VIII. CUBIC MEASURE, OR MEASURE OF SOLIDITY.

COMPOUND MULTIPLICATION.

To Multiply any Compound Quantity by an Integer less than 13.

First. Multiply the Quantity of the lowest name in the Multiplicand. Reduce Product to next higher name.

Set down and carry as in Compound Addition.

Second. Proceed similarly with the other quantities of the Multiplicand.

FIRST EXAMPLE WORKED OUT. What will 9 articles cost at £3 11's. 81d. each?

They will evidently cost 9 times £3. 11's. 84d. or £3′ 11∙s. 84d. × 9.

This process is founded on PRINCIPLE XXV. (Page 172.)

SECOND EXAMPLE WORKED OUT. Find the extent of

5. fields, each being 4· ac. 2. r. 35 po.

THIRD EXAMPLE WORKED OUT. If 3 lb. 11. oz. 13 dwts. cost a crown, what weight of goods, at the same rate, would cost £1.?

Now, a crown

of £1; hence 4 times as much may be bought

for £1 as for 1 crown.

lb. Oz. dwts.

3. 11. 13

4.

FOURTH EXAMPLE WORKED OUT. If 4 cwt. of sugar cost £8 17's. 6 d., what is the rate per Ton?

44 17.

5.

.. A Ton will cost 5 times as much as

value of 4 cut.

6. = value of 20 cwt., or 1 Ton.

The tables of Aliquot Parts will be of service in Examples like these last two.

EXERCISE XCII.

EXAMPLES IN COMPOUND MULTIPLICATION BY INTEGERS LESS THAN 13.

Find the 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, and 12th Multiples of each of the following sixteen Compound Quantities, describing each Multiple in writing.

1 415 13's. 81d. 5. 14's. 6d.

2. £743 5's. 11ğd.

9. 8d. 13. 1's. 44d.

6. 11's. 91d.

10 11 d. 14 3's. 6d.

3. £1542 16's. 5 d. q. 7. 3's. 4 d. 4. £59 11's. 7 d. §q. 8° 15′s. 11∙d.

q.

11. 141d. 15′ 5′s. 7ąd.

q.

12. 20ąd. 16° 8's. 4}1⁄2d.

How much rice will cost one shilling,

4 oz. 8 dr. cost 6'd.? | 20. If 1 lb. 1oz. 2.dr. cost 2.d.? 8 oz. 2.dr. cost 4'd.?

23. When 56 lb. cost £3.14's. 11d.? | 25 When 14 lb. cost £1.15's. 83d.? 24. When 28 lb. cost £2.19's. 74d.? 26 When 28 lb. cost £1 2's. 7 d.? What weight of goods will cost £1.

27 If 1 cwt. 2. qr. 21 lb. cost 10's. ?
28. If 3 qr. 13 lb. 7 oz. cost 6's. S'd.?
29. If 3 lb. 11 oz. 15 dwt. cost 5's. ?
30. If 4 lb. 5 oz. 14.875 gr. cost 3's. 4 d.?
31. If 7.3 23 1
32. If 4 lb. 15 oz.

cost 2's. 6'd.? cost 1 s. 8.d.?

41. At £11·14's. 10 d. for 10 cwt.? | 43. At £1. 6's. 8.d. for 2 cwt. 2.qr.? 42. At £7. 17's. 9 d. for 4 cwt.? 44 At £5 14's. 8 d. for 2 cwt.?

45. How much is corn per bushel when a peck costs 1's. 114d.? 46. If a gallon of beans cost 1's. 1d. what will half a bushel cost? 47. If 2 oz. of tea cost 111⁄2d. what will 1 lb. cost?

48. If 4 oz. of cochineal cost 1's. 44d. what is the price per lb.? 49. What will a doz. lb. of flour cost when 4 lb. are worth 54d.? 50. If a parcel be carried 7 mi. 6. fur. for 1's. 8 d. how far should it be carried for 5's.?

