of a cube equal to both ? 
 
 10. A cubic block of marble is 8 ft. in the side ; what are 
 the length and breadth of another 3 times the weight, whose 
 thickness is 3 ft., and length twice the breadth ? 
 
 11. The solid content of a cube is 407 ft. 1673-in. ; how 
 many square ft. are in its surface ? 
 
 12. A vessel contains 411540 c. in., and has its sides in 
 proportion to the numbers 3, 4, and 5 ; what are its sides? 
 
 COMPOUND INTEREST. 
 
 When a sum of money is put out to interest, and its 
 amount at the end of a fixed period is considered the 
 principal for the same period and at the same rate, the 
 original sum is said to be improved at Compound Interest. 
 Case I. Given the principal, rate, and time ; to find 
 the amount and the interest. 
 
 Ex. 1. Find the compound interest of £100 for 3 
 years at 2 per cent, per annum, the interest payable 
 yearly. Here 2 per cent. =: j^-^ = ^\^. 
 
 j5»5 ) £1 00 Principal for 1 st year. 
 
 2 Interest for 1st year, 
 
 jig) 102 Principal for 2d year. 
 
 2*04 Interest for 2d year. 
 3^) 104-04 Principal for 3d year. 
 2-0808 Interest for 3d year. 
 106-1208 Amount at end of 3 years. 
 100 Principal for 1st year. 
 
 £6, 2s. 5d. = £6*1208 Interest for 3 years. 
 
 1. Find the compound interest of £875 for 5 years at 2, 2|, 
 4, 5, 7|, and 10 per cent., the interest payable yearly. 
 
 2. Required the amount of £450, 10s. for 6 years at 2, 2^, 
 4, 5, 7^, and 10 per cent, per annum, compound interest. 
 
 When the number of payments of interest is small, and 
 the rate an aliquot part of 100, this method answers very 
 well. The followiner method is suitable for all cases : 
 
COMPOUND INTEREST. 69 
 
 The amount of £1 for 4 years at 3 per cent., when the in- 
 terest is payable yearly, is that power of the amount of £1 
 for 1 year (1'03) which corresponds with the number of years 
 (4), i.e. (l-OS)* ; when the interest is payable half-yearly, the 
 amount of £1 for half-a-year is 1-015, and for 4 years or 8 
 half-years it is (1-015)« ; in the same way when the interest 
 is payable quarterly the amount of £1 for 4 years is (1 -0075) ^ «. 
 
 Ex. 2. Find the compound interest of £375 for 5 years 
 at 5 per cent., the int. payable (1) yearly, (2) half-yearly. 
 
 Sol. 1. Amt. of £1 for 5 ye. at 5 p. cent.=(l-05)s=l -276282 
 
 Multiply by 375 
 
 Amt. of £375 for 5 ye. at 5 per cent. = £478*605750 
 
 Subtract 375 
 
 gQj^ 2. Compound interest of £375=£103,12s.l4d. 
 
 Amt.of£lfor5ye.,i.e.l0h.-ye.at5p.c.=(l-025)^<'=£l-28008 
 
 Multiply by 375 
 
 Amt. of £375 for 10 h.-ye. at 5 p. cent, per an.=:£480-03000 
 
 Subtract 375 
 Compound interest of £375=£105,0s.7^d. 
 
 3. What is the compound interest of £750 for 5 years at 3 
 per cent., 8 years at 4 per cent., and 7 years at 3 J per cent., 
 the interest payable yearly ? 
 
 4. What is the amount of £350 for 6 years at 2 p. c, 8 ye. 
 at 2 J p. c, and 10 ye. at 3i p. c. compound interest, the in- 
 terest payable yearly ? 
 
 6. What is the compound interest of £120, 10s. for 4 ye. at 
 2 p. c, 5 ye. at 4 p. c, and 6 ye. at 5 p. c, interest payable 
 half-yearly ? 
 
