creases with the increase of weight, called gravity, of á moving body, but not in proportion to the additional weight or gravity and to the contrary, it decreases with the decrease of weight, but not in proportion to the weight deducted. Again, friction decreases with the increase of velocity, and it increases with the diminution of velocity. This is well known to us all who "eat our bread by the sweat of the brow;" for, if we start a loaded carriage, or a mill wheel, a greater power is required to overcome the inertia, than to continue motion afterwards. This proves that the increase of velocity decreases the power of friction: But to calculate the proportions of the decrease of friction in this case, would require as many statements as there are seconds or half seconds in the time from the starting of the wheel, till it is moved with its highest degree of velocity. Respecting these principles of friction, Mr. Evans of Philadelphia, the noted millwright, has made the following experiments. He placed a flat-sided glass bottle on an piled steel plate; and when the bottle was loaded with 10 pounds, it was drawn by a power of 1 pound-when loaded with 22 pounds, it was drawn by 2 pounds; and when loaded with 60 pounds, it was drawn by 44 pounds. In this last trial of 60 pounds drawn by 44 pounds, he says the motion was greatly accelerated, which gives reason to conclude that, less weight would have continued the motion after once begun. He then goes on partly by guess, and partly by calculation, to prove the above theory and establish some partial rules: that is to say, If 10 pounds are moved by 1 pound, then so small a body possesses a resisting power of part of the whole22 pounds being moved by 2 pounds, the resisting power was of the whole; and 60 pounds being moved by 44 pounds, the power of resistance by friction appeared to Inertia, a power in matter which disposes it to continue in the same state; inactivity, sluggishness, be about of the whole. Then he argues, if this small body of 60 pounds, possesses a resisting power of only + part of the whole, then a large body, such as a mill wheel of 4000 pounds weight, will possess not more than, and at the same time the gudgeons shall be equal in diameter with the wheel, in order to coincide with the principle of plain surfaces rubbing together like the bottle and the steel plate. He then gives the following RULE. As the diameter of the wheel, is to the diameter of the gudgeons; So is one twentieth part of the weight of the wheel, to the weight which will balance the friction, Then follows an example which we will take for LESSON 1. If a mill wheel weighing 4000 pounds be 15 feet in diameter, and the gudgeons 3 inches in diameter, how many pounds on the rim of the wheel will balance the friction? Ans. 3.333 pounds. OPERATION. 20)4000 pounds the weight of the wheel. 200 a twentieth part. 15 feet x 12 = 180 In. Diam. wheel. Gud. Ib. 180 3200 to a fourth number. 3 180)600(3.3+ pounds. 540 .600* 540 We will try one lesson more and quit the subject. If the diameter of a wheel be 18 feet, the weight 3600 pounds, and the gudgeons 3 inches in diameter, how many pounds on the rim of the wheel will balance the friction? Ans. 2.5 pounds. 3600 ÷ 20 = 180 a twentieth part of the weight of the wheel. 18 feet x 12216 inches the diameter of the wheel. W. G. lb. 216 : 3 :: 180 3 216)540(2.5 pounds. 432 1080* 1080 EXERCISING QUESTIONS. LESSON 1. In £346, how many shillings, sixpences, threepences and farthings? Answer, 6920s. 13840 sixpences, and 332160 farthings. Root, p. 50. Root, p. 50. 2. Reduce 27680 threepences into pounds. Make it £ 346. 3. In £386, how many shillings, ninepences, sixpences, fourpences and pence, and of each an equal number? 12d.+9d. + 6d. + 4d. + 1d. = 32d. for a divisor. £ 386 = 92640d. 32 = 2895 the answer. 4. In 49 bushels how many quarts? 