II. Construction by Irvin E. Kline, Atlantic City, N. J. Note: Mr. Kline appends proof of the construction but it is omitted for lack of space.-Ed. Construction: Through point B erect a perpendicular to a. Through A draw a line so that it will form with c and this perpendicular an isosceles triangle. With vertex B, of this isosceles triangle as center and B1 A as radius, describe a circle. Through A erect a perpendicular to c, and through C draw a line so that it will form with b and this perpendicular an isosceles triangle. With vertex A, of this isosceles triangle as center and A, C as radius, describe a circle. Likewise at C draw a perpendicular to b and construct an isosceles triangle. With C1 as center and CB as radius, describe a circle. These three circles will intersect in a point P such that PAB < PBC = /PCA. = Another point may be found by going around the triangle in the opposite direction. These points are called Brocard's Points. See Weber and Wellstein: Encyclopadie der Elementar Mathematik, Vol. II. Solutions were also received from Philomathe, and Nelson L. Roray, one incorrect solution was received.-Ed. PROBLEMS FOR SOLUTION. Algebra. 566. Proposed by R. T. McGregor, McArthur, Cal. Solve the equation √x+27+√55-x = 4. Geometry. 567. Proposed by N. P. Pandya, Sojitra, India. Circumscribe a triangle about a given circle, the ratio of the angle bisectors being known. 568. Proposed by Murray J. Leventhal, Stuyvesant High School, New York City. The line that joins the orthocenter of a triangle to any point on the circumscribed circle bisects the line joining the feet of the perpendiculars dropped from this point upon the three sides of the triangle. 569. Proposed by N. P. Pandya. The vertex A of a triangle is the center of a given circle. P and Q are points of intersection of AB, AC respectively, with the circle. The tangents at P and Q divide the base in the ratios kl and m : n, respectively. Construct the triangle ABC. SCIENCE QUESTIONS. Conducted by Franklin T. Jones. University School, Cleveland, Ohio. Readers are invited to propose questions for solution-scientific or pedagogical—and to answer questions proposed by others or by themselves. Kindly address all communications to Franklin T. Jones, University School, Cleveland, Ohio. Science Tests. To those who have asked to be enrolled as cooperating on science tests some lists in physics have already been mailed. Chemistry will follow. Suggestions are desired. Returns will be compiled as rapidly as received and communicated to all as quickly as possible. J. P. Drake, Emporia, Kan., and Katherine Weaver, Emma Willard School, Troy, N. Y., have asked to be added to the list of those who wish tests. Acknowledgment. The receipt of examination papers is acknowledged with thanks from Charles J. Pieper, University High School, Chicago, Ill.; H. E. Hammond, Kalamazoo, Mich.; Katherine Weaver, Troy, N. Y. QUESTIONS AND PROBLEMS FOR SOLUTION. 302. What do you think of the following test in General Science, especially Part II? UNIVERSITY HIGH SCHOOL, CHICAGO-SECOND SEMESTER-FEBRUARY 6, 1918. General Science-Part I. Answer all questions in order. Each question counts 15 points. 1. Why is a room cooled more rapidly if a window is opened at the top than when opened at the bottom? Would the change of air be more or less rapid if the window were opened at both the top and bottom? Why? 2. Explain, using a drawing if you think it will help you in the explanation, how a simple mercury barometer is made. How does it work? 3. How does yeast cause bread to rise? Explain fully. 4. How are carbohydrates made in the leaf blade, and what are four parts of the blade which take part in its manufacture? 5. Name three important gases of the air. How may one of these be made in the laboratory? 6. Tell about two experiments performed in the laboratory which prove to you that air is matter. General Science-Part II. There are forty blank spaces in the paragraphs that follow. To complete each statement write the proper word in the blank space. In several cases one of several words may be used. written counts 1-2 point. 1. Air pressure is measured by means of a are two kinds: and Each word correctly There If either of these in struments is taken up in an aeroplane it will show a day it is while on a rainy 2. The instrument which is used to take the temperature of the air is called There are two kinds: and kind on which the average temperature of a living room should be approximately degrees and the normal temperature of the body is 3. Air Therefore warm air will cold air has a when heated and degrees. when cooled. from the warm ground because the weight. The air is warmer in summer than in winter because the rays of the sun strike the earth more in summer. Also the days are 4. In a cloud from which rain is falling the in winter than in summer. is per cent. If the temperature is below 32 degrees F. the If the water vapor will come out of the air in the form of temperature is above 32 degrees F. the water vapor will come out in the form of When the air is nearly saturated and the air is will appear. then cooled a to an area of of pressure area. If 5. Winds blow from an area of pressure. The velocity of the wind depends upon the the pressures. A cyclone occurs in a the wind sets in from the south or southeast and the air pressure is decreasing a is approaching from a direction. humidity and often A south wind from the brings rain because it is Gulf has a as it comes north. 