 6. What is the amount of £240, 12s. 6d. for 2 years at 3 
 p. c, 3 ye. at 4 p. c, and 2f ye. at 5 p. c. compound interest, 
 the interest payable quarterly ? 
 
 7. What is the compound interest of £375, 14s. for 3J ye. 
 at 3 p. c, 4 ye. at 2J p. c, and 4^ ye. at 6 p. c, the interest 
 payable three times yearly ? 
 
 8. A merchant began business with £1000, which he in- 
 creases every half-year by J ; what will his capital be at the 
 end of 5 J years ? 
 
 Case II. To find the interest on bonds when the in- 
 tervals between the payments are great. 
 
 Ex. Lent on bond £1050 at 4 per cent., Aug. 12th, 
 1855; and received on Sept. 15th, 1856, £300; on Oct. 
 
70 COMPOUND INTEREST. 
 
 20th, 1869, £350 : what was the balance due, including 
 the interest on Dec. 15th, 1870 ? Ans. £502, 19s. 84d. 
 Aug. 12, 1867. Lent at 4 per cent., . . . £1050 
 
 Interest on ditto for 399 days, 45-9123 
 
 Amount, 1095-9123 
 
 Sept. 15, 1868. Received in part, 300 
 
 Balance, 795-9123 
 
 Interest on ditto for 400 days, 34-8893 
 
 Amount, 830-8016 
 
 Oct. 20, 1869. Received in part, 350 
 
 Balance, 480-8016 
 
 Interest on ditto for 421 days, 22-1827 
 
 Amount, 502*9843 
 
 Dec. 15, 1870. Received in full, 502-9843 
 
 9. A bond of £975 became due on January 15th, 1866, of 
 which was paid April 21st, 1867, £250; July 29th, 1868, £200; 
 Oct. 16th, 1869, £300; and the balance on Dec. 17th, 1870: 
 what was then paid, including interest at 4J per cent. ? 
 
 10. Lent on bond £1225, at 2^ per cent., on March 4th, 
 
 1864, and received £320 on June 17th, 1865 ; £250 on Aug. 
 7th, 1866, £300 on Nov. 12th, 1867; £200 on Jan. 13th, 
 1869 ; and the balance on April i9th, 1870 : what was then 
 due, including the interest ? 
 
 11. Borrowed on bond, at 3 per cent., £875 on Jan. 4th, 
 
 1865, and paid £200 on March 7th, 1866; £150 on June 13th, 
 1867 ; £200 on Sept. 11th, 1868; £150 on Nov. 17th, 1869; 
 and the balance on Jan. 4th; 1871 : what was then paid, in- 
 cluding the interest ? 
 
 12. Borrowed, at 3 J per cent, £1500 on June 4th, 1865, of 
 which was paid, Aug. 1st, 1866, £350; Oct. 9th, 1867, £250; 
 Nov. 21st, 1868, £400; and the balance on Dec. 31st, 1869: 
 what was then paid, including the interest ? 
 
 MISCELLANEOUS QUESTIONS. 
 
 1. How many francs, each 9^d., are equal in value to 209 
 half-crowns ? 
 
 2. If whisky at 14s. 6d., 15s. 6d., 16s., and 17s. a-gallon, 
 be mixed in equal quantities ; what should a gallon of the 
 mixture be sold for to gain 5 per cent, and allow a discount 
 of 6| per cent. ? 
 
 3. A cubic foot of water weighs 1000 oz. ; how many tons 
 of water will a cistern 16 ft. 6 in. long, 15 ft. 4 in. broad, 
 and 5 ft. 6 in. deep contain ? 
 
MISCELLANEOUS QUESTIONS. 71 
 
 4. Find the value of § gui. ; reduce 5s. 7^d. to the frac. of 
 9 gui., and 3 ml. 2 fur, to the frac. of 1 ml. 6 fur. 12 poles. 
 
 5. A ladder, 45 ft. long, reaches to a window 27 ft. from 
 the ground on one side of a street, and, without moving the 
 foot, it reaches to a window 36 ft. high on the other side ; 
 find the breadth of the street. 
 