49 × 32=1568 the answer. Root, p. 50. Root, p. 51. = 5. Two men were shoveling a cargo of salt out of a vessel, and it was judged that each man threw out six quarts at a time, and the cargo contained one thousand bushels— I demand the number of shovel-fulls for each man to throw out? Root p. 52. 6. How many days will a barrel of cider last if you draw six quarts a day, allowing the barrel to hold 314 gallons? Root p. 52. Ans. 26663. Ans. 21 days. 7. How many apples will it take to make a load or ton of cider, allowing 3 apples to make a gill, and 252 gallons a ton? Ans. 24192 apples. Root, p. 52. 8. How many times will a carriage wheel, 154 feet in circumference, turn round in going from New-York to Philadelphia, it being 95 miles? Ans. 32713 times and 8 in. over: Root, p. 52. 9. The forward wheels of a waggon are 144 feet in cir cumference, and the hind wheels 15 feet 9 inches; how many more times will the forward wheels turn round than the hind wheels, in running from Boston to New-York-it being 248 miles? Ans. 7167 Root p. 52 10. In a room 16 feet square; how many square feet? Root, p. 53. Ans. 256. 11. How many shingles will cover a house 40 feet long and 30 feet rafters, allowing shingles to be 4 inches wide, and each course 6 inches? Ans. 14400 Root, p. 53. NOTE.-We may add 240 shingles to form a double course over the eaves. 12. In a field 60 rods square, how many acres? Ans. 221 acres. Root, p. 53. 13. How much carpeting 3 qrs. wide will cover a floor 18 feet long and 16 feet wide? Ans. 42 yds. 2 qrs. 6 inches. PROOF OF THE LAST QUESTION. Root, p. 53. 14. How many square inches in a piece of carpeting 42 yds. 2 qrs. 6 inches long, and 27 inches wide? Ans. 1536 inches. 15. How many seconds from the birth of Christ to Christmas 1795, allowing each year to contain 365 days 6 hours? Root, p. 54. Ans. 56,645,892,000. 16. Sound goes 1142 feet in a second: suppose in a thunder storm you see the lightning 24 seconds before you hear the thunder; at what distance are you from the explosion? Ans. 5 miles, 1 fur. 21 yds. 1 ft. 6 in. Root, p. 55. 17. The inhabitants of the whole world are computed to be 953 millions; supposing they all stood in a line, how long would it take you to count them all, if you could count 20 in a minute and continue counting 12 hours in a day? Ans. 181 yrs. 115 days, 6 hrs. 40 min. Root, p. 55. 18. How many pounds of sugar can you buy for £11 11s. at 4 d. a pound? Ans. 5 cwt. 2 qrs. Root, p. 66. p. 66. bush 19. What cost 17 cwt. 3 qrs. 14 lb. at 5 cents a pound? Ans. $100, 10 cents. Root, 20. If 5 tons of hay will keep 3 cattle over the winter, how many tons will it take to keep 37 cattle the same time? Ans. 61 tons, 13 cwt. 1 qr. 94 lb. Root, p. 66. 21. A gentleman farmer had 21 bushels Indian corn which he wished to mix with buckwheat so that every el of provender should contain 13 quarts of Indian corn; I demand the quantity of buckwheat in the mixture? Ans. 30 bush. 2 pecks, 6 qts. Root, p. 66. Say, as 13 qts. of corn are to 19 qts. of buckwheat :: so are 21 bush. corn or 672 qts.: to 30 bush. 2 pecks, 6 qts. buckwheat. 22. Seventy-five pounds sterling of Great Britain are equal to £100 New-England currency; how much NewEngland currency is £410 19s. 2d. sterling money of Great Britain? Ans. £547 18s. 104d. Root, p. 66. 23. When a staff 3 feet long will cast a shade 21 feet, what is the height of a steeple that casts a shade 107 feet at the same time of the day? Ans. 128 feet. Root, p. 67. 24. A Merchant agreed with his debtor that if he would pay him down 12s. 6d. on the pound, he would give him up a note of hand of £69 5s. 4d.; Idemand what the debtor must pay for the note? Ans. £43 5s. 10d. Root, p. 67. 25. Two boys are playing tag, one boy has 6 rods the start, but the other boy can run 15 to his 13; I demand how far the hindermost boy must run before he will overtake the other one? Ans. 45 rods. Root, p. 67. State thus: If 2 rods deficiency will 6 rods deficiency arise from? 26. Suppose stock in the United arise in 15 :: what 2 : 15 :: 6 : 45 States Bank to be 15 |