LESSON LXV. Spell and Define. 1. Ge-om'e-try, the science of magnitude. 3. Con-tig'u-ous, touching, joining. 4. Cyl'in-der, a long, round body. 6. An'gles, corners. 7. Rhomboid, obliquely-square. 10. Sculp'tor, a carver of wood or stone. ERRORS.-1. Reg-e-lar'i-ty for reg-u-lar'i-ty; 1. won'der-fly for won'der-ful-ly ; 2. diffi-kilt for diffi-cult; 2. marter for matter; 5. in'stid for in'stead ; 5. keerds for cards; 6. ac'too-al-ly for act'u-al-ly; 8. six'tiths for six'ti-eths; 10. chis'il for chis'el. ARCHITECTURAL SKILL OF THE BEE. [The pupil may point out some words in this piece, which are emphatic by contrast. See rule, p. 42.] 1. FROM the time of Pappus to the present day, mathematicians have applied the principles of geometry to explain the construction of the cells of the bee-hive; but though their extraordinary regularity, and wonderfully selected form, had so often been investigated by men of the greatest talent, and skilled in the refinements of science, the process by which they are constructed, involving also the causes of their regularity of form, had not been traced, till Mr. Huber devoted himself to the inquiry. 2. As the wax-workers secrete only a limited quantity of wax, it is indispensably requisite, that as little as possible of it should be consumed, and that none of it should be wasted. Bees, therefore, have to solve this difficult geometrical problem. "A quantity of wax being given, to form of it equal and similar cells of a determinate capacity, but of the largest size m proportion to the quantity of matter employed, and disposed NOTES.-a Pap'pus; a celebrated mathematician of Alexandria, who lived near the elose of the fourth century. bHuber (Francis); a distinguished naturalist, who wrote a work on bees, born at Geneva, in Switzerland, in 1750. in such a manner as to occupy the least possible space in the hive." This problem is solved by bees in all its conditions. 3. The cylindrical form would seem the best adapted to the shape of the insect; but had the cells been cylindrical, they could not have been applied to each other, without leaving a vacant and superfluous space between every three contiguous cells. 4. Had the cells, on the other hand, been square or triangular, they might have been constructed without unnecessary vacancies; but these forms would have both required more material, and been very unsuitable to the shape of the bee's body. The six-sided form of the cells obviates every objection; and while it fulfills the conditions of the problem, it is equally adapted with the cylinder to the shape of the bee. 5. Mr. Reaumur further remarks, that the base of the cell, instead of forming a plane, is usually composed of three pieces in the shape of the diamonds on playing cards, and placed in such a manner as to form a hollow pyramid. This structure, it may be observed, imparts a greater degree of strength, and still keeping the solution of the problem în view, gives a great capacity with the smallest expenditure of material. 6. This has, indeed, been actually ascertained by mathematical measurement and calculation. Maraldi determined, by minutely measuring the angles, that the greater were one hundred nine degrees and twenty-eight minutes, and the smaller seventy degrees and thirty-two minutes. 7. Mr. Reaumur, being desirous to know why these particular angles are selected, requested Mr. Koenig, a skilful mathematician, to determine, by calculation, what ought to be the angle of a six-sided cell, with a concave pyramidal base, NOTES.- a Reaumur (rỡ'mur); a French philosopher and naturalist, and the inventor of Reaumur's thermometer, born in 1683. Maraldi (mä-rālīdē); a distinguished mathematician, born at Perinaldo, in Italy, 1665 © Koenig (keu'nig); an able mathematician of Switzerland; he died in 1757 formed of three similar and equal rhomboid plates, so that the least possible matter should enter into its construction. 8. By an elaborate process, Mr. Koenig found that the angles should be one hundred nine degrees and twenty-six minutes for the greater, and seventy degrees and thirty-four minutes for the smaller, or about two sixtieths of a degree more or less, than the actual angles made choice of by the bees. The equality of the inclination in the angles, has also been said to facilitate the construction of the cells. 9. It may, however, be said not to be quite certain that Reaumur and others have not ascribed to bees the merit of ingenious mathematical contrivance and selection, when the construction of the cells may more probably originate in the form of their mandibles, and other instruments employed in their operations. 