 6. 248 trees are planted in the breadth of a plantation at 
 a distance of 5 ft. 4 in. from each other; what is the breadth 
 of the plantation, allowing the same distance between the 
 trees and the fence on both sides ? 
 
 7. If £435 gains £58, 14s. 6d. in 4 J years ; what is the rate 
 per cent. ? 
 
 8. The side of a cubic piece of marble is 32 ft. ; find the 
 side of a piece 7^ times as large. 
 
 9. Find the value of a rectangular piece of ground 48 ft. 
 
 4 in. by 34 ft. 6 in., at 24s. per s. ft. 
 
 10. Exchanged 19 cwt. 2 qr. 12 lb. of cofiee at £9, 6s. 8d. 
 p. cwt. for sugar at 7^d. and tea at 4s. 6d. per lb. ; there was 
 
 5 times as much sugar as tea : how much was there of each ? 
 
 11. If 7 lb. sugar be equal to 3 of cofi^ee, and 6 of cofiee to 
 2^ of tea; how many lbs. tea are equal to 168 lbs. sugar? 
 
 12. A cask is f full, and after 40 gals, were run off", it was 
 ^5 full ; how many gals, could the cask contain ? 
 
 13. If a globe 9 in. diameter weighs 27 lbs. ; what will a 
 globe weigh whose diameter is 25 in. ? 
 
 14. Purchased 1260 lbs. tea at 4s. per lb., but J of it being 
 damaged, 25 per cent, was lost in selling it ; the remainder 
 was sold at 4s. 6d. per lb. : how much per cent, was gained 
 at the latter price and on the whole ? 
 
 15. In 1854, the number of births registered in England 
 was 324069 males and 310336 females; how many males 
 were bom for 100 females ? 
 
 16. What fraction multiplied by the square of 1^, and the 
 product divided by the cube root of §i§, produces 3 ? 
 
 17. Invested £10710 in new 2^ per cents at 74f ; how 
 much must I invest in 3 per cents at 90J to produce an in- 
 come of £500 yearly ? 
 
 18. In 1801 the population of Scotland was 1608420, and 
 in 1851 it was 2888742 ; what was the increase per cent, 
 during that time ? 
 
 19. What is the thickness of a solid foot of stone that is 
 9 ft. 4 in. lon^ and 2 ft. 6 in. broad? 
 
 20. A certain number of persons were fined 5s. 6d. each, 
 but 3 of them having no money, each of the others had to pay 
 Is. lOd. more than their fine ; how many persons were there ? 
 
72 MISCELLANEOUS QUESTIONS. 
 
 21. Reduce 14s. 11 Jd. to the dec. of £5, 19s. 6d., and y\ of 
 2f d. to the dec. of half-a-crown. 
 
 22. In 1855 the number of births registered in Scotland 
 was 93498, of which 47872 were males, and 45626 females ; 
 what decimal of the whole were males and females ? 
 
 23. Find the present value of £475, 15s. due 4 years hence, 
 at 2^ per cent, simple interest. 
 
 24. A grocer buys sugar at 5d. and 7d. per lb. and mixes 
 them in the proportion of 3 ; 5 ; what will he gain per cent, 
 by selling it at 7id. per lb. ? 
 
 25. A square contains exactly 2^ ac. ; find its side. 
 
 26. In the Centigrade thermometer the freezing-point is 
 zero, and the boiling-point 100°; in Fahrenheit's the freezing- 
 point is 32° and the boiling-point 212° : what degi*ee C. corre- 
 sponds to 68"" F., and what degree F. corresponds to 45° C. ? 
 
 27. What is the shortest piece of cloth that shall at the 
 same time be an exact number of yards, EngHsh ells, Flem- 
 ish ells, and French ells ? 
 
