DEPARTMENT OF SCIENCE QUESTIONS. FRANKLIN T. JONES, University School, Cleveland, O. This department is designed to serve as a medium for the exchange of ideas on questions and questioning in the sciences. Questions will be printed from various sources-college entrance examinations, textbooks, etc., etc. Comment is invited. Suggestions and criticisms as to character, adaptability, and usefulness are desired. Readers of this journal are invited to propose questions and problems which will be of general interest, or of a type which will be useful in the class-room. It is not expected that questions which will not be useful to pupils will be frequently printed. Since the majority of the questions will be of a comparatively simple character, solutions and answers will not be published unless specifically asked for. Teaching suggestions are wanted. Address all communications to the editor of the department. The following questions among others have been proposed. On account of the summary mentioned below some are postponed to be printed in a later number. 21. J. L. Riley, Jonesboro, Ark. Why can not fluorine be thus obtained as its kindred elements are? CaF2+MnO2+ 2H2SO, = CaSO4 + MnSO, + 2H2O + F. 22. John J. Farrell, South Norwalk, Conn. To what height would a person have to rise above the earth's surface to observe its revolutions, providing it was possible to remain stationary and to see so far? (Answers are desired.) 23. A. Haven Smith, Sioux City, Iowa. Explain by the aid of a diagram how a cat-boat is sailed into the wind. 24. J. H. Clo, Pullman, Washington. Why does the water in hot-water pipes freeze sooner than in coldwater pipes, both being at the same temperature? (Answers are de sired.) In view of the present discussion concerning the physics course and the proposed physics syllabus the editor has compiled some statistics concerning questions that have been asked by representative examining bodies since 1900. The numbers which follow were found in a careful attempt to classify topics covered by the college entrance examiners. It is evident that no two persons would be likely to classify in just the same way. Where a single question touched on more than one topic, it was classified under both. The examinations considered were College Entrance Examination Board, 1901, '03-'06; Case School of Applied Science, '03-'06; Cornell, '04-'06; Harvard, '01-'06; Massachusetts Institute of Technology, '04-'06; Princeton, June, '00, '02-'06; September, '05-'06; Sheffield Scientific School, '00-'06. In the month of June practically every high school and academy in the country holds examinations. Teachers will confer a great favor upon the editor if they will send to him copies of all examination papers in the sciences used at this time. Extracts will be published next fall. A NOTE. The following is so simple that I presume it is the possession of everybody, if so-to the waste basket! Which is the condition that o, x, and (r+1 are sides of a right triangle. Therefore (1) gives the right triangle whose sides are intigers. Simply substitute any odd number, except 1, for o, and solve for ♬ and (+1) and get a right triangle whose sides are r, x+1, and 0. Many times in teaching elementary Mathematics, especially in Geometry and Trigonometry, I have found it desirable to give for supplementary work a varied list of easy right triangles. This gives any number of such triangles. S. L. MACDONALD, Fort Collins, Colo. AN APPLICATION OF GROUP THEORY. T. M. BLAKSLEE, Ames, Iowa. Professor Miller's article in the December number of SCHOOL SCIENCE AND MATHEMATICS suggests that an application that I began making in 1898 might be of interest. If r1, r.....are the roots of an equation, we will call the equation having the roots 1/r, 1/r.....the reciprocal equation of this. I call the equation having the roots 1-r, 1-r.....the unit-complement or complemental equation of the first from which it is obtained by diminishing the roots by 1, then changing their signs. Ex. Form equation (1) having the roots 2, 3, 4. Find the reciprocal equation (2) from (1). Find the complemental equation (3) from (2). Then the reciprocal and complimental alternately till (7). This will be found to be the same as (1). By varying the roots assigned, a large class is easily drilled in four of the important operations in the theory of equations. equations for the above are: x-9x+26r-24-0 (1) The 24y-26y+9y-1=0 (2) 242-462*+29z -6-0 (3) 6u3-29u2+46u-24-o (4) 6v-11v+6v+1=0 (5) w*+6w1 +11w+60 (6) t-912+26t-24-0 (7). COMMENTS ON MR. CAVANAGH'S ARTICLE. Editor SCHOOL SCIENCE AND MATHEMATICS: May I venture to offer some comments on Mr. Cavanagh's article on Optics, in the April number? There is no doubt that the pupil's ideas concerning light will be very imperfect after a few weeks' study of the topic by any method, and by giving it more time we can make some of those ideas more definite and nearer to the truth. But we are obliged to draw the line somewhere: with all that we can tell the pupil about ether waves, he will still have a very imperfect notion of what the ether is, or how waves are propagated in it. And if we spend more time and effort on this part of the theory of light, we shall have less for studying facts directly-optical instruments, color phenomena, etc., or else we must sacrifice some other topic in the course. This remark applies especially to reason