Question 64.

25

100 yards per minute equal 5 feet per second: 5X564-8,39 of a foot for the perpendicular height, or fall of the water: then 62,5 X,39 24,375 lbs. the pressure upon each square foot: then 15 multiply & equal 60 feet, the area of the obstacle: then 24,375 multiply 60 equal 1462,5 lbs. going with the velocity of 5 feet per second: therefore 1462,5 multiply 5 equal 7312,5 lbs. Ans. (See page 207.)

Question 65.

1560,25 multiply 2 equal 3120,5; then 3161, (sum of their squares,) less 3120,5 equal 40,52 equal 20,25, whose square root is 4,5, half the diff. and the square root of 1560,25 equal 39,5, (half sum,) and 4,5, (half diff.) equal 44, the greater number. Then 39,5, (half sum,) less 4,5, (half diff.) equal 35, the lesser number. Ans.

Question 66.

600-8 equal 75; then 75 multiply 75 equal 5625 feet, the height the body raust fall from, to acquire the velocity of 600 feet per second. Ans.

RULE for this and such like questions. The square root of the feet in the space fallen through, will always be equal to one-eighth of the velocity ac quired at the end of the fall; therefore divide the velocity by 8, and the square of the quotient will be the distance fallen through, to acquire that velocity.

Question 67.

12 multiply 12 equal 144, the square of the semidiameter; then 144 multiply 2 multiply 20, and divide by 144, equal 40 feet, the solidity, when hewn square. Now, to find the whole solidity, 24 multiply 24, (whole diameter,) multiply,7854 multiply 20 ÷ 144 62,8, the whole content, from which take 40, the content, when hewn square, and there remains 22,8 feet, the content of the slabs. Ans.

RULE. Multiply twice the square of the semidiameter by the length, and divide the product by 144, and the quotient will be the answer.

Question 68.

9 multiply 9 equal 81, and 5 multiply 10 equal 50 feet: then say, As 5 81: 50 to 810, whose square root is 28,46 inches, the answer.

Question 69.

Weight of 2 passengers, 336 lbs. and of the body of the chaise, 84 lbs. making 420 lbs. 8 ft. X 12

96 inc. Then say,

A, B and C, can do it in 15 days. Then say,

Then say, as 1 1: 1 to 120 days by C. Ans.

120

Question 71.

by A and B. As 12: 1 :: 1 to

1

As 2011 to by A+B+C. Then Then say,

12

20

1 to 30 days by C. Ans.

Question 72.

$1,25 less 1,20 equal 5 cents loss on every 125 cents. Then say,

As 125: 5. ::

100 to 4 dolls. Ans. 4 per cent.

Question 73.

As $115 $100 :: $2,30 to 2, first cost per yard: then 2,40 less 2 equal 40 ets. profit on $2.

Then say, as 2: 40: 100 to 20 per cent. gain.

Question 74.

46 multiply 46 equal 2116, square of the greater, and 35 multiply 35 equal 1225, square of the lesser. 3341, sum of the squares. Ans.

=

161046 35, the lesser number. 46, (the greater number,) less 35, (the lesser number,) equal 11, the difference: then 11 multiply 11 multiply 11 equal 1331, the cube of their difference. Ans.

Question 75.

+/

17

+=1; then 1-1. Then say,

$14,40 less $12,24 equal $2,16; then say, as 9 yds.: $2,16: 1 yard to 24 cents per yard, the answer.

Then $14,40 add $12,24 equal $26,64. Then say, as 24 cts.: 1 yd. :: $26,64 to 111 yards in both pieces. Ans.

Question 77.

81034X18X4—5834448 qts. then say, as : 1 :: 5834448 to 6563754 bottles. Then 6563754-144-45581 gross 74 dozen. Ans.

Question 78.

As 6 10 9 to 15 footmen: then 5 wagons at 25 cts. each is 125 cts. 9 horsemen at 124 cts. each is 1123 cts. and 15 footmen at 63 cts. each, 933 cts. amounting in all to 3314 cts. Then say, as 3314: 1 :: 1325 to 400. Then 400X5=2000 wagons, 400×9=3600 horsemen, 400X156000 footmen. Question 79.

A 2, B4, C5, D6, E 8: then 2+4+5+6+8=25, the sum. Then As 25 : 2000 :: 2 to $160 for A.

Suppose 20 admirals each $1, which is $20, the 30 post-captains each 80 cts. which 824, the 24 sailing-masters each 50 cts. which is $12, and the 24 lieutenants each 331 cts, which is 8. Then 20+24+12+8=64%

4×20=80 dolls. paid by 20 admirals. 3,20×30=96 dolls. paid by 30 post-captains. 2X24=48 dolls. paid by 24 sailing-masters. 1,33×24 32 doffs. paid by 24 lieutenants. Ans.

10

Now to find their proportion. 4 admirals paid each 4 dolls. amounting to 16 dolls. 5 post-captains paid each 3 dolls. 20 cts. amounting to 16 dolls, post-captains paid 32 dolls. 16 sailing-masters paid each 2 dolls. amounting to 32 dollars. 8 sailing-masters paid 16 dolls. and 12 lieutenants paid cash1 dollar 331 cents, amounting to 16 dollars.

Then say, as,276982: 3 :: 1 to 10,8309505 days, all working together. Then 14-10,8309505=3,16905. Then say, as 3,16905: 10,83095 :: 14 to 47,848 days by A. Then 15-10,830954,16905. Then say, as 4,16905: 10,83095 :: 15 to 38,969 days by B. Then 18-10,83095 7,16905. Then say, as 7,16905: 10.83095 :: 18 to 27,194 days by C. Then 12-10,83095-1,16905. Then say, as 1,16905: 10,83095 :: 12 to 111,176 days by D.