 28. A person spends £10, 4s. 2d. in 35 days, and he saves 
 £93, 10s. lOd. yearly; what is his income? 
 
 29. ^ of an army was killed in battle, j'jj was taken pris- 
 oners, Y*^ died from sickness, ^'^ was in hospital, and 31375 
 effective men remained ; how many were there at first ? 
 
 30. A person being asked his age, answered, if to my age 
 you add ^ and i of it, the sum will be 59 ; what was his age? 
 
 31. The corn produced by a field was found to be 200 qrs. 
 or ^ more than what was sown ; how much was sown ? 
 
 32. Bought £126 worth of tea at 4s. 6d. per lb., some of 
 which being damaged, I sold the remainder at 4s. 9d. per lb., 
 which produced £106, 17s. 6d. ; what quantity was damaged? 
 
 33. A gentleman gave to three persons £78, 6s. 6d. ; the 
 second received § of the first, and the third f of the second : 
 what did each receive ? 
 
 34. A person bought a horse, gig, and harness for £60 ; the 
 horse cost 7 times as much as the harness, and the gig was A 
 the price of the horse and harness ; what was the price of each? 
 
 35. What must be the depth of a cistern which is 6 ft. 3 in. 
 long and 4ft. 6 in. broad, to contain 481*665 gals, of water? 
 
 36. Light travels at the rate of 192000 miles per sec. ; how 
 long does it take to travel from the sun to the earth, a dis- 
 tance of 95 millions of miles ? 
 
73 
 
 DECIMAL COINAGE. 
 
 The pupil, having worked the Elementary Exercises in 
 Decimal Coinage, at the end of the " Lessons in Arith- 
 metic," and also those given under Decimal Fractions 
 (page 30), may now solve the following questions. 
 
 TABLE OF DECIMAL MONEY. 
 
 lmil(m.) =£^^V^ = |4f. 
 
 10 mils = lcent(c.) =£'iio = 2|d. 
 
 100 mils = 10 cents = 1 florin (fl.) = £^V = 2s. 
 
 1000 mils = 100 cents = 10 florins = £l = 20s. 
 
 Ex. 1. Reduce £12, 17s. 9d. from the present to the 
 
 proposed system. Ans. £12-8875 = £12, 8 fl. 8 c. 7i m. 
 
 Here, bv Case V. p. 32, £12, 17s. 9d. = £12-8875 = £12, 
 
 8fl. 8c. 7^m. 
 
 Ex. 2. Reduce £7, 8 fl. 2 c. 5 m. from the proposed to 
 the present system. Ans. £7, 16s. 6d. 
 
 Here, by Case VI. p. 32, £7, 8fl. 2c. 5m. = £7-825 = £7, 
 16s. 6d. 
 
 Reduce from the present to the proposed system, 
 
 1. 6s. 6d. 
 
 2. 7 3 
 
 3. 18 4 
 
 4. 19 7 
 
 Reduce from the proposed to the present system, 
 
 5. 
 
 14s. 
 
 2^d. 
 
 9. 
 
 £2, 8s. 9d. 
 
 13. 
 
 £12, 13s 
 
 4d. 
 
 6. 
 
 13 
 
 7^ 
 
 10. 
 
 4 15 8 
 
 14. 
 
 15 16 
 
 8 
 
 7. 
 
 15 
 
 8i 
 
 11. 
 
 7 6 8 
 
 15. 
 
 17 14 
 
 7 
 
 8. 
 
 17 
 
 5 
 
 12. 
 
 9 10 10 
 
 IG. 
 
 21 12 
 
 8 
 
 17. 
 
 £-425 
 
 18. 
 
 •675 
 
 19. 
 
 •850 
 
 20. 
 
