mium costs one dollar plus 12 hundredths of a dollar ($1.12), $347.13 will cost 347.13 times $1.12, which is $388.785+.

(b.) Since $1. worth of stock at 12 per cent. discount costs one dollar minus 12 hundredths of a dollar, ($1.—$0.12=$0.88), $347.13 will cost 347.13 times $0.88, which is $305.474+.

RULE.-I. When stock is at a premium, add the to $1., and multiply the sum by the amount of stock.

per cent.

II. When stock is at a discount, subtract the per cent. from $1., and multiply the difference by the amount of the stock.

445. What is the market value of 36 shares of New York and Erie R. R. stock at 37 per cent. discount?

446. What must be paid for 15 shares of Providence railroad stock at a premium of 93 per cent.?

447. What must be paid for 13 shares of U. S. stock at 2 per cent. premium, the par value being $1000. per share?

448. I purchased 37 shares of Hudson River R. R. stock at 15 per cent. discount, and sold them at an advance of 13 per cent.; how much did I gain?

QUESTIONS.-What is the use of surveyor's square-measure? (93.) Repeat the table. (93., a.) What is a cube? (94.) Give the analysis of a cubic yard. (94., b.) What is the use of cubic measure? (94., c.) Repeat the table. (136., a.) What are measures of capacity? (95.) What is the use of Liquid measure? (95., a.) Repeat the table. (95., b.) Repeat the table of miscellaneous measure. (95., c.)

LESSON XLIX.

205. To find the quantity of stock that may be purchased for a given sum.

How many shares of railroad stock may be purchased for $3885. at 5 per cent. advance?

ANALYSIS.-1. Since $1 stock at 5 per cent. advance is worth $1.05, as many dollars' worth of stock can be purchased for $3885. as $1.05 is contained times in $3885, which are 3700. 2. If $100 will buy one share, $3700 will buy as many shares as $100 are contained times in $3700, which are 37.

Therefore, at 5 per cent. advance, 37 shares of R. R. stock can be purchased for $3885.

NOTE-Require the pupil to write a rule from the analysis.

449. How many shares of bank stock, at 5 per cent. advance, can be purchased for $6300?

450. I invested $4678.73 in the Home Insurance Company, at 11 per cent. discount; how much stock did I pur. chase?

451. I sent my agent $8964.39, with which to purchase Illinois Railroad stock after deducting his commission of 24 per cent., the stock being at a premium of 13 per cent. How much stock did he purchase?

452 I sold 50 shares of the Providence Railroad stock at a discount of 8 per cent., and received $4600.; what is the par value of a share?

QUESTIONS.-What is the use of dry-measure? (96) Repeat the table. (96., a.) Repeat the table of comparative measures. (96., c.) What is the measure of time? (97.) Repeat the table. (97., a.) How is the calendar year divided? (97., b.) What is circular measure (98.) Repeat the table. (98., a.) Repeat the table of particulars. (99., a.) Of paper. (99., b.) Of books. (99., c.) Of copying. (99., d.)

LESSON L.

MISCELLANEOUS EXAMPLES.

453. An agent buys 26896 pounds of wcʊl at 67 ets. per pound, and receives a commission of 23 per cent.; what amount does he receive?

454. My agent purchases, in New Orleans, 400 bales of cotton, each bale weighing 570 lbs., for which he gives 9 cts. per pound; how much must I remit to him, including his commission of 2 per cent.?

455 How much must I send a broker to purchase 38 shares of Hudson River R. R. stock at 3 per cent. discount, including the brokerage of 4 per cent ?

456. A broker purchased for me 128 shares of Virginia State Bonds, at 464 per cent. discount. He sold them, on my account, at an advance of § per cent., allowing cent. brokerage for buying and selling; did I make or lose by the operation, and how much?

per

457 A commission merchant in New York sells 437 barrels of flour, at $7.50 per barrel; 43 firkins of butter, each containing 97 pounds, at 231 cts. per pound; 136 cheeses, each weighing 103 pounds, at 83 cts. per pound: how much is his commission for selling, at 5 per cent.?

458. A man purchased 73 shares of stock in the Newark City Bank, at 7 per cent. discount, and sold it for 3 per cent. premium; what was his gain?

QUESTIONS.-What is reduction descending? (80.) Analyze at the blackboard an example in reduction descending. (100., a.) Give the rule. (100., b) What is reduction ascending? (81.) Analyze (at the blackboard) an example of reduction ascending. (101., a.) Give the rule, (101,6) Analyze an example of compound addition, at the blackboard, (102., a.) Give the rule. (102, 6.) Prove the same example. (102., ¿.)

LESSON LI.

459. Fred. Curtis exchanged 13 shares railroad stock at 11 per cent. premium, for 26 shares of bank stock at 8 per cent. discount. He paid the difference in cash; how much cash did he pay?

460. S. J. Brundige sends $6384. to a broker to be invested in government funds after deducting his commission of 2 per cent.; how much was invested?

461. I sent to J. H. Johnston $600 with which to purchase a silver tea set after deducting his commission of 21⁄2 per cent.; how much did it cost?

462. An agent sold a quantity of oil for $375.85, and charged 24 per cent. commission; how much did the owner receive?

463. I sent my agent $375.75 with which to purchase oil at $1. per gallon, after deducting his commission of 24 per cent.; how much oil did I receive?

464. A widow invested $3968 in Beverly Bank stock at par. She afterward sold it at 98 per cent. discount; how much did she lose?

465. A man bought $3784.40 worth of cotton, and afterward sold it at a gain of 50 per cent.; what did he receive for it?

466. I sold 6 pieces of cloth, each containing 31 yards, at $2.87 per yard; I charged 23 per cent. commission, and 3 per cent. for guaranteeing payment; how much should I pay over?

467. I bought 13 shares of bank stock at 4 per cent. premium; how much did it cost me?

QUESTIONS.-Analyze an example of the subtraction of denominate numbers. (103., a.) Prove the same example. (103., h.) Give

the rule. (103., g.) Analyze an example of the multiplication of denominate numbers. (104., a.) Analyze an example of the division of denominate numbers. (105., a.)

LESSON LII.

PROFIT AND LOSS.

206. Profit and Loss are commercial terms indicating gain or loss in business transactions, and are always estimated from the cost price.

207. To find the amount of gain or loss, the cost and the gain or loss per cent. being given.

A man bought a cow for $39.25, and afterward sold her for 15 per cent. more than her cost; how much did he gain?

MODEL OPERATION.

$39.25$0.15=$5.887+.

ANALYSIS. Since on $1. he gained $0.15, on $39.25 he must have gained 39.25 times $0.15, which are $5.887+.

Therefore, the man must have gained $5.887+.

NOTE.-Require the pupil to write a rule from the analysis.'

468. A grocer bought a hogshead of sugar for $96.37, and sold it at 15 per cent. profit; what was his gain?

469. A miller bought 346 bushels of rye at 87 cts. per bushel. He sold the flour made from it for 29 per cent. more than the cost; what was his gain?

470. A wool merchant bought 43874 pounds of wool at 57 cts. per pound; he paid 13 per cent. for storage and insurance, and then sold it at an advance of 331 per cent.; what was his gain?

471. If I buy a hogshead of sugar containing 1280 pounds, at 61 cts. per pound, and wish to sell it at an advance of 18 per cent., for how much must I sell it per pound?