154.-A circular field contains 7.854 acres; there is a dog in its center and sheep on its circumference; the dog runs to catch the sheep, and the sheep runs around on the circumference at the same rate that the dog runs; a line passing from the sheep to the dog always points to the circle's centre. How far must the dog run to catch the sheep? We give two solutions, which differ in results; also a general solution: The course of the dog will describe one-half the circumference of a circle, the center of which may be found, in the radius of the field, equally distant from cir. cumference and center; the radius to form a right-angle with a line from sheep to dog, at starting. 7.854×160-1256.64 rods in field. 1256.64+3.1461-400. 400= 20 radius 20 × 2=40 diameter 40 x 3.1461=125.664 circumference of field. 125.664+ 4-31.416 rods-Ans.-W. H., Eagle Point. The dog runs on the circumference of a circle whose diameter is the semidiameter of the field, and so overtakes the sheep 90 degrees from where she started. They will then have run equal distances, and at all times kept in a straight line with the center of the field. Since the circumference of two circles are to each other as their diameters, 7.854 × 320 × 3.141592+2=998.459+ rods. -Ans.-M. E. C., River Falls. General Solution.-A point starts from the center of a circle towards another which is moving with uniform velocity in the circumference. If the interior point move with times the velocity of the exterior, and keep always on the radius drawn to the latter, how far will the former move before the two coincide? Let z be an arc of the polar curve traversed by the interior point, z' the corre sponding circular are in which the exterior point moves, r the radius vector to the outer extremity of z, the pole being at the center of the given circle, and z' a measure of the angular motion of the radius vector. Estimating 2 from the center of the circle and integrating, we obtain Now, when the two points coincide, r=radius of circle=1, and if dz=dz as" per problem-this value of 2 reduces to infinity. Wherefore, if the dog and sheep be regarded as geometric points, the one will overtake the other after making an infinite number of revolutions.-ALEX. H. CHRISTIE, Lowell, Wis. NEW QUESTIONS. 159.— Are a, e. i, o, and u long, elementary sounds?—— M. K., Eagle Point. 160.- Must the dividend and divisor be of the same denomination ?—IB. 161.— Parse that in the sentence, “the climate of the north temperate zone resembled that of the tropics?”—IB. 162.- Has the supreme court of the United States exclusive jurisdiction over any cases?-IB. 163.- If I start from Fond du Lac, for instance, at sun rise to day, April 19, to circumnavigate the earth, and travel directly westward, I will, in course of time, reach Fond du Lac again. Now, I have been informed that if I keep time correctly, by counting every sunrise a day, I will be one day behind time. I would like to have some one account for the loss of the day. - JOHN BROWN Fond du Lac. 164.- An eagle soaring in the air, sees a pheasant 660 feet directly below him, flying horizontally. The eagle instantly flies in pursuit, with velocity twice as great, and directing his course always exactly towards the pheasant, and not ahead of it. What distance will the eagle make before he overtakes his prey? -M. K., Eagle Point. 165.- The area of a triangle is 100, the sum of the sides 100, and one of the angles 100°. Required the sides ?—A. S. J., Sparta. 166. Will some teacher give a method of teaching history whereby we can teach our pupils the real value of the study and its true philosophy ?-L. H. BRAINARD, Amherst. 167.-How often is it noon at the north pole in a year?-J. D. BOWLES, Bos cobel. 168.-What would be the width of all the zones, if the earth's axis were inclined 25° instead of 23%-Ib. 169.-Why are the tropics drawn 23° from the equator?—Ib. 172.-In what regions does the air constantly rise, and why?—Ib. 173. When does the sun shine vertically over the tropic of Capricorn?-Ib. 173.-If you were at the north pole on the 21st of June, 12 o'clock, noon, in what direction would your shadow fall?—Ib. 175.-Two men went hunting and killed a deer. Their weights respectively were 192 lbs. and 147 lbs. They wished to weigh the deer, and having no scales, they place a pole across a log in such a way that the deer would balance the man weighing 192; then placing the deer on the other end of the pole, it would balance the other man weighing 147 lbs.; what is the weight of the deer?—H. P. T., Hartford. 176.-How would you compare the word "false" in this sentence-" He is a false man"?—Ib. 177.-How many acres of land in a square lot whose diagonal is 20 rods?—Ib. 178.-A man bought a house for $3,000, agreeing to pay 7 per cent. interest and to pay principal and interest in five equal annual instalments; how much was the annual payment?-H. M. L., Ripon. 179.-On the supposition that (one-third) of six is three, what will the 4 (one-fourth) of 20 (twenty) be?—Ib. 180.-Geometrical problem.