 •925 
 
 21. £-763 
 
 22. ^574 
 
 23. -235 
 
 24. -075 
 
 25. £4-6375 
 
 26. 6-8125 
 
 27. 7-4025 
 
 28. 9-7875 
 
 29. £10-7750 
 
 30. 12-6666 
 
 31. 15-3333 
 
 32. 17-8166 
 
 33. A man earns £58, 7fl. 7c. 5m. per annum, his expenses 
 are £49, 8fl. 9c. 7m. ; how much does he save ? 
 
 34. What is the value of 27oz. of silver at 2fl. 7c. 5m. 
 per oz. ? 
 
 35. A man's wages are £1, 2fl. 7c. 5m. weekly ; how much 
 do they amount to in a year ? 
 
 36. What is the weekly rent of a house, when the yearly 
 rent is £65, Ifl. 4m. ? 
 
 37. If 35 quarters of oats cost £53, 3fl. 7c. 5m. ; what is 
 the rate per quarter ? 
 
74 DECIMAL COINAGE. 
 
 38. A bankrupt who owed £3595, paid his creditors £2786, 
 Ifl. 2c. 5m. ; how much did he pay per £1 ? 
 
 39. If 15 gallons of whisky cost £13, Ifl. 2c. 5m.; what 
 should he paid for a cask containing 125 gals. ? 
 
 40. Find by practice the value of 17cwt. 2qrs. 14 lbs. of 
 sugar at £2, 4fl. 5c. per cwt. 
 
 41. A man's wages are £50, 2fl. 2c. 5m. for 146 days; how 
 much is this per annum ? 
 
 42. What is the commission on £575, 2c. 5m. at 2 and 3J 
 per cent, ? 
 
 43. What is the brokerage on £796, 2fl. 5c. 6m. at J, J, 
 and § per cent. ? 
 
 44. How much should be paid for insuring £5750, 2fl. 5c. 
 at 3 per cent., and policy Ifl. 2c. 5m. per cent. ? 
 
 45. What is the interest on £487, 7fl. 5c. for 4 years, at 
 2^ and 4 per cent. ? 
 
 46. Find the amt. of £896, 5fl. for 3 years, at 2 and 5 p. c. 
 
 47. Find the interest on £228, Ifl. 2c. 5m. for 198 days, at 
 4 and 4^ per cent. 
 
 48. What should £2851, 5fl. 6c. 2Jm. amount to in 1 year 
 and 99 days, at 4 per cent. ? 
 
 49. What sum will amount to £251, 8fl. 7c. 5m. in 4 
 months, at 2^ per cent. ? 
 
 50. Divide £153, Ifl. 4m. among 4 persons, so that J the 
 share of the first, J of that of the second, J of that of the 
 third, and \ of that of the second may make up the same sum. 
 
 51. What is the rent of a farm of 525 ac. 3 ro. 25 per. at 
 £3, 5fl. 2c. 8m. per acre ? 
 
 52. A bill of £919, 8fl., dated Feb. 14, at 6 months, was 
 discounted June 13, at 3^ per cent. ; what was the net pro- 
 ceeds, deducting commission ^ per cent. ? 
 
 53. If 7 1 per cent is gained by selling tea at £22, 5fl. 7c. 
 5m. per cwt. ; what is gained or lost per cent, by selling it 
 at £22, 8fl. 9c. per cwt. ? 
 
 54. In what proportions should tea at Ifl. 2c. 5m., and 2fl. 
 per lb. be mixed to reduce the price to Ifl. 7c. 5m. per lb. ? 
 
 55. What part of £9, 7fl. 5c. is £8, 4c. 3|m. ? 
 
 56. In what time will the interest of £437, 6fl. 7c. 5m. pay 
 a debt of £52, 5fl. 2c. Im., at 4 per cent, per annum? 
 
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 English Grammar.... 3 
 
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 English Composition 7 
 
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 Progressive Geogy 10 
 
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 Ancient Geography..ll 
 
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 Atlas 11 
 
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 Reid's First Book of Geography.. 10 
 
 Modern Geography .',..10 
 
 Sacred Geography 10 
 
 Atlases 11 
 
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 nomy 11 
 
 Phys. Geography..ll 
 
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 White's Abstract of Geography... 9 
 
 System of Geography.,.. 9 
 
 Atlas 11 
 
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 School Psalmody 17 
 
 Household Economy. 
 Gordon's Household Economy 8 
 
 History. 
 
