8. August 21, 1883, Mr. John F. Sanders, of Hoboken, N. J., purchased of B. J. Murray & Co., N. Y., 32 tons large stove coal @ $7.50; 13 tons nut coal @ $8.00; 15 cords wood @ $5.50; 25 bbl. kindling wood @ $0.50. Make out bill for amount.

9. Make out an appropriate bill on the supposition that you sold a gentleman 4 articles from a hardware store.

10. D. & J. Sadlier, New York, bought of Sower, Potts & Co., Philadelphia, the following articles, June 22, 1883 20 Quackenbos' Natural Philosophy @ $0.90; 12 Shaw's Literature @ $1.00; 20 Robinson's Geometry @ $0.85; 16 Robinson's University Algebra @ $0.95. They paid $30 in cash, and returned books to the amount of $20. Make out bill showing entire statement.

11. M. J. Fuchs & Co., of New York, purchased of B. J. Vanere, Paris, February 16, 1882, the following : 25 gal. alcohol @ $2; 20 gal. brandy (Cognac) @ $7.50 ; 20 gal. Scotch gin @ $3.50; 35 gal. Holland gin @ $4.50; 20 gal. Century whiskey @ $4.00. What was the amount of the bill?

12. Chas. H. Schreiber, of Cincinnati, shipped to T. F. Clarkson, of Buffalo, May 31, 1880, the following: 12 bales, 5272 lb., Mid. Upland cotton @ 184; 10 bales, 4870 lb., Mid. Gulf cotton @ 204; 18 tierces Carolina rice, 10800 lb., @ 64. Make out bill, receipted.

13. On October 16, 1883, Mr. F. J. Quirk sold to Mr. L. A. Quigley, of Memphis, the following articles: 8 lb. camphor @ 504; 8 oz. quinine @ $3; 6 lb. Epsom salts @54; 4 oz. morphine @ $5; 7 lb. gum shellac @ 754; 5 lb. aqua ammonia @ 84; and gave a receipted bill for

amount.

14. Make out a bill of ten purchases from a grocery store.

DENOMINATE

NUMBERS.

133. A Denominate Number is a concrete number whose unit is arbitrary.

134. There are two sorts of units; viz., natural and arbitrary.

135. A Natural Unit is a unit furnished by the nature of the quantity measured. Thus, in a row of houses, the unit is a house.

136. An Arbitrary Unit is a unit which is determined by custom or law. Thus, in the length of a road, the unit is the yard.

137. These units or measures produce two sorts of quantity: discrete and continuous.

138. Discrete Quantities are those which are composed of similar but distinct objects; as, a regiment of soldiers, a row of trees.

139. Continuous Quantities are those which do not present distinct parts; as, a surface, a solid, the weight of a body.

140. A Compound Number is a concrete number composed of different units of the same kind of quantity.

Denominate Numbers treat of :

MEASURES OF VALUE.

141. The Value of a thing is its price estimated on a piece of metal of determined weight.

142. Money is the measure by which we estimate the value of things.

143. Currency is money used as a circulating medium.

UNITED STATES CURRENCY.

144. The Unit of United States currency is the gold dollar.

NOTE.-The gold coins are the $1, $2, $3, $5, $10, and $20 pieces; the silver coins are the 10, 25, 50, and $1 pieces; the nickel coins are the 3 and 5

pieces; the 19 piece is made of

bronze.

ORAL

EXERCISES.

1. How many mills in a cent? In 34? In 54 ? 2. How many cents in a dime? In 2 dimes? In 4

dimes? In 10 dimes? In 15 dimes?

3. How many mills in 10 cents? Mills in a dime? Cents in 8 dimes?

In 24 dimes? Cents in a dime?

Mills in 20 dimes?

4. How many cents in a dollar? In $6? In $8? 5. How many mills in 124? In 604? In 90¢ ? 6. How many mills in 100 cents? Cents in a dollar? Mills in a dollar? Mills in 60 cents?

7. How many dimes in a dollar? In $10? In $7 ? 8. How many dimes in $2.50? In $6.40? In $9.30?

In 70 m. ? In 93 m.?

In 1104?

In 924?

In 2154 ?

9. How many cents in 90 mills? In 30 m.? 10. How many cents and mills in 65 m.? 11. How many dimes in 804? In 204? 12. How many dimes in 65¢? 13. How many dollars in an eagle? In a double eagle? In 6 eagles? In 9 eagles? In 15 eagles?

14. How many cents in 8 dimes 9 cents? 6 dimes 2 cents? 7 dimes 3 cents? 10 dimes 4 cents?

15. How many cents in the silver coins, taking one. of each? 5 of each? 10 of each?

16. How many dollars in the gold pieces, taking one' of each? 3 of each? 6 of each ?

ENGLISH MONEY.

145. English Money is the legal currency of Great Britain.

146. The Unit of English money is the pound sterling.

NOTE. The gold coin valued at one £, is called a sovereign. Its value in U. S. money is $4.8665. The gold coins of Great Britain are the sovereign, half-sovereign, and guinea; the silver coins are the crown, half-crown, florin, shilling, six-penny, and three-penny pieces; the copper coins are the penny, half-penny, and farthing.

ORAL EXERCISES.

1. How many farthings in a penny? In 6 pence? In 7 pence? In 11 pence? In 9 pence? In 12 pence? 2. How many farthings in 3d. 2 far.?

In 4d. 3 far.?

3. How many pence in a shilling? In 4 shillings? In 8 shillings? In 7 shillings? In 11 shillings?

4. How many farthings in 12 pence? Pence in a shilling? Farthings in a shilling?

5. How many farthings in 3s. ? In 10s.? In 15s. ? 6. How many shillings in a £? In £7? In £13? In £25? In £15? In £20 ? In £40 ?

7. How many shillings in a crown? In 6 crowns? In 14 crowns? In 20 crowns? In 9 crowns ?

8. How many pounds in 60 shillings? In 100s.? In 80s. ? In 480s.? In 360s.? In 640s.?

9. How many pence in 16 far.? In 18 far.? In 36 far.? 10. How many shillings in 72d.? In 96d.? In 240d.? 11. What will 5 lb. of beef cost at 9d. per pound? 12. How many yards of cloth at 6s. a yard can be purchased for £3? For £6? For £11 ?

13. What cost 36 combs at 9d. apiece? At 3d.? 14. How many bats at 2s. each may be bought for 120d.? For 240d.? For 144d.? For 72d.?

REDUCTION DESCENDING.

1. Reduce £3 11s. 9d. 2 far. to farthings.

OPERATION.

£ S. d. far.

3 11 9 2

20

71s.

12

861d.

4

3446 far.

adding 11s. to this, we have 71s. Since 1s. = 12d., 71s. 852d., which, together with 9d.,. give 861d. And, since 1d. 4 far., 861d. 3444 far., which, plus 2 far., give 3446 far. Hence, £3 11s. 9d. 2 far. = 3446 far.

=