following rule, which will be found very useful in rural economy, commerce, and shipping : To reduce bushels to feet: To the number of bushels add of itself. To reduce feet to bushels: From the number of feet subtract of itself. If we have 1728 for the given number of bushels, we shall, by the rule, find its equivalent in cubic feet to be 2160, which is too great by 10, or part of itself, the true equivalent being 2150. Therefore, in finding by the rule, the equivalent, in feet, of a given number of bushels, we must, if we wish it exact, diminish it by 1 of itself. Again, if we have 2150 for the given number of cubic feet, we shall, by the rule, find, for its equivalent in bushels, 1720. But this is too little by 8 bushels, or part of itself, the true equivalent being 1728. Therefore, in finding by the rule the equivalent in bushels, of a given number of cubic feet, we must, if we wish it exact, increase it by of itself. 215 289. We may however observe, that for any practical purpose, such as the construction of corn-cribs, caves, bins, granaries, pits, boxes, &c., for the preservation of corn, roots, or any other articles measured by Dry Measure, or for the calculation of the capacity of such cribs, granaries, &c., the rule will be found sufficiently exact without the addition or subtraction of the fractional part. Suppose we would construct a crib to hold 1500 bushels of corn. As corn is put away in the ear, and as it requires, in measuring, to allow two bushels for one, and one of these well heaped, we shall allow 2 times the whole quantity of shelled bushels. We therefore say, 1500 × 23300; adding to this of itself, we have 33008254125, the content of the crib in cubic feet. Now as this is a quantity of 3 dimensions, one of which is arbitrary-seeing that the average width of a corn-crib is generally not more than 4 or 5 feet inside, that the air may pass freely-we find the factors of 4125, or inside dimensions of the crib thus: dividing by any convenient width, say 5 feet, we have — 825, for the area or content of the side. Then, if we wish the crib to be of a certain height, or length, we must divide the area of the side by that height or that length, and the quotient will be the remaining factor; that is the length or height accordingly. Thus, if we say 10 feet high, we have 4125 825821 feet, for the length. If we say 55 feet long, we have 82515 feet, for the height of the crib. If the crib be made only 4 feet wide at the bottom, it must be 6 feet wide at the top, because the sum of these will give the average width, 5 feet. What must be the length of a crib to hold 3600 bushels of corn, the average width being 5 feet, and the height 12 ? Answer, 165 feet. What must be the height of a crib to hold 500 bushels of corn, the average width being 4 ft. 2 in., and the length 40 ft. 6 in ? Answer, 8 ft. 17 in. 290. If, of several factors, any one be diminished in a certain ratio, that is, by a certain part of itself, the whole product of those factors will be diminished in the same ratio; that is, by the same part of itself. Let P represent the product of the undiminished factors, and A the factor we intend to diminish. Then PA is the total product. Now, if we diminish A by of itself; thus, A-4, the remainder 34, multiplied by P, will be 34. PA 4PA PA ЗА ЗРА But PA 3PA. Wherefore, the total product of PA is diminished in the same ratio as the factor A. Having a granary 43 feet long, 10 ft. wide, and 10 ft. high, we wish to know how many bushels of grain it will hold. Now, as by the rule (228) we must, from the content of the granary in cubic feet, which is 43 × 10 × 10, subtract of itself; we subtract from 10, which is of the factors, of itself, which gives 43 X 10 X 8 = 3440 for the content in bushels. But this is too little by We therefore say, 3440 16, and 3440 +16: of itself. = કૈ 3456, the number of bushels 215 required. Having 6912 bushels of grain, we wish to know to what depth it will cover a floor that is 43 ft. long and 25 ft. wide. 216) 8640 c. ft., by the Rule too great. 8600 true content of grain in c. feet. 43 × 25 = 4300 = 1075 area, or surface of floor. 8600 ÷ 10758 feet, the required depth. Proof. 43 X 20 X 86880, too little by 1 of itself. 6880 = 32; then, 6880 +32=6912 bushels. 215 291. In the heaped bushel, used in measuring fruit, roots, &c., it is found that, according to pretty general usage, the heaped part is only about of the capacity of the vessel, which, as we shall shortly see, is by no means a large allowance. But custom is law, at least to the calculator; wherefore, applying to this our approximate rule, (288,) as the internal capacity of the bushel (called the strick bushel) compared with the cubic foot, is as 5 to 4, and the heaped part of 5, or 1, we have, for the ratio of the heaped bushel to the foot 6 to 4, or 3 to 2; hence the following rule : To reduce heaped bushels to cubic feet: To the number of heaped bushels, add its half. To reduce cubic feet to heaped bushels: From the number of cubic feet, subtract its third part. To what length must a pit, 4 ft. wide and 3 ft. deep, be dug, in order to contain 3000 bushels of potatoes? Ans. 375 feet. bushels of coal can be stored in a cellar which How many is 16 ft. long, 10 ft. wide, and 9 ft. high? Ans. 960. 