6. Of the three forms of matter the molecules are farthest apart in the form. The gases in the air do not separate into layers according to their weights because they An is smaller than a molecule, and a molecule of water is composed of two of and one of 7. Plants which do not contain chlorophyll are called plants. Of the three kinds of plants which occur in the air causes milk to sour. Please answer questions numbered 303 and 304 in the following list. SHEFFIELD SCIENTIFIC SCHOOL-SEMI-ANNUAL EXAMINATION-JUNIOR CLASS JANUARY 29, 1918. Physics Engineering Science Group. 1. (a) Find the torque acting on a bar magnet when placed in any position in a magnetic field. 303. (b) Find the magnetic intensity on the prolongation of the axis of a bar magnet 30 cm. from one of the poles, the strength of each pole being 1200 units and the distance between the two poles being 20 cm. 2. (a) Derive an expression for the potential at a point due to a charge of electricity at some distance. (b) Find the potential at the center of a square 10 cm. on a side, due to charges of +50, +100, 150, and +200 units placed at the middle points of the sides of the square. (c) Find the electrical energy of a sphere of radius 10 cm. when charged with 200 units of electricity. 3. (a) Give a rule for telling the direction of the magnetic field about a current. (b) Obtain a value for the magnitude of the magnetic field inside of a solenoid. 4. (a) What are the essential features of a voltmeter; of an ammeter? (b) A galvanometer of 20 ohms resistance gives a deflection of 50 divisions for a current of 1 milliampere. How should the instrument be modified to serve as an ammeter with one division per ampere? 5. Define, isogonic line, electrostatic capacity, electromagnetic unit of quantity, neutral temperature for a thermo-electric couple, a henry. 6. Two cells each having an E. M. F. of 1.6 volts and an internal resistance of .4 ohm are connected in parallel and joined to two resistance coils of .2 and .3 ohm respectively, which are also connected in parallel. What is the current in the .3 ohm coil and what is the drop of potential between its ends? How much heat is generated in this coil per minute? 7. (a) Define magnetic induction; magnetic flux; magnetic permeability. (b) What is the character of the relation between the magnetic induction in iron and the magnetizing field? 8. (a) Obtain an expression for the electromotive force in a circular coil of wire rotating in a uniform magnetic field. 304. (b) What is the maximum E. M. F. in such a coil of 50 turns having a diameter of 40 cm. when this rotates 1200 times per minute about an axis perpendicular to a field of 300 units? 9. (a) Give Fleming's rule for the direction of the force acting on a conductor when placed in a magnetic field. (b) Find the force per unit length in a conductor carrying 20 amperes whose length is parallel to the direction of a magnetic field of .3 unit. (c) What is the nature of the interaction between two parallel conductors carrying_currents? 10. (a) Explain the theory of ionization by collision, and tell how it accounts for a spark discharge. (b) What are radioactive substances? (c) State the main facts about each of the different kinds of rays given off by radioactive substances. SOLUTIONS AND ANSWERS. Apropos of the answers to question No. 284 in the March issue. By H. E. Hammond, Central High School, Kalamazoo, Mich. Messrs. Smith and Drake both are in favor of having all the laboratory notes made in the laboratory. The problem is not one to be dismissed in a few words, but depends largely on the time for laboratory work that is available. In many small schools this is the same as a class period, forty-five minutes, and elsewhere it runs up to three hours, 180 minutes. We have seventy-five minutes, and it is difficult to get it more than once a week. Manifestly, all this time must be used to get the first draft of the results, but we use a carbon copy book for rough work, and the duplicate is left at the end of the period. The complete write-up has to come later. All possible efforts have been made to allow the pupils to have every minute of the seventy-five for actual work, and the large