-By Euclid (I-32 corollary) a right-angled triangle may be constructed having one of its acute angles double of the other, and by Euclid (IV-10), an acute-angled triangle may be constructed having one of its angles double of the other; required to complete the investigation by construct ing an obtuse-angled triangle having one of its acute angles double of the other. A. GOUGH, Chippewa Falls. 181.-Arithmetical question.-A merchant bought a cask of wine for $48, and sold a quantity exceeding three-fourths of the whole by two gallons, at a profit of 25 per cent. He afterwards sold the remainder, at such a price, as to clear 60 per cent. by the whole transaction, but if he had sold the whole quantity at the latter price, he would have gained 175 per cent. How many gallons were in the cask?-Ib. 182.-Algebraical question.-The sum of two numbers multiplied by the sum of their cubes is 112, and the cube of their sum is to their difference as 32 to 1; required the number.—Ib. SCRAPS. CONTRIBUTED BY PEN. South American Enterprise.-One of the grandest works of modern engineering is now in progress in South America. It is the Oroya railway, which, starting from Callao, passes over and through the double range of the Andes in Peru. Following the tortuous course of the Rimac river, the first mountain range is passed; then a deep gorge interferes with the progress of the work. It is the valley of Berrugas, a mighty chasm which, walled in by steep declivities, tries the skill of the engineers. But the latter triumphs over every obstacle by constructing a bridge six hundred feet long, which spans the fearful gorge. difficult and dangerous is the work of cutting the railway through rocks and along the edge of precipices, that sailors had to be engaged to do this part of the work, as the common laborers refused to risk their necks. So Veterans of the Forest. The largest oak in Europe is to be found near Saintes (Dep. Charante). It is above sixty feet high, and its diameter near the ground is twenty-eight feet. The trunk is hollow in its lower part, and has been transformed into an arbor twelve feet wide and nine feet high. A bench lines a part of the wall which is 'gaily decorated with mosses and ferns, and a window cut out in the thick trunk admits the cheery sunlight. This oak is supposed to be at least 1,800 years old. Another large oak is to be seen near Leipsic; it is somewhat smaller than the one first described, but is quite sound and gives promise of many years' duration. Prince Bismark's Estate. The new possession of Prince Bismark (the present of Emperor William), which is is known in Germany as the "Saxon Forest" (Sachsenwald), has quite a history. It has changed owners as often as a South American republic changes its presidents; now belonging to Denmark, now to Lauenburg, Holstein, or the Hansa (free cities). Twice it was the subject of law. suits, one of which lasted 121, the other 135 years. It was finally "annexed" to Prussia, and is now the new home of the "Iron Count." CONTRIBUTED BY MRS. S. C. SIRRINE. WIND UP YOUR HEARTS toward heaven in the morning, and they will go the better through the day. A gallant school boy's Toast: The girls, may they add charity to beauty, subtract envy from friendship, multiply genial affections, divide time by industry and recreation, reduce scandal to its lowest denomination and raise virtue to its highest power. It is always safe to learn, even from enemies; seldom safe to venture to instruct, even our friends. What is often found where it is not? Fault. Why is a petroleum dealer like an epicure? Because he lives on the fat of the land. SELECTIONS FROM CERMAN POETS. TRANSLATED BY PEN. [From Mirza Shaffy.] 16. THE PRIZE OF EXCELLENCE. Not without contentions sore Life's great treasures harvest shall you- 17. WORLDLY INFLUENCE. Let thy life be ever so lonely and still, 18. EXCELLENCE UNRECOGNIZED. 19. VALUE OF ENERGY. Be of purpose good thy life, In the tide of battle fall! 20. NATURE'S NOBILITY. Of higher, nobler natures there are two One that was made to live for all that's higher, All that is good, and beautiful and true The other to behold this and admire. 21. WOMAN'S LOGIC. "This easy to subject a woman, If men to do it have a mind, But to convince were superhuman-- Tears, kisses, fainting-fits! [From Schiller.] I. CASTE. There's a nobility, too, in the moral world—thus the vulgar II. THE MUSE. What I without thee were, Muse-I know not! With terror III. TO A REFORMER. "All I have sacrificed for the welfare of mankind, Leave to the Merciful Hand that hath sustained them before! IV. MY FAITH. Ask you what faith I profess? Not one of the many That you have mentioned. Why not? For Religion's sake, friend! V. PHILOSOPHY. What philosophical system will live? This I know not; That philosophy will ever endure, is my hope. VI. WOMAN'S JUDGMENT. Men judge from reasons, but woman from love-where her love is Silent, her heart hath already adjudged! VII. GOODNESS AND GREATNESS. There are two cardinal virtues that should be united- VIII. ELEMENT OF COMBINATION. How doth Nature unite in man the greatest and lowest IX. HIGH AND LOW. It is either the highest degree, or the lowest, to be above X. FRIENDS AND ENEMIES. Dear to me is the friend, but enemies, too, have their uses; When I behold fortunes favorites, IIeaven's Divinities |