292. In England, a bushel of potatoes is used consisting of 80lbs. weight Avoirdupois. This was probably based upon the following experiment: Let a tight half-bushel measure be filled with good-sized potatoes, by packing them with the hand; then, if water be poured into it amongst the potatoes, it will contain about 8 quarts before the water begins to run over, which proves that, when a half-bushel is thus filled, only one half its solid capacity is occupied by the potatoes; much less when, as usual, it is filled with the shovel. If we measure 80 lbs. of potatoes, shovelling them on the halfbushel as long as they will conveniently lie, the measure will be thus filled 3 times. A bushel, therefore, as they are frequently measured, will only weigh about 53 lbs. Now, as a bushel of good wheat, which weighs from 62 to 64 lbs., is often lower in price than a bushel of potatoes, the student will see that it is important to estimate as well as calculate. In Maine the bushel of potatoes is 60 lbs, Avoirdupois. 293. By the following measure are measured brandy, spirits, cider, vinegar, molasses, oil, &c. Honey is sold by the pound Avoirdupois. The gallon contains 231 cubic inches. Ten gallons make ..1 puncheon, pun. 2 hogsheads, or 126 gallons.....1 pipe, p. or butt, b. 2 pipes, or 252 gallons...........1 tun, T. The following measure is used for malt liquor only. The gallon contains 282 cubic inches. 3 kilderkins, or 11 bar.....1 hogshead, hhd. OF TIME, AND THE REGULATION OF CLOCKS-ASTRONOMICAL AND GEOGRAPHICAL MEASURE. 294. No subject that we can contemplate is of deeper interest, or more serious consequence to mankind, than time. The wise in all ages have testified that on the proper improvement of it depends our present as well as future happiness; and, though to some it may appear irrelevant to introduce in this place sub-jects of graver import than mere calculation, it may not be amiss to remind the student, in the words of Don José de Cadalso, (in a little satirical work entitled Los Eruditos á la Violeta, published in honour of those who pretend to great knowledge with little study,) that the common object of all the sciences, and their utility to man, may be divided into two parts: one of which is, to obtain a less imperfect knowledge of the Supreme Being, by which the heart of man is disposed to render him more profound and sincere worship; the other is, to render men more social; for, by imparting to each other the productions of their understanding, they become united, as we may say, in spite of ocean and distance. The word time, though of frequent recurrence in conversation, is by no means easy to define. Perhaps we may call it the measure of existence or the regular flow of duration. Duration, if unlimited, is called eternity: time is therefore a limited duration. We have already observed (4) that time is measured by the revolution of the earth about its axis, which is a sublimely regular motion. By this revolution, which is from west to east, the sun, the fixed stars, and other celestial objects, are made, apparently, to perform a revolution round the earth from east to west. Besides the motion of the earth about its axis, it continually revolves about the sun from west to east, in an elliptical* orbit, at the mean or average distance of about 95 millions of miles. The period of this revolution is called a tropical year. The mean diameter of the earth's orbit is therefore nearly 190, or, as we say, in round numbers, nearly 200 millions of miles. This distance, however, compared with that of the nearest of the fixed stars, is a mere point, so very insignificant, that they are seen from any part of our orbit, exactly in the same point of the heavens. From the observations of the most skilful astronomers, made with the finest instruments, it is concluded that Sirius, or the Dog Star, which, from its superior magnitude and brilliancy, has been considered the nearest of them all, cannot be at a less distance from the sun than ten millions of millions of miles; some have supposed that it is not nearer than 300 millions of millions; from which the student will infer, that with respect to the distance of these splendid orbs from each other, man, with all his boasted science, is reduced to mere conjecture; yet he must by no means imagine that the observations made upon *Elliptical, somewhat oval. |