10. In the case of insects, we have repeatedly noticed that they use their bodies, or parts of them, as the standards of measurement and modeling; and it is not impossible that bees may proceed on a similar principle. Mr. Huber replies to this objection, that bees are not provided with instruments corresponding to the angles of the cells; for there is no more resemblance between these and the form of their mandibles, than between the chisel of the sculptor and the work which he produces. QUESTIONS. 1. Who was Pappus? 1. Who first observed the process by which bees construct their cells? 1. Who was Huber? 4. Why do the bees make their cells six-sided in their form? 5. Who was Reaumur? 5. How is the base or bottom of the cell constructed? 5. Why do the bees choose this form? 6. Who was Maraldi? 7. Who was Koenig? 10. Is the shape of the cells owing to the form of the bees? How did the bees gain their knowledge of architecture? 4. Phe-nom'e-non, a remarkable appear- 6. Fire'-en-gines, machines for extin ERRORS. -1. Stawm'y for storm'y; 2. mys-te'rus for mys-te'ri-ous; 2. trap'lin for travel-ing; 2. mild for mile; 3. dreatful for dreadful; 3. thou'san for thou'sand; 5. col'yums for col'umns; 6. tor'runts for torrents. A SCENE AT SEA, 1. A DARK cloud, which every moment became blacker and blacker, was fast extending over the sky on our left. From the lower part of this ominous and stormy curtain, projected three jet black columns, which kept curving and swinging backward and forward, as if they were endowed with life. 2. These were the grand and mysterious hydrostatics of nature, and we were rapidly traveling into the influence of their vast machinery. At this fearfully interesting crisis, we approximated within half a mile of the nearest. So sudden had been their formation, that no time was allowed to put the ship about. We felt, or fancied we could feel, a whirlinga motion of the atmosphere; and more than one of us imagined, that we were already in the power of the fatal tornadoes and their vortex. 3. Every second was of consequence; a minute or so might have sealed our doom. On, on, went the ship, and before she turned, we were frightfully near to the dreadful water-spouts. Onward and downward, these gigantic hose-pipes of cloud and water uncoiled. Now they curved like a reaper's hook; anon they twisted like a serpent's tail! I could imagine that two NOTES. — a Whirlwinds are supposed to be caused by two winds meeting each other and then turning upon a common center. b See water-spout, p. 237, note G. of them were at least a thousand feet in length, with a body as thick as the Washington monument at Baltimore." 4. Their contortions and convolutions were interesting and wonderful, and I found it impossible to withdraw my attention, even for a moment, from the grand phenomenon. At length the ship was put about, and we began to increase our distance from what we had regarded as a watery death. The spouts straightened out, and the lower ends of two of them, approached the surface of the deep. I 5. The sea beneath rose in a hillock of waves, as if attracted or twisted into a rising tumulus by the cloud, or formed by the whirlwind. And now two of the columns were perpendicular, resting upon a mount of foaming, roaring waves. should say that from one hundred and fifty to two hundred feet above the sea, these columns were transparent as crystal, and the water might be seen traveling up them. This appearance lasted for six minutes and a half, the third spout never reaching the sea at all. 6. Meanwhile, the entire aqueous pageant was slowly and magnificently moving toward the north; but at last the two columns broke, one after the other, near the sea. Within a few seconds, the rain descended in such torrents that I can only compare its fury to the playing of ten thousand millions of fire-engines, pointed perpendicularly down from the sky. Ten minutes after, scarcely a cloud was to be seen; the sun shone forth in its beauty, and blazed with all the intensity of its summer heat. NOTES. -a Washington mon'ument; a Doric column 140 feet in height, and 20 feet in diameter at the base. It stands upon a pedestal, elevated 20 feet from the ground, and on the top is a colossal statue of Washington. b Baltimore; the larg est city in Maryland, containing 201 thousand inhabitants. QUESTIONS. 1. What projected from the cloud? 2. What motion did the atmosphere appear to have? 2. How are whirlwinds supposed to be caused? 3. What was the appearance of these water-spouts? 3. What is the Washington monument? 3. What is Baltimore? 5. How did the sea appear beneath the spouts? 6. What became of them, and what followed A |