 Corkran's History of England 12 
 
 Simpson's Scotland 13 
 
 Goldsmith's England..l3 
 
 Greece ...,13 
 
 Rome 13 
 
INDEX. 
 
 Tytler's General History P. 13 
 
 Watt's Scripture History 13 
 
 White's Universal History 12, 13 
 
 England for Jun. Classes 12 
 
 History of France 12 
 
 Great Britain and Ireland 12 
 
 Sacred History 13 
 
 Histories of Scotland 12 
 
 History of Rome 13 
 
 Writing, Arithmetic, etc. 
 
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 Hutton's Arithmetic, etc 15 
 
 Ingram's Principles of Arithmetic 15 
 
 Maclaren's Arithmetic 16 
 
 Book-keeping 16 
 
 Melrose's Arithmetic 15 
 
 Scott's Arithmetical Works 16 
 
 .-, Copy Books & Copy Lines..l6 
 
 Smith's Arithmetical Works 14 
 
 Stewart's Arithmetical Works 15 
 
 Trotter's Arithmetical Works..l4, 16 
 
 New Code Arithmetic... 4 
 
 Hutton's Book-keeping. 15 
 
 Gaelic. 
 Forbes's Gaelic Grammar 16 
 
 Mathematics, etc. 
 Ingram's System of Mathematics. .16 
 
 Mensuration, by Trotter 16 
 
 Trotters Key to Ingram's Mathe- 
 matics 16 
 
 Manual of Logarithms...l6 
 
 Ingram's Euclid 16 
 
 Algebra 16 
 
 Nicol's Sciences 17 
 
 French. 
 Beljame's French Grammar, etc. ..20 
 Caron's First French Class-Book ..20 
 
 First French Reading- Book. .20 
 
 French Grammar 20 
 
 Chambaud's Fables Choisies 18 
 
 Christison's French Grammar 20 
 
 Fables et Contes Cboisis 20 
 
 Fleury's History of France. .20 
 
 French New Testament IS 
 
 Gibson's Le Petit Fablier 18 
 
 Hallard's French Grammar 20 
 
 Schneider's First French Course.. .18 
 
 Conversation- Grammar.lS 
 
 French Reader 18 
 
 French Manual 18 
 
 ficrin Littdraire 16 
 
 Surenne's Dictionaries P. 19 
 
 New French Manual, etc.. .19 
 
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 French Classics 19,20 
 
 French Reading Instructor 20 
 
 Wolski's French Extracts '20 
 
 French Grammar .20 ' 
 
 Latin and Greek. 
 
 Ainsworth's Latin Dictionary 23 
 
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 Cato Major, De Officii8....24 
 
 Clyde's Greek Syntax 21 
 
 Dymock's Csesar and Sallust 22 
 
 Edin. Academy Class-Books: — 
 Rudiments of Latin Language... 21 
 
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 Rudiments of Greek Language.. .21 
 
 Greek Extracts 21 
 
 Ciceronis Opera Selecta 21 
 
 Selecta e Poetis 21 
 
 Ferguson's (Prof.)Gram. Exercises 24 
 
 .....<r. Latin Delectus, 24 
 
 Ovid's Metamorphoses24 
 
 Fergussou's (Dr) Xenophon^s Ana- 
 basis 23 
 
 Greek Gram. Exercises 23 
 
 Homer's Iliad, witli Vocab. 23 
 
 Geddes' (Prof.) Greek Grammar.. .21 
 
 Greek Testament, by Duncan 23 
 
 Hunter's Ruddiman's Rudiments .22 
 
 Sallust, Virgil, & Horace 22 
 
 Livy, Books 21 to 25 22 
 
 Latin Testament, by Beza 23 
 
 Macgowan's Latin Lessons 22 
 
 Mair's Introduction, by Stewart... 23 
 Massie's Latin Prose Composition 22 
 
 M'Dowall's Csesar and Virgil 22 
 
 Melville's Lectiones Selectae 22 
 
 Neilson's Eutropius 22 
 
 Stewart's Cornelius Nepos 23 
 
 Veitch's Homer's Iliad 23 
 
 German. 
 Fischart's New German Reader... 24 
 
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 Port-Royal Logic (Prof, Bayne6')24 
 
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10 GEOGRAPHY AND ASTRONOMY. 
 
