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(20) Suppose, with Dr. Keil, the distance of the sun to be

from us 115 of his diameters; how much hotter is it

then at the surface of the sun than under our equator? (21) A ball, descending by the force of gravity from the top

of a tower, was observed to fall half the way in the last second of time. Required the tower's height, and the

whole time of descent. The less porous a body is, the greater is its density. (22) The compactness or density of the moon is to that of

the earth, as 132] is to 100. What proportion then is there between the quantity of matter in the earth and that in the moon, since the earth's diameter is

7970 miles, and that of the moon 2170? (23) There is a vast country in Ethiopia Superior, to whose

inhabitants the moon always appears to be most en. Jightened when she is least enlightened, and to be least when most, according to Gordon's Geographical Grammar. Admitting the mean distance of the earth and moon's centres 240,000 miles, in what proportion is this illumination?

Velocities acquired by heavy Bodies fulling. The velocity acquired by heavy bodies falling near the surface of the earth is 161 feet in the first second: and as 16{ feet are to the square of one second, or 1, so is the given distance to the square of the seconds required : or, on the contrary, to determine what space a heavy body has passed in any time given, is,

By multiplying 161, the descent of a heavy body in one second of time, by as many of the odd numbers, beginning from unity, as there are seconds in the given time, viz. by i for the first, 3 for the second, 5 for the third, 7 for the fourth, &c.: the sum total will give the space it has passed. (24) Suppose a stone let go into an abyss should be stopped

at the end of the eleventh second after its delivery,

what space would it have gone through? (25) What is the difference between the depth of two wells,

into each of which should a stone be dropped at the same instant, one will meet with the bottom at 6 se

conds, the other at 10? (20) If a stone be 191 seconds in descending from the top of a precipice to the bottom, what is the height of the

same? (27) In what time would a'musket ball, dropped from the top

of Salisbury steeple, said to be 400 feet high, be at the

bottom ? (28) If a hole could be bored through the centre of the earth,

in what time after the delivery of a heavy body on its surface would it arrive at its centre:

LIX. The DOUBLE RULE of THREE in DECIMALS.

REDUCE the fractional parts to decimals, and then proceed as in whole numbers.

EXAMPLES. (1) If 11. 2s. worth of wine will suffice a club of 12 persons

when the wine is sold at the rate of 251. 45. per hhd. how many persons will il. 128. worth serve, when the

wine is sold after the rate of 18 guineas per hhd. (2) If 6 lb. of pepper be worth 13 lb. of ginger, and 19 lb.

of this be worth 4b. of cloves, and 10 lb. be equivalent to 63 lb. of sugar'at 5d. per lb. what is the value

of I cwt. of pepper? (3) What money, at 31 per cent. will clear 381. 10s. in a

year and a quarter's time?

QUESTIONS for Exercise at leisure Hours. (4) A. lent his good friend B. fourscore and eleven guineas,

from the 11th of Dec. to the 12th of May following ;
B. on another occasion, let A. have 100 marks, from
September 3 to Christmas following. Quere, how
Jong ought the person obliged to let his friend use 401.

fully to retaliate the favour? (5) A. B. and C. will trench a field in 12 days; B. C. and

D. in 14; C. D. and A. will do it in 15, and D. A. and
B. in 18. In what time will it be done by all of them

together, and by each of them singly?' (6) A young hare starts 5 rods before a greyhound, and is

not perceived by him till she has been up 34 seconds; she scuds away at the rate of 12 miles an hour; and the dog, on view, makes after her at the rate of 20. How long will the course hold, and what ground will be run, beginning with the outsetting of the dog?

VIBRATION of PENDULUMS. IT has been found by experiment, that a pendulum 39,2 inches long, in our latitude, vibrates 60 times in one minute; and that the lengths of the pendulums are to one another reciprocally as the square of the number of their vibrations made in the same space of time. (7) What difference is there between the length of a pen

dulum that vibrates half a second, or 120 times in a minute, and another that swings double seconds, or

30 times in a minute? (8) What difference will there be in the number of vibra

tions made by a pendulum of 6 inches long, and an

other of 12 inches long, in an hour's time? (9) Whạt difference is there in the length of two pendu

lums, the one swinging 30 times, the other 100 times

in an hour? (10) Give the length of a pendulum that will swing once in a

third, ditto in a second, ditto in a minute, ditto in an

hour, ditto in a day. (11) Observed, that while a stone was descending to measure

the depth of a well, a string and plummet, that from the point of suspension, or the place where it was held, to the centre of oscillation, or that part of the bob, which, being divided by the circular line, struck from the above centre, would divide it into two parts of equal weight, measured just 18 inches, had made 8 vibrations. Pray what was the depth, allowing 1150 feet per second for the return of sound to the ear?

LX, FELLOWSHIP. How to perform fellowship, either single or double, without

that tedious and laborious task of making so many different statings as there are persons concerned.

RULE. 1. DIVIDE the whole gain or loss by the whole stock.

2. Multiply the quotient by each person's particular stock; and the several products will be the respective gain or loss of each.

Note. This rule is best adapted for decimals.

EXAMPLES (1) Three persons making a joint stock: A. puts in 7501.

B. 4501. C. 3001, with which they trade certain time; and, when they balance accounts, find that they have gained 3001.

What is the share of each? (2) Three merchants, A. B. and C. traded together; A. put

in 1201. for 8 months; B, 2501, for 4 months; and c, 1001. for 5 months : tbęy gained 18. 108. What is

each man's share of the gain?
(3) Once as I walk'd upon the banks of the Wye,

To see the purling streams glide gently by,
And hear the pretty birds to chirp and sing,
Making the groves with melody to ring;
I, in the meads, three beauteous nymphs did spy,
That for their pleasure came as well as I;
And unto me their steps they did direct,
Saluting me with most benign respect,
Saying, "Well met! we've business to impart,
wnich we cannot decide without your art.
Our grannam's dead, and left a legacy,
Which is to be divided amongst three:
In pounds it is two hundred twenty-nine,
Also a good mark, being sterling coin."
Then spake the eldest of the lovely three,
I'll tell you how it must divided be;
Likewise our names I unto you will tell;
My name is Moll, the others' Anne and Nell.
As oft as I five and five-ninths do take,
Anne takes four and three-sevepths her part to make;
As oft as Anne four and one-ninth does tell,
Three and two-thirds must be took up by Nell.”

For more examples, see Sections XXV. and XXVI.

Of Simple Interest, Annuities, or Pensions, &c.

LXI. SIMPLE INTEREST.

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Here are five letters to be observed, viz. P=any principal or sum put to interest. I=the interest. T=the time of the principal's continuance at interest. A=the amount, or principal and interest. R=the ratio, or rate per cent. per annum. Note.-The ratio is the simple interest of 11. for one year,

at any given rate; and is thus found, Viz, 100: 5::1: ,05 the ratio at 5 per cent. per ann, Or, 100: 6:31:,06 the ratio at 6 per cent. per ann. &c. And in this manner the ratios in the following table are

found.

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Case 1. When the principal, time, and rate per cent, are given, to find the interest.

RULE. Multiply the principal, rate, and time, continually into one another, the product is the interest sought.

Or, if p=the principal, t=the time, r=the rate, and I= the interest, then the theorem will be as follows:

THEOREM 1. pir=l.

EXAMPLES. (1) What is the interest of 2601. 17s. 6d. for 5 years at 41

per cent. per annum?

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