Question 82.

RULE. From the sum take the difference, and half the remainder is the square of the less, which taken from the sum of their squares, will give the square of the greater.

*208-80=128÷÷÷2=64; then 208-64-144. The square root of 144 is 12, the greater; and the square root of 64 is 8, the less number; and 12 less 8 equal 4, A had more than B. Ans.

2

Question 83.

RULE. From the square of their sum take the sum of their squares, and from the sum of their squares take this remainder, and the square root of the difference will be the difference of the two numbers.

50X50 equal 2500; then 2500 less 1300 equal 1200; then 1300 less 1200 equal 100, whose square root is 10, the difference of the two numbers.

50, (the sum,) 2 equal 25, half the sum; and 10-2 equal 5, half the difference. Then to half the sum add half the difference, and from half the sum take half the difference, thus: 25 add 5 equal 30, the greater number; and 25 less 5 equal 20, the lesser number. Ans.

Question 84.

Suppose 1 boy got 1 dollar, 1 woman 2 dollars, and 1 man 4 dollars. Then 1X9 equal 9, 2×6 equal 12, and 4X4 equal 16, making 37. Then say, As 37: 316,962 :: 9 to 877,10÷98,563 cts. for each boy. Ans As 37: 316,962 :: 12 to 102,80--6-17,131 cts. for each woman, As 37; 316,962 :: 16 to 137,63÷÷4=34,262 ets. for each main

Y

Question 85.

Suppose the greatest 150×3-450, and the lesser 116 × 5-5834; then 5834-450-133, error.

Again, suppose the greatest 140x3-420, and the lesser 1262×5-6333; then 6333-420=213}, error.

1st sup. 150

Error 1334

56000

2133-1333=80×3240, because the result of the multiplication is thirds.

140 2nd sup.

X

2151 error.

96000
56000

40000÷240=166%, the great est number; and 2663-1663100, the lesser number. Ans.

PROOF. 100×5=500, and 166×3=500.

Then his age was to her's, as 2 to 14.

She must be 15 years.

30

She must be 45 years.

Then say, as 1 : 2 :: 45 to 63

years he should be. Then 63 less 60 equal 3, error.

Then say, as 14: 2 :: 40 to 56 yrs. he should be. Then 56-50=6, error.

-120÷3➡ 40 yrs. he was, when married, and cons sequently she must be 20 years. Ans.

PROOF. When married, he was double her age, that is, as 1 to 2; thereore 40÷2=20, her age. Then 30 years after, his was to her's as 2 to 14. Then he was 70, and she was 50; thus, as 2:14:: 70 to 50, her age at that time. Then 30 years more makes him 100, and her 80; and his proportion to her is as 2 to 13; thus, as 2:13:: 100 to 80, her age at that time.

Question 87.

RULE. The velocity of the two hands of a watch or clock, are to each other as 12 to 1; therefore the difference of velocity is 12-1-11. Then say,

Question 88.

RULE. From the sum of their squares take the square of their difference, and to the sum of their squares add the remainder, and the square root of this sum will be the sum of the required numbers. Then to half the sum add half the difference, and from half the sum take half the difference, and you will have the two numbers separately

12500-50X50 10000+12500-22500, whose square root is 150, sum of the two numbers: then 150÷2 equal 75, the half sum: then 50 is their difference: then 50÷÷÷2 equal 25, half difference: then to 75, half the sum, add 25, half the difference, making 100 the number belonging to A; and 75 less 25 equal 50, the number belonging to B. Ans.

Question 89.

14 add 14 equal 28, what both had; then 336-28 equal 12, the difference. Then 282 equal 14, half sama; and 12÷2 equal 6, half the difference. Then 14 add 6 equal 20, the number Tom retired with: then 14 less 6 equal Jack had still; therefore it will be that Jack lost 14-8-6 he lost. Ans.

Question 90.

288-12 equal 24, the sum, and 242 equal 12, the half sum, and 12, the difference: then to half the sum add half the difference, and from half the sum take half the difference, to find the two numbers. 12 is half the sum, and 122 equal 6, half the difference: then 12 add 6 equal 18, William's share, and 12 less 6 equal 6, John's share. Ans.

Question 91.

RULE for all such questions. As unity is to the distance, so is the number in rank, less by one, to a fourth number. Next do the same with the file, and multiply the two numbers found together by the proportion stated, and the product will be the answer, thus:

As 1 : 4 :: 56-1 to 220

As 1 : 4 :: 36-1 to 140.

Then 220 X 140 equal 30800 square feet. Ans.

Question 92.

RULE for all such questions Say as the ratio in length is to the ratio in breadth, so is the number of trees to a fourth number, whose square root is the number in breadth; and as the ratio in breadth is to the ratio in length, so is the number of trees to a fourth number, whose square root is the num ber in length, thus:

As 3 : 2 ::
As 2 : 3 ::

600 to 400, whose square root is 20.
600 to 900, whose square root is 30.

That is, 20 in breadth, and 30 in length. Ans.

Then say, as 1 7:: 20-1 to 133.

As 17: 30-1 to 203.

Then 203 multiply 133, equal 26999 square yards. Ans.

Question 93.

6 multiply 6 equal 36, and 4 multiply & equal 16, multiply 3 equal 48: then say inversely, as 36; 4:: 48 to 3 hours. Then for double say, as 1 : 3 :: 2, (direct proportion,) to 6 hours. Aos.

Question 94.

60 multiply 60 equal 3600, and 37 multiply 37 equal 1369, and 23 multiply 23 equal 529: then 3600 less 1369 equal 2231, square root thereof, 47, 23+ Then 3600 less 529 equal 3071, whose square root is 55,41+. Then 47,28 add 55,41 equal 102,64 feet. Ans.