Question 27:

Suppose the breadth 2 feet, then the height must be 10 feet, and length 80: then 2 multiply 10 multiply 80 equal 1600: then 2 multiply 2 multiply 2 equal 8: then say, as 1600: 8:: 18225 to 91,125, whose cube root is 4,5, which is the breadth. Then 4,5 multiply 5 equal 22,5, the height, and 22,5 multiply 8 equal 180, the length.

Question 28.

39 multiply 39 equal 1521, and 15 multiply 15 equal 225: then 1521 less 225 equal 1296, whose square root is 36 feet, the piece standing, and the piece broken off 39 feet, both which added together make 75 feet, the whole length of the pole. Ans.

Question 29.

(By Euclid, 6, 4.) As 4,1 : 5 :: 65 to 79,26 feet. Âns.

Question 30.

The solidity and superficies is as 1 to 6: when the axis of the globe is f, then say, as 18: 8:: 6 to 23, answer for No. 31.

Question $1.

If the diameter be 1, the solidity will be ,5236, and the superficies 3,1416, that is, as 1 to 6: and to find the superficial content, multiply 3,1416 by the square of the axis, and the product is the superficial content. For the solidity, multiply,5236 by the cube of the axis, and the product is the solid content. Therefore, because ,5236 is a sixth part of 3,1416, you must take 6 for the diameter sought. Therefore 6 is the answer for No. 30.

Question 32.

RULE. From the square of the length of the pole, (that is, of the sum of the hypothenuse and perpendicular,) take the square of the base, and divide the remainder by twice the length of the pole, and the quotient will be the perpendicular height, where it was cut off.

16 multiply 16 multiply 16 equal 4096; then say, as 1:,5236 :: 4096 to 2144,66562=1072,3328, which is the solidity of the metal of the greater shell, as also the concavity. Then say, as ,5236: 1 :: 1072,3328 to 2048, whose cube root is 12,699, which is the diameter of the second shell. Then add 5 equal 12; and say, as 12:5:: 1072,3328 to 446,805, the solidity of the concavity of the second shell. Then say, as ,5236: 1 :: 446,805 to 853,333, whose cube root is 9,485, the diameter of the least shell. Then 9 add 4 equal 13; and say, as 13:4:: 446,805 to 137,47846, the solid content of the concavity of the third shell. Then say, as,5236: 1 :: 137,47846 to 262,5639, whose cube root is 6,4034, the diameter of the least shell's concavity. Then 16, the diameter of the greatest, less 12,699, the diameter of the second, equal 3,301 ? = 1,65, the thickness of the metal of the greatest. Then from 12,699, the diameter of the second, take 9,485, the diameter of the least, and there remains 3,314-2=1,657, the thickness of metal of the second. Then from 9,485, the diameter of the least, take 6,403, the diameter of the concavity, and there remains 3,082 ÷ 2 = 1,541, the thickness of metal of the least.

The metal of the greatest is 1072,33 solid inches, which divide by 4, (for every 4 solid inches is one-fourth of a pound,) and the quotient is 268,03 ìbs.

The metal of the second is 625,52 solid inches, which divide by 4, and the quotient is 156,38 lbs. the weight of the second. The metal of the least is 309,32 solid inches, which divide by 4, and the quotient is 77,33 lbs. the weight of the least shell.

The diameter of the second shell is 12,699 inches, and of the least shell, 9,485 inches. The thickness of the metal of the greatest is 1,65 inc. of the second, 1,607 ine. and of the third, 1,541 inc. The weight of the greatest is 268,08 lbs. of the second, 156,38 lbs. and of the least, 77,33 lbs.

-18 X 14 252 ÷ 3 = 84 ÷ 8 — 10 inches. Ans

Question 36.

1296 inches make a square yard, and 16 feet 5 inches equal 197 inc. then. 1296 divided by 197, equal 6114 inc. from the edge. Ans.

Question 37.

The square root of 2500 equal 50 each side; then 2500 divided by 2, equat 1250, the square root whereof is 35,35: then 50 less 35,35 equal 14,65 yards, the breadth of the walk. Ans.

Question 38.

20 multiply 20 equal 400, and 10 multiply 40 equal 100, and again, 10 multiply 10 equal 100: then 100 add 100 equal 200, the two floors; and 400 less 200 equal 200 feet. Ans.

Question 39.

12 multiply 12 multiplv 6 equal 864, a solid half foot.
6 multiply 6 multiply 6 equal 216, half a foot solid.

2X3X4X5X6=720+1=7217103 peaches. Ans.

Question 41.

The dog runs 16 miles an hour, and the hare 10 miles, the dog gaining 6 miles in running 1 hour: then say, as I: 10 :: 45 to 660 feet; and 12 rods added to 660 feet, make 858 feet, the distance the hare was when the dog started. Then say, as 6: 858:: 16 to 2288 feet, run by the dog. Now, as 16: 12288 to 973 seconds, or 1 min. 37 sec. the length of the chase; and the length of ground run by the dog, was 2288 feet, or 3 fur. 183 rods.

