Note.-Four pennyweights of gold being divided into 24 equal parts, these parts are called carats; but gold is often mixed with some baser metal, which in the mixture is called alloy; and according to the proportion of pure gold which is in every 4 pennyweights, so the mixture is said to be so many carats fine. Thus, if only 20 carats of pure gold and 4 of alloy, it is 20 carats fine; if 22 carats of pure gold and 2 of alloy, 22 carats fine; and if there be no alloy, it is 24 carata fine or pure gold. A carat is 4 grains.

To compute the fineness of any gold coin from the foregoing

table.

RULE.

As the weight of the coin, Is to its contents in pure gold, So is 24 carats, To the fineness required.

Examples.

1. The weight of the American Eagle, coined prior to July 31st, 1834, was 270 grains, its contents in pure gold is 247.5 grains-I wish to know how many carats fine it is.

As 270 247.5:: 24: 22 carats fine. Answer. 2. Required the fineness of the American Eagle coined after July 31st, 1834.

As 258 3. I wish to Fonducli.

As 53

232 :: 24: 21 carats 2 know the fineness of the

grains. Ans.

Turkish Sequin

42.5: 24: 194 nearly. Answer.

4. I demand the fineness of the sequin of Rome.

As 52.5 52.2 :: 24 : 23.86 carats fine. Ans.

5. Required the fineness of Rupee of Madras.

As 180 165 :: 24 : 22 carats fine. Ans.

:

6. Required the fineness of the Spanish Doubloon. As 417 360.5 : 24: 20 nearly. Answer. 7. I wish to know the fineness of Ruspone of the kingdom of Etruria.

As 161.25 161: 24: 23.96 carats fine, or nearly pure gold. Answer.

MISCELLANEOUS QUESTIONS.

1. A hare starts 5 rods before a greyhound, and is not perceived by him until she has been up 34 seconds; she scuds away at the rate of 12 miles an hour, and the greyhound on view makes after her at the rate of 20 miles an hour-How long will the course hold, and what ground will he run, beginning with the outsetting of the greyhound?

Ans. 58 seconds: 17024 feet run. 2. A. leaves New Italy at 4 o'clock in the morning for Harrisburg, and goes at the rate of 6 miles an hour, without intermission: B sets out of Harrisburg for New Italy at 5 o'clock the same morning, and rides at the rate of 5 miles an hour constantly-the question is, whereabouts on the road will they meet, and at what time; the distance being 55 miles ? Ans. 32 miles from Harrisburg, at 27 past 9 in the morning.

min.

3. There is an island which is 36 miles in circumference; now if at the same time and from the same place, two footmen, A and B, set forward to travel round about the said island, and follow one another in such a manner that A travels every day 9 miles and B7 miles-the question is to find in what space of time they will meet again, and also how many miles, and how many times round the island each footman will then have travelled.

Ans. They will meet at the end of 18 days from their first parting, and then A will have travelled 162 miles, (or 4 times the circumference of the island) and B will have travelled 126 miles, (or 3 times the circumference of the island.)

4. An Italian Mulberry orchard in New Italy measures as follows, viz: south side 42.9 perches, west side 37.2 perches, north side 33.4 perches, east side 36.1 perches; the north-east and south-east corners are each a right angle-I wish to know how much longer the diagonal from the northeast to the south-west corner is than that from the north-west to the south-east corner. Ans. 6.89 perches.

5. During the memorable storm of sleet and snow on the 8th and 9th of January, 1836, a tree (near the compiler's door,) 80 feet in height, was broken in such a manner as to touch the ground 60 feet from the foot of the tree-I wish to know the length of the piece broken. Ans. 62 feet.

Rule for such questions.

Add the square of the height of the tree to the square of the distance from the foot of the tree to the top (after it fel!); divide the sum by twice the height of the tree, the quotient will be the length of the broken piece.

6. Required the diameter of a circle that will comprehend within its circumference the quantity of an acre of land. Ans. 235 ft. 6 in.

7. A may pole 50 ft. 11 in. in length, at a certain hour of the day casts a shadow 98 ft. 6 in. long; I would hereby find the breadth of a river, that, running 20 feet 6 inches from the foot of a steeple, 300 feet 8 inches high, the extremity of the shadow of the steeple reaching 30 feet 9 inches beyond the Ans. 530 ft. 5 in. nearly.

stream.

8. If 6 men can perform a piece of work in 4 days, how many men will accomplish another four times as large in one fourth the time?

Ans. 96.