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GEOGRAPHY AND ASTROXOMY. 11 
 
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12 
 
 HISTOEY. 
 
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 interest too often wanting in larger historical works. The information 
 
 conveyed is thoroughly sound; and the utility of the book is much 
 
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HISTORY. 13 
 
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14 WRITING, ARITHMETIC, AND BOOK-KEEPING. 
 
 WKITHTG, AKITHMETIO, AND BOOK-KEEPINa. 
 
 This section will be found to contain works in extensive use in many of the 
 best schools in the United Kingdom. The successive editions have been 
 carefully revised and amended. 
 
 ARITHMETIC ADAPTED TO THE NEW CODE, in 
 
 Three Parts. By Alexander Trotter, Teacher of Mathematics, etc., 
 Edinburgh. Parts I. and IL, embracing the first four Standards^ are now 
 Beady. Each containing 36 pages, 2d., stifif wrapper. Answers to 
 Parts I. and II., price 3d. each. Part III. in Preparation, 
 
 PRACTICAL ARITHMETIC FOR JUNIOR CLASSES. 
 
 By Henry G. C. Smith, Teacher of Arithmetic and Mathematics in 
 George Heriot's Hospital. 64 pages, 6d. stiff wrapper. Answers, 6d. 
 
 From the Rev. Philip Kelland, A.M., F.R.SS. L. & E., late Fellow oj 
 Queens^ College, Cambridge, Professor of Mathematics in the University of 
 Edinburgh. 
 
 "I am glad to learn that Mr Smith's Manual for Junior Classes, the MS, 
 of which I have examined, is nearly ready for publication. Trusting that 
 the Illustrative Processes which he has exhibited may prove as efficient in 
 other hands as they have proved in his own, I have great pleasure in 
 recommending the work, being satisfied that a better Arithmetician and a 
 more judicious Teacher than Mr Smith is ndt to be found." 
 
 PRACTICAL ARITHMETIC FOR SENIOR CLASSES; 
 
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 Answers, 6d. Key, 2s. 6d. 
 
 *** The Exercises in both works, which are copious and original, have been 
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 LESSONS IN ARITHMETIC FOR JUNIOR CLASSES. 
 
 By James Trotter. 66 pages, 6d. stiff wrapper; orSd. cloth. Answers,6d. 
 
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 Trotter, Teacher of Mathematics, etc., Edinburgh ; and to the present 
 edition Exercises on the proposed Decimal Coinage have been added. 
 
 LESSONS IN ARITHMETIC for ADVANCED CLASSES; 
 
 Being a Continuation of the Lessons in Arithmetic for Junior Classes. 
 Containing Vulgar and Decimal Fractions; Simple and Compound 
 Proportion, with their Applications; Simple and Compound Interest; 
 Involution and Evolution, etc. By Alexander Trotter. New Edition, 
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 wrapper ; or 8d. cloth Ansioers, 6d. 
 
 Each subject is also accompanied by an example fully worked out and 
 minutely explained. The Exercises are numerous and practical. 
 
WRITING, ARITHMETIC, AND BOOK-KEEPING. 15 
 
 A COMPLETE SYSTEM OF ARITHMETIC, Theoretical 
 
 and Pi'actical; containing the Fundamental Rules, and their Application 
 to Mercantile Computations; Vulgar and Decimal Fractions; Involution 
 and Evolution; Series; Annuities, Certain and Contingent. By Mr 
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 *^* All the 3400 Exercises in this work are new. They are applicable to the 
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 tion to Mercantile Calculations; Vulgar and Decimal Fractions; Ex- 
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 and Contingent, etc. Re-arranged, Improved, and Enlarged, with Exer- 
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 Each Rule is followed hy an example worked out at length, and minutely 
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16 COPY-BOOKS, MATHEMATICS, ETC. 
 