number 1. With regard to Mr. Cavanagh's second reason, I should like to ask what explanation we are to give for the reflection of waves. The fact is that each ether particle (or point in the ether) at the reflecting surface becomes the center of a new wave front, and that the resultant wave-front is the envelop of all these new wave-fronts. Shall we tell that to high school pupils? We cannot use the term “envelop" until they have studied a little calculus, so we must get some other way of making a plane wave-front (or whatever its shape may be) out of an infinite number of curved wave-fronts. This may not be very difficult, except when both the mirror and the incident wavefront are curved, but it certainly will take more time than we use by the geometrical method. And in the end, the pupil will have no reason for taking this envelop rather than any other surface drawn through the new wave-fronts, until you explain the effect of interference. And, finally, we have still not really told how or why the wavemotion is reflected at the surface. We have simply asserted that it is. We can do that much by the geometrical treatment. I submit that this does not really explain what takes place at the reflecting surface; and indeed (I ask for information) are we not obliged to assume that the ether does suffer a stress and strain analogous to the bounding ball? Is not a disturbance reflected back through the ball in just the same way, and is not the fact that the angle of reflection equals the angle of incidence in the case of the ball due to exactly the same cause as with the ether waves, viz., interference? One statement is surely a slip. On p. 295 he says: "When a wavefront falls on a polished surface, it is reflected as a wave-front. Its velocity may or may not be changed." Surely we are obliged to assume that the velocity is never changed by reflection. That is the only possible way to construct his Fig. 1, e. g. (And by the way, he does not explain how the center A' is found. Apparently it is done by locating enough points on the reflected wave-front to decide that it is going to be a circular arc, and then by geometry finding the center of this.) His Fig. 2 is good, but in Fig. 3, I submit that it is not half so easy for a pupil to determine the exact curvature of the refracted wave-front as to determine the direction of the refracted ray. Again, Mr. Cavanagh's objection to the use of trigonometric funetions "before they are understood." can just as well be used to show that a taste of trigonometry should be given to the pupil as to show that the sine definition of the refractive index should not be used. And indeed, this seems to be demanded anyway. Electrical World, March 30, 1907. p. 620.) (See, e. g.. The In conclusion, Mr. Cavanagh admits that the wave-treatment "does not lend itself well to quantitative demonstrations." But he is willing to give up such demonstrations for the sake of a method which, after all, does not give an ultimate explanation of any of the phenomena. Respectfully yours, WM. B. BORGERS, A.B., Teacher of Physics, Central High School. ARTICLES IN CURRENT MAGAZINES. American Naturalist for March: "Studies on the Ophioglossaceae," Prof. D. H. Campbell: "Polygamy and other Modes of Mating among Birds,' Dr. R. W. Shufeldt; "On the Wood Rails, genus Aramides, occurring north of Panama," Outram Bangs. American Inventor for April: "The Call of the Sky." "The Modern Torpedo," "How Candles are made," "North Carolina's New Waterway." Condor for March-April: "Among the Pelicans" (photos), Wm. L. Finley: "Migration and Nesting of the Sage Thrasher." M. French Gilman: "An Experience with the South American Condor." Samuel Adams: "Nesting Ways of the Western Gnatcatcher," Harriet Williams Myers; "The California Distribution of the Roadrunner," Joseph Grinnell. Farming for April: "Planting the Small Grains," J. I. Schulte (photographs by the author); "The Farmer's Garden," W. R. Beattie (photographs furnished by the author); "Reclaiming an Unprofitable Orchard," C. G. Woodbury (photographs by the author and S. W. Fletcher); "The Great Value of Japan Clover to the South." C. B. Smith (photographs by the author); "Sweet Potatoes in Western Kansas," Viola McColm (photographs by the author); "Big Raspberries and Blackberries." W. H. Jenkins (photographs by the author): "Making a Cranberry Bog." A. S. Atkinson (photographs by A. Radclyffe Dugmore and Dr. Frank Overton); "An Alfalfa Experience in New York State." M. W. Jenkins (photographs by W. H. Jenkins); "Commercial Muskmelon and Cucumber Growing," Lyman H. North; "Planting Table for Farmers and Gardeners." Journal of Pedagogy for Dec.-March: "The_Organization of the Department of Education in Relation to the Other Departments in Colleges and Universities." "The Relation of the Department of Education to Other Departments in Colleges and Universities." Literary Digest for April 27: "Light as an Enemy to Panama Diggers." "A Detector of the Invisible," "Is Paranoa Curable?" "Our Railroads Breaking Down." "Life-saver for Mercury-workers," "The Founder of Modern Synthetic Chemistry." Ores and Metals for April 20: "Cutting Down Cost of Ore Production," "Industrial Value of Aluminum and Aluminum Minerals," "Role of Copper in Future of Colorado." "Topography of South Platte Valley." "The Principles of Copper Smelting": "Possible Dangers in Increasing Gold Pro |