widow for life; the children's legacies were found to be $257,16;cts. different :-pray what sum did he leave the widow the use of? Ans. $635,04,62cts. 43. A had 12 pipes of wine, which he parted with to Blat 49 per cent. profit, who sold them to C for $40, 60cts, advantage; C made them over to D for $605,50cts., and cleared thereby 6 per cent. :-how much a gallon did this wine cost A? - Ans. 33 6 454cts. 44. Laid out $165,75ets. in wine at 21 cts. a gallon; some of which receiving damage in carriage, I sold the rest at 31%cts, a gallon, which produced only $110,831 ets. ; whai quantity was damaged ? Ans. 430gals." 45. A young hare starts 40 yards before a greyhound, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of ten miles an hour, and the dog, on view, makes after her at the rate of 18; how long will the course hold, and what ground will be run over by the dog? Ans 60,5 sec. and 530yds. run.. · 46. If I leave Hallowell at 8 o'clock on Monday morning for Newburyport, and ride at the rate of 3 miles an hour without intermission; and B sets out from Newburyport for Hallowell at 4 o'clock the same evening, and rides 4 miles an hour constantly: supposing the distance between the two towns to be 130 miles, whereabout on the road shall we meet ? Ans. 69miles from Hallowell, which will be in Saco. 47. X, Y, and Z, can, working together, complete a staircase in 12 days; Z is man enough to do it alone in 24 days, and X, in 34; in what time, then, could Y get it done himself? Ans. 81 days. 48. A and B together can build a boat in 18 days, and with the assistance of C, they can do it in 11 days; in what time then, would C do it by himself? Ans. 284 days. 49. Laid out in a lot of muslin £500, upon examination of which 3 parts in 9 proved damaged, so that I could make but 5s. a yard of the same; and by so doing, find I lost £50 by it; at what rate per ell Eng. am I to part with the undamaged muslin, in order to gain L50 upon the whole ? - Ans. 11s. 730. 50. If the sun move, every day, one degree, and the moon thirteen; and, at a certain time, the sun be at the beginning of. Cancer, and, in three days after, the moon at the beginning of Aries; the place of their next following conjunction is required. Ans. 10° 45' of Cancer. 51. A person being asked the time of day, answered, it is between 4 and 5; but a more particular answer being required, he said, that the hour and minute hands were then exactly together; what was the time ? Ans. 21,min. past 4. 52. What weight, hung at 70 inches' distance from the fulcrum of a steelyard, will equiponderate a hhd. of tobacco, weighing 950 11. freely suspended at 2 inches' distance on the contrary side ? Ans. 27 th. 2oz. 4. drs. • 53. If two places lie so much due east and west of each other, that it is found, by observation, to be noon at the former 2 hours, 6 min. and 30 seconds sooner than at the latter ; how many degrees are they apart ? Ans. 31° 37' 30 seconds. 54. If Paris, in France, be in 2° 20' east longitude from Greenwich, and Hallowell in 69° 42' west longitude from Greenwich; when it is noon at Paris, what time of day is it at Hallowell ? Ans. 7h. 11m. 52s, in the morning. david MEASUREMENT OF GRINDSTONES. ; GRINDSTONES are sold by the stone, and their contents found as follows :* Rule.To the whole diameter add half of the diameter, and multiply the sum of these by the same half, and this product by the thickness; divide this last number by 1728, and the quotient is the contents, or answer required. EXAMPLES. 1. What are the contents of a grindstone 24 inches diameter, and 4 inches thick ? 24+12x12x4 - =1 stone. Ans. 1728 2. What are the contents of a grindstone 36 inches diameter, and 4 inches thick: Ans. 24 stone. *24 inches in diameter, and 4 inches thick, make a stone. MENSURATION of Superficies and Solids. Section 1.-OF superficies. Superficial measure is that, which relates to length and breadth only, not regarding thickness. It is made up of squares, either greater or less, according to the different measures by which the dimeosions of the figure are taken or measured. Land is measured by this measure, its dimensions being usually taken in acres, rods, and links. The contents of boards, also, are found by this measure, their dimensions being taken in feet and inches. Because 12 inches in length make 1 foot of long measure, therefore 12x12=144, the square inches in a superficial foot, &c. CASE 1. To find the Arca of a square having equal sides. Rule.