when rubbed with silk is called 4. Bodies may be by induction. pole. 5. The direction of the current through the external circuit is always from the to the 6. When we look along a wire in the direction in which an electric current is flowing, the pole of the needle near the wire is in which the hands of a clock move. deflected 7. The speed of the waves depends upon two quantities only; viz. and the linear density (i.e. the ....) of the vibrating cord. per unit is the electrical pressure required to drive a curof 1 ohm. 8. The rent of 1 ampere through a 9. 10. 11. The mechanical advantage of a composite machine is the bodies possess energy of their motion. is measured by the of the mass and the velocity. 12. The earth's action on a is a couple. 13. An induced current exists only when the of 14. The shortest resonant length of an open pipe is wave length, and there is wave length. at any of 15. The surface of a body of water at rest, for example a pond, is at right angles to the acts upon it; and second, the force of gravity acting on a 16. To find the component of a force in any given direction, construct upon the given force as a diagonal 17. Waves will not travel in a medium unless it has both and A STUDY IN AN AMERICAN DESERT. One of the driest parts of the United States is what is called the Papago country, a region including about 13,000 square miles in southwestern Arizona, so called because it was long ago inhabited by the nomadic Papago Indians. This broad expanse of desert country, which lies between Gila River and the Mexican boundary, contains many groups of volcanic and other mountains separated by broad alluvial basins, which, though the rainfall is small and the temperature is high, sustain a scant growth of desert plants, including orchard-like groups of strange trees. Here the bold slopes of the mountains, the general absence of watering places, and the peculiar forms of the vegetation impress the traveler strongly with the majesty and the mystery of the desert, and excite his wonder as to the origin and history of the natural features. A report on this region by Kirk Bryan has just been published by the United States Geological Survey, Department of the Interior, as Bulletin 730-B, under the title "Erosion and Sedimentation in the Papago Country, Arizona." The report describes the geology briefly as a setting for a consideration of the agencies that have produced the forms of the land and presents detailed conclusions as to the mode of origin of the desert landscape. The paper is illustrated with diagrams, views, and maps and should be of interest to all students of topography and physiography, particularly those who are endeavoring to solve problems of erosion by wind and water in desert regions. THE TANGENT OF 2X. WILLIAM F. RIGGE, Creighton University, Omaha, Neb. The object of this article is to show an interesting and practical application of one of the well-known formulas of trigonometry that appear to be so dry and valueless to the student who must memorize them, and so purely theoretical and pedagogical to the instructor who exacts them. It is the formula tan 2x= 2 tanx/(1-tan x). This can be used to find the focal length as well as the position of the camera in certain cycloramic pictures. The essential element of this picture must be a straight wall of some kind or its equivalent, or at the very least, certain five points that we need must be in a straight line, such as the points, A, B, P, E, D, in the diagram, and this line must be so placed that it will contain the foot of the perpendicular P dropped to it from the camera C. With this requirement we combine the fact that, as the camera lens revolves, equal fractional lengths of the film will correspond to equal horizontal angles in space, the exact proportion being unknown at the start. These two, the straight wall and the equiangular film, will solve the problem. 1. The first step in the proceeding is to find the point P on the wall by means of its image on the picture. In order to do this without defacing the original photograph, it is advisable to cover it with transparent paper and make our marks on that. As all horizontal lines in space become sine curves on the film of a cycloramic camera, the nearest portion P of the wall is the vertical line passing through the highest points of the sine curves. To locate this vertical line more accurately, it will be well, by means of an adjustable curve ruler, to supply on the transparent paper the breaks in the sinusoids, such as the spaces between windows. Then we draw a horizontal line on the paper, note its points of intersection with a sinusoid, bisect the distance between them, and draw the vertical line P through this bisection. The photograph that was actually used in solving this problem is not reproduced here, because it is rather long and dark and its parts would suffer too much by reduction. It represents a group of students standing before the east front of the north wing of Creighton College in Omaha. 2. The second step is to measure off from P equal horizontal lengths on the picture. In this case, by using a scale of fiftieths of an inch and estimating to tenths of these by means of a magnifying glass, the length ped on the film between the images of P and the north end of the building D, was found to be 8.532 inches. PCD or p Cd is then a certain unknown angle, and ed its corresponding arc, which we will call 2x. The point e on the film, halfway between p and d, is 4.266 inches from each. We note this point e very carefully on the picture, even to the fraction of a brick, as well as we are able. PCE and ECD are then equal angles in space, each equal to x. Р 3. We now go to the building and measure the distances PE and PD. They were 21.521 and 65.719 feet respectively. 