51. When lyd 3′ na. of ribbon cost 7d. what length will cost a crown?

FIFTH EXAMPLE WORKED OUT. FORM OF SHOP-BILL. Make out a bill for the undermentioned articles, purchased at Millport, November 30th, 1858, by Mrs. Railton, of Willis & Co., Drapers and Haberdashers: 8 yds. damask, at 2's. 9 d. per yard; 12 yds. alpaca, at 1's. 71d. per yd.; 11 yds. ribbon, at 1's. 1 d. per yd.; 2. pairs gloves, at 2 s. 8 d. per pair; 4 doz. buttons, at 74d. per doz.; 12. yds. shirting, at 62d. per yd.; 9 yds. ditto, at 61d. per yd. The parcel was delivered by an assistant, John Froude, who received the amount for his employers, and discharged the bill in their name.

John Froude,
For Willis & Co.

* Shillings and pence are thus expressed by men of business.

EXERCISE XCII. (continued.)

Make a bill for each of the following sets of commodities, supplying names of buyer, seller, &c.

52. A GROCER'S BILL. 3 lb. coffee, at 20.d.; 2∙lb. tea, at 5's. 4.d.; 12 lb. moist sugar, at 5d.; 10 lb. rice, at 34d.; 8 lb. loaf sugar, at 74d.; 9 lb. raisins, at 61d.; 7 lb. currants, at 5ąd. 53. A BUTCHER'S BILL. Ribs of beef, 9. lb. at 74d.; shoulder of veal, 8 lb. at 61d.; loin of pork, 11 lb. at 64d.; leg of mutton, 9-lb. at 63d.; breast of veal, 8 lb. at 7'd.; quarter of lamb, 9-lb. at 81d.; 3 lb. of suet, at 6'd. 54 A STATIONER'S BILL. 5'quires letter paper, at 10 d.; 5 quires black-edged note paper, at 7.d.; 3quires pink blotting, at 1's. 6'd.; 2 boxes envelopes, at 2's. 8'd.; 10 boxes steel pens, at 1's. 9'd.; gross* pen-holders, at 8'd. per doz.; 1 doz. slates, at 94d.;quire + drawing, at 4'd. per sheet. 55 A DRAPER'S BILL. 6 yds. flannel, at 173d.; 11′ yds. lawn, at 14.d.; 4 yds. chintz, at 164d.; 9 yds. diaper, at 83d.; 4 pr. kid gloves, at 3's. 10'd.; 12 yds. ribbon, at 124d.; 8 yds. shirting, at 73d.; 11 yds. damask, at 2's. 4 d.; 7 yds. sheeting, at 13.d.; 7 yds. Russia ditto, at 2's. 1'd.; 5. pr. cotton stockings, at 1's. 5d.; 12 yds. print, at 72d.

Find the 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, and 12th Multiples of each of the following Compound Quantities, describing each Multiple in writing.

56. Of 14. T. 13' cwt. 15 lb. 11 oz. 7. dr. | 63∙ Of 34 su. yd. 8. ft. 2′ 8′′ 57. Of 14 lb. 11 oz. 17 dwts. 13. gr. 58. Of 9. lb. 3·3 6·3 2. 15. gr. 59. Of 22 yd. 2. ft. 9 in. 6. li. 60. Of 17 mi. 4. fur. 15 po. 33 yd. 61 Of 16 yd. 1. qr 3. na. 2. in. 62. Of 8. E. E. 3 qr. 3 na. 13 in.

To Multiply any Compound Number, having Factors each less

64. Of 14 ac. 38' po. 29 yd.
65 Of 5 ld. 3 qr. 6. bu. 3. pe.
66 Of 4.0 11.3 5.3 48. m.
67. Of a Julian year.
68. Of a tropical year.
69. Of a lunar month.

Quantity by a Composite
than 13.

Multiply continually by any set of Corresponding Factors of the Multiplier. (PRINCIPLE XI. and pp. 63′, &c.) EXAMPLES WORKED OUT. I. Mult £18·14 s. 6d. by 42·. II. Find the weight of 63 hhd. each 3 cwt. 2 qr. 21·lb.