Question 42.

6 hours in the forenoon, and 3 in the afternoon, make 9 hours, the messenger from Washington was before the other: then 9 multiply 4 equal 36 miles he travelled, before the other messenger started. Then 7 add 4 equal 11 miles, both lessen the road per hour. Then 100 miles, (the distance between both places,) less 36 equal 64. Then say, as 11: 4 :: 64 to 23-3 miles, (the messenger from Washington travelled, after the other from Pittsburgh started,) add 36, (he travelled before he left Pittsburgh,) equal 59–8 miles, from Washington, where they meet, and 40 miles from Pittsburgh, that is, 100 less 592 equal 408. Ans.

Question 43.

As 22: 2 :: 1 to, or

Then

34

Then as 11 : 1

187

As $4
TT.
Then say, as 1

:: 22 to 17.

to 17, the number of times they go

round the field, before B overtakes A. Ans.

Question 44.

As 57: 60 to 84 gallons in 1 hour. As 17: 20 :: 60 to 7010 gallons in 1 hour. Then 84 gallons, (filled in 1 hr.) less 7010 gallons, (emptied in 1 hour,) equal 13, gallons, (difference in 1 hour.) 13 2hrs. 2614 gallons. Then x = 100-2614-73, galls. remaining to be filled. Then say, As 7 5 73,3 to 5111 min. past 6 o'clock. Ans.

As

1800

Question 45.

to 4800 dollars. Then 4800+6000⇒

10800 of his fortune. Then say,

As: 10800 :: to 15120 dollars. Ans.

Question 46.

12×10-120, whose square root is 10,954 lbs. Ans.

Question 47.

of 18. Then say, as : 1500 to $6000. Ans. Question 48.

1+1+}=11.

+1+1 Then 1-11; therefore, is equal to 50+30=80. Then as : 80:: to 960, number of trees.

1

12

Question 49,

Suppose A and B had 50 dollars: then say, as 5:7:: 50 to 70, B's and C's: then say, as 7: 170 to 10, C's-B's. Then 70-10-60÷2=30 for B; and 30-10-20 for A. Then 30+10=40 for C. Then it will be, A 20 + B 30+

112,8-12=9,4= the second number: then as 4: 9,4 :: 12 to 28,2-fourth number: then 28,2-9,4-18,8, difference of the second and fourth. Ans.

Question 51.

40×7-280, and 40×8=320, and 40×9-360: then A will travel 280 miles, B 320, and C 360: then 280÷7, and 320÷8, and 360÷9=40 days, after they started. Ans.

5 leagues equal 16,5 miles; then 16,5-42056462+6 x6-13,943 miles, equal to 73619 feet nearly: then 73619x 73169-42056462=129 feet nearly. Ans.

As 2163: 234: 100 to 108 A's
As 2163: 234 :: 663 to 72 B's
As 2163: 234 50 to 54 C's
Question 56.

Suppose $16 the first time, 48 the second time, 144 the third time, and 432 the fourth or last time, all amounting to $640. Then say, as 640 320 :: 16 to $8, the first time. Again, as 640: 320: 432 to $216, the last time..

Suppose the assembly consisted of 60 members; then half of 60 equal $0, and 20, (a third of 60,) add 10 equal 30, and 20+3050 Then 60 less 50 equal 10, which 10 should equal the third of 60, and 10 absent: thus 30 less 10 equal 20, error too little.

Again, suppose 90, half of which is 45+20=65. Then 90÷$30k 1040: then 90-65-25, should equal 40; therefore 40-25=15, error. too little.

1st sup. 60

90 2nd sup.

X

PROOF. 180-2+20=110, and 180÷S+10=70; then 110 (met) + 70 (absent) = 180. Ans.

Question 60.

Then three vents in one hour will empty 220 gailons. Then say,
As 220 : 1 :: 120 to 32 min. 4311 sec. Ans.

Question 61.

6000 divided by 120 equal 50 cubic feet. 11325 oz. is the specific gravity of a cubic foot of lead: then 11325 multiply 50 equal 566250 oz. or 15 tous 15 cwt. 3 qrs. 26 lbs. 10 oz. Ans.

Question 62.

30 multiply 4,5 equal 195 feet, area of the side; and 135 multiply 2, (the centre of gravity,) equal 270: then 270 multiply 62,5, (the specific gravity in pounds of a cubic foot of running water,) equal 16875 lbs. or 7 tons 10 cwt. 2 qrs. 19 lbs. Ans. (See page 207.)

Question 63.

S multiply 5 equal 15 square feet, the area of the bottom. 15 multiply 4 equal 60 cubic feet in the vessel: then 60 multiply 62,5, (the specific gravity in pounds,) equal 3750 lbs. or 1 ton 13 cwt. 1 qr. 26 lbs. Ans. (See page 207.)