4. Let us put R for the unknown distance PC, m for PE and n for P D. We then have tanx=m /R, and tan 2x=n/R. Placing these values in the formula tan 2x=2 tanx /(1-tan*x), we get after reduction R=m√[n /(n−2m)]=36.64 feet distance of camera from wall. = = 5. Prudence suggested taking angles and distances to the left of P also. The length p a between the images of P and the south end of the wing on the picture was 3.788 inches and its half p b and b a 1.894 inches. On the wall these were P A = 18.463 and P B 8.835 feet. Calling the equal angles y and proceeding as before, R turned out to be 42.63 feet. As this y value was six feet longer than the x value, great consternation prevailed for a while. When no mistake whatever could be found in the principle, the measurements and the computation, the error was judged to be due to the erroneous location of P on the photograph. 6. The point P was therefore shifted on the picture one-tenth of an inch to the left. This called for entirely new measurements on the photograph and on the wall, as well as a new computation. The second approximation then made R equal to 37.35 and 40.26 feet, with a difference of only about half of its former value. 7. The point P was accordingly shifted on the picture another tenth of an inch to the left. The new measurements then made pd=8.732, pe=4.366, p a=3.588, p b = 1.794, inches, PD = 66.655, PE=22.102, PA 17.527, PB-8.342 feet, and R was found to be equal to 38.08 and 38.04 feet. The mean, 38.06 feet, was then accepted as the true distance of the camera from the wall. = 8. Then the angles x=30°8′ and y = 12°22′ were easily found. Knowing that abped=2x+2y=85°0′ = 12.320 inches on the picture, we have 1° 0.145 inch. As a radian is 57.03, the focal length of the camera was 57.3X0.145 8.30 inches. The total length of the film was 32.8 inches or 226 degrees. 9. To determine the height of the camera, we stretch a fine thread over the photograph and try to find a row of bricks or stones or a mortar line that is perfectly straight not only across all projections and recesses in the wall, but also across all buildings whatever. This was then in the same horizontal plane with the camera. The oversight made in not determining this line before locating the point P is, of course, mainly responsible for the erroneous values of R obtained at the start. The surest safeguard against such errors, especially in the case in which the thread method cannot be employed, is to measure both to the right and to the left of P. 10. When a cycloramic photograph is bent into a cylinder abped with a radius C a equal to the focal length of the camera, and the eye placed in its axis c and in the plane of the horizontal line, the view is identically the same as one would see if he stood in the same spot that the camera occupied and looked at the real objects. The sinusoidal or bulging appearance that a near building presents in the plane picture, together with the alignment of all the buildings as if they all faced the same point of the compass, then disappear completely in the cylindrical one, and the photograph is as true to its original as any mathematical critic could desire. SALT IN 1921. The United States Geological Survey reports that the production of salt in the United States in 1921 was 4,981,154 tons, valued at $24,557,966, a decrease of twenty-seven per cent in quantity and eighteen per cent in value as compared with 1920. THE MUSEUM, THE ORIGINAL EXPONENT OF VISUAL BY FRANK C. BAKER. University of Illinois. We hear a great deal in these days about the value of visual education, and a society has been organized for the promotion of this method of teaching. This is indeed one of Nature's most effective methods of teaching her children the laws of the universe. It is said that we acquire much more information through the eye than through any other sense organ of the body. One often hears the expression "seein' is believin," which expresses this truth in a homely way. The museums of science and art have been for many years pioneers in the field of visual education, bringing to the public, more or less imperfectly in the earlier years, the facts of Science and the beauties of Art. The museum is often called the "people's university," and it is quite true that the great majority of the population of our large cities acquire their only knowledge of the great world about them by visits to the museums, art galleries, and zoological gardens, where the fowls of the air, the beasts of the field, and the fishes of the sea, past and present, are gathered together in such an assemblage as Noah never dreamed of in his day and generation. The value of the museum as an efficient aid in educational work is fully realized by but few educators. Even in many of the large cities there is little real cooperation between the local museum and the educational system, and this is by no means entirely the fault of the museum administrators. Visual education seems to center about pictures, lantern slides and moving pictures, and the aid that may be rendered by the museum exhibits is, in the main, unthought of. Perhaps many of our museums are to be held responsible for this condition, their exhibits being so often entirely useless to the teacher because of faulty installation, of value to the systematic student, but valueless to the general teacher. The cooperative association of school and museum in New York, Chicago, Milwaukee, and some other cities, augurs well for the future of the museum in finding its true place in the educational system of the present age. In a recent article on the "Contribution of Museums to Public School education," Mr. Peter A. Mortenson, Superintendent of Public Schools of Chicago, says: "The value of Contribution from the Museum of Natural History, University of Ill., No. 25. |