3. 4. 5. 6. For he doth sometimes seem Dost rest not, night or day. The morning stars,a When first they sung o'er young creation's birth, Lo! yon birds Do venture boldly near, bathing their wing Who sport unharmed upon the fleecy cloud, But as for us, it seems Scarce lawful with our broken tones to speak Were profanation. NOTE. a See morning stars, Job xxxviii. 6, 7. 7. Thou dost make the soul A wandering witness of thy majesty; And while it rushes with delirious joy To tread thy vestibule, dost chain its steps, MOUNT WASHINGTON.a GRENVILLE MELLEN. 8. MOUNT of the clouds, on whose Olympian height Beneath the far-off mountain, distant, calm, and slow. 9. Mount of the clouds! when Winter round thee throws Thy towers in bright magnificence appear! NOTES. -a Mount Washington; the highest peak of the White Mountains, situated in New Hampshire, being 6,234 feet, or 14 miles, high. b Olympian; pertaining to Olympus, a celebrated mountain in Macedonia. QUESTIONS. What is said of Niagara Falls? 1. How is the rainbow formed over the cataract? What is Mount Washington? 8. What is meant by Olympian height? 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. 9. Man'di-bles, the jaws. 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. mar'ter for mat'ter; 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 See rule, p. 42.] contrast. 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 in proportion to the quantity of matter employed, and disposed NOTES. 18 a Pap'pus; a celebrated mathematician of Alexandria, who lived near the close of the fourth century. b Hü'ber (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 in 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 (rō'mur); a French philosopher and naturalist, and the ir.ventor of Reaumur's thermometer, born in 1683. Maraldi (mä-rāl'dē); a distinguished mathematician, born at Perinaldo, in Italy, 1665. c 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 bot tom of the cell constructed? 5. Why do the bees choose this form? 6. Who was Maraidi? 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? |