majority can finish the usual amount of work in that time, though seldom can more than four trials be taken, and often only two. Are many trials necessary or desirable in high school? The writer would like to hear from others who have the same problem to meet. Second-Year Physics. Comment by W. A. Zinzow, Wausau, Wis. I have but recently become a very much interested reader of SCHOOL SCIENCE AND MATHEMATICS, and particularly of the "Science Questions Department.' I have been in charge of the Physics Department of the Wausau High School during the past three years. This year I have introduced, with the cooperation of the Board of Education and our Superintendent and Principal, a second year's work in physics in the form of a year's course in electricity. In my regular physics work I am giving the usual amount of time to the study of electricity, but during the second year we are taking up the subject in a more intensive manner. During the past semester we reviewed some of the fundamental principles of electricity, going into details a little more than usual. After that we spent about six weeks on measurements, such as Ohm's Law problems in their various forms, measurements of resistance and power. We devoted the last six weeks of the semester to a somewhat comparative study of storage batteries. I am enclosing a copy of the examination questions that the class worked on at the end of the semester. During the present semester we are studying the theory of direct and alternating current generators, laying special stress on why certain actions result, rather than their mathematical relations. Up to the present time we have been using Millikan-Crocker-Mills Practical Lessons in Electricity and Evans Manual of Electricity as textbooks, together with Archbold A Laboratory Course in Practical Electricity as a laboratory outline. From now on for about six weeks the class is going to spend its laboratory periods in the various electric shops about town under the supervision of the men in charge of the shops. After that brief period of training is over they will go out individually with the workmen from the various shops as helpers for wiremen, electric instrument testing, telephone work, etc. In this way these boys will be able to fill the places of men who will be drawn in the next draft, in addition to making their course to a certain extent practical rather than purely theoretical. I have a class of twelve boys, and every one of them has been at work with all kinds of spirit, and I believe they are getting a great deal out of it. RESEARCH IN PHYSICS. Conducted by Homer L. Dodge. State University of Iowa, Representing the American Physical Society. It is the obiect of this department to present to teachers of physics the results of recent research. In so far as is possible, the articles and items will be nontechnical and it is hoped that they will furnish material which will be of value in the classroom. Suggestions and contributions should be sent to H. L. Dodge, Department of Physics, State University of Iowa, Iowa City, Iowa. THE QUANTUM THEORY AND MOLECULAR STRUCTURE. By Robert C. Colwell, Geneva College, Beaver Falls, Pa. The inability of the classical mechanics to explain the spectra of the elements is at once apparent if we fix our attention upon the hydrogen spectrum. The atom of this element consists of a single electron rotating about a central nucleus. Under the inverse square law, its energy should be gradually expended in radiation, and the molecule should eventually reach a state in which no radiation will take place. Then, too, it seems impossible for a single rotating electron to give the complicated line spectrum of hydrogen. Bohr, however, has shown how a modification of the quantum theory will account for all the lines of the hydrogen spectrum. In this theory, he supposes that the electron may rotate about the central nucleus in a series of rings, and that the electron jumps at once from one ring to the other without revolving in the intermediate orbits. The development of this theory depends upon two very simple theorems in elementary physics. First: When a body is moving uniformly in a circle, the centripetal force is given by the equation: in which is the velocity of the body of mass m, and r the radius of the circle. Second: The potential energy of an electron e at a distance r from a nucleus E is given by the equation: in which E and e denote the charges of the nucleus and the electron respectively. Suppose the electron revolves in its orbit n times per second. Then, sincer is the radius, the Under the Newtonian Law, the force of attraction between the nucleus and the electron is If there is equilibrium this force is equal to the centripetal force. Thus from (1) and (4) mv2 Ee The potential energy of the electron becomes, from (2), (3), and (5) |