 LESSONS IN ARITHMETIC FOR JUNIOR CLASSES. 
 By James Maclaren, Master of the Classical and Mercantile Academy, 
 Hamilton Place, Edinburgh. 6d. stiff wrapper. 
 
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 MATHEMATICS, NATUKAL PHILOSOPHY, ETC. 
 
 INGRAM'S CONCISE SYSTEM OF MATHEMATICS, 
 
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 TROTTER'S MANUAL OF LOGARITHMS AND PRAC- 
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MUSIC, DRAWING, SCHOOL REGISTERS. 17 
 
 INTRODUCTORY BOOK OF THE SCIENCES. By 
 James Nicol, F,R.S.E.,F.G.S., Professor of Natural History in the Uni- 
 versity of Aberdeen. With 106 Woodcuts. Is. 6d. 
 
 SCHOOL SONGS WITH MUSIC, 
 
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 ELEMENTS OF VOCAL MUSIC: An Introduction to the 
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 *** This Work has been prepared with great care, and is the result of long 
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 pupil. The exercises are printed in the standard notation, and the notes are 
 named as in the original Sol-fa System. 
 
 Contents. — Music Scales. — Exercises in Time. — Syncopation. — The 
 Chromatic Scale.— Transposition of Scale. — The Minor Scale.— Part 
 Singing. — Explanation of Musical Terms. 
 
 HUNTER'S SCHOOL SONGS. With Preface by Rev. 
 James Currie, Training College, Edinburgh. 
 
 FOR JUNIOR CLASSES : 60 Songs, principally set for two 
 
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 FOR ADVANCED CLASSES : 44 Songs, principally set for three 
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 GEOMETRICAL DRAWING-. 
 THE FIRST GRADE PRACTICAL GEOMETRY. In- 
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 SCHOOL REGISTER. Pupil's Daily Register op Marks. 
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 SCHOOL REGISTER OF ATTENDANCE, ABSENCE, 
 
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18 FRENCH. 
 
 CLASS-BOOKS BY CHAS. HENRI SCHNEIDER, F.E.I.S., M.C.P., 
 
 Senior French Master in the Edinburgh High School, the Merchant 
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 Is. 6d. 
 
 *** This work forms a Complete Course of French for Beginners, 
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 THE EDINBURGH HIGH SCHOOL FRENCH CONVER- 
 
 SATION-GRAMMAR, arranged on an entirely New Plan, with Ques- 
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 3s. 6d. Key, 2s. 6d. 
 
 THE EDINBURGH HIGH SCHOOL NEW PRACTICAL 
 FRENCH READER : Being a Collection of Pieces from the best French 
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 THE EDINBURGH HIGH SCHOOL FRENCH MANUAL 
 
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 In this work, Phrases and Idiomatic Expressions which are used most 
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 Readings, Dictation, and Recitation. 3s. 6d. 
 
 Letter from Professor Max Mijller, University of Oxford, May 1867. 
 
 "My dear Sir, — I am very happy to find that my anticipations as 
 to the success of your Grammar have been fully realized. Your book 
 does not require any longer a godfather; but if you wish me to act as 
 such, I shall be most happy to have my name connected with your 
 prosperous child. — Yours very truly, Max MUller. 
 
 " To Mons. C. H. Schneider, Edinburgh High School." 
 
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 Protestant Version, and the one in general use in the French 
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 CHAMBAUD'S FABLES CHOISIES. With a Vocabulary 
 
 containing the meaning of all the Words. By Scot and Wells. 2s. 
 
 LB PETIT FABLIER. With Vocabulary. For Junior 
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FRENCH. 19 
 
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LATIN AND GREEK. 21 
 
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