-Multiply the side of the square into itself, and the product will be the area, or superficial content, of the same name with the denomination taken, whether inches, feet, yards; rods and links, or acres. · EXAMPLES. J. How many square feet of boards are contained in the floor of a room which is 20 feet square ? 20x20=400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres does it contain ? 26.x26 As 160 square rods make an acre: therefore =4ac. 36 rods. 160. Ans. CASE 2. To'measure a parallelogram or long square. Rule --Multiply the length by the breadth, and the product will be the area, or superficial content, in the same name as that, in which the dimension was taken, whether inches, feet, or rods, &c. EXAMPLES 1. A certain garden, in form of a long square, is 96 feet long, and 54 feet wide ; how many square feet of ground are contained in it ? 96x54=5184 square feet Ans. 2. A lot of land, in form of a long square, is 120 rods in length, and 60 rods wide; how many acres are in it? 120 x 60=7200 sq, rods. And 7200-160=45 acres. Ang 3. How many acres are in a field of oblong form, whose lepgth is 14,5 chains, and breadth 9,75 chains ? Ans. J4ac. Oroo 22 rods. Note.-'The Gunter's chain is 66 feet or 4 rods long, and contains 100 links. Therefore, if dimensions be given in chains and decimals, point off from the product one more decinal place than are contained in both factors, and it will be acres and decimals of an acre ; if in chains and links, do the same, because links are hundredths of chains, and, therefore, the same as decimals of them. Or, as I chain wide, and 10 chains long, or 10 square chains, or 100000 square links, make an acre, it is the same as if you divide the links in the area by 100000. 4. If a board or plank be 21 feet long, and 18 inches broad, how many square feet are contained in it? 18 inches =1,5 foot. And 21x1,5=31,5 feet. Ans. Or, in measuring boards, you may multiply the length in feet by the breadth in inches, and divide the product by 12; the quotient will give the answer in square feet, 21X18 Thus, in the preceding example, 31 sq. feet as before. 12 5. If a board be 8 inches wide, how much in length will make a foot square? . RULE.—Divide 144 by the width; thus, 8)144 Ans. 18 inch. 6. If a piece of land be 5 rods wide, how many rods in length will make an acre ? RULE.—Divide 160 by the width, and the quotient will be the length required ; thus, 5)160 ·32 rods in length. Ans. NOTE. When a board, or any other surface, is wider at one end than the other, but yet is of a true taper, you may take the breadth in the middle, or add the width of both ends together, and halve the sum, for the mean width : then multiply the said mean breadth in either case, by the length; the product is the answer, or area sought. 7. How many square feet in a board 10 feet long, and 13 inches wide at one end, and 9 inches wide at the other ? , 13+9 --=11 inches mean width. ft. in. =9jft. Ans. 12 8. How many acres are in a lot of land which is 40 rods long, and 30 rods wide at one end, and 20 rods, wide' at the other ? 30+20 -=25 rods mean width. 2 Then, 25x40 -=6 acres. Ans. 160 9. If a farm lie 250 rods on the road, and, at one end, be 75 rods wide, and, at the other, 55 rods wide, how many acres does it contain ? Ans. 101ac. 2roo. 10ro. Case 3.- To measure the surface of a triangle. Definition.--A triangle is any three cornered figure which is bounded by three right lines. * Rule.—Multiply the base of the given triangle into half its perpendicular height, or half the base into the whole perpendicular, and the product will be the area. EXAMPLES. 1. Required the area of a triangle whose base or longest side is 32 inches, and the perpendicular height 14 inches. 14:2=7= the perpend. and 32x7=224 sq. in. Ans. 2. There is a triangular or three cornered lot of land, whose base or longest side is 514 rods; the perpendicular, from the corner opposite to the base, measures 44 rods; how many acres does it contain ? 44:2=22=half perpendicular. And 51,5x22 -=7 acres, 13 rods. Ans. 160 * A triangle may be either right-angled or oblique ; in either i case, the teacher can easily give the scholar a just idea of the base and perpendicular, by marking it down on a slate or paper, &c. In a right-angled triangle, the longest of the two legs which include the right-angle, is called the base ; but in such as are oblique, the longest of the three sides is so calle.i. |