the radius of this circle and R of the given circle, then the fourth proportional to R',R and A'B' will be AB, the side of the desired triangle. AC and BC may be constructed in a similar manner.

If N' lies between B' and M' the arc M'N' would be described on the same side of B'C' as the semicircles and a slight change of notation would be necessary to carry through the same argument for this case as for the preceding.

The Editor recognizes that this is a devious method and will welcome a simple one.

587. Proposed by W. T. Harlow, Portland, Ore.

A merchant takes $1,000 every year out of his income for personal expenses. Nevertheless his capital increases every year by a third of what remains. At the end of three years it is doubled. How much had he at first? (From Chrystal's Algebra.)

588. Proposed by Daniel Kreth, Wellman, Ia.

589. Proposed by N. P. Pandya, Amreli, Kathiawar, India.

(1)

(2)

AB is a chord of a circle. Find a point C on AB, such that if tangents CD and CE be drawn to the circle, and if EF, parallel to AD, cuts CD in F, CD may be bisected at F.

590. Proposed by Daniel Kreth, Wellman, Ia.

AB is a chord in a given circle, bisected in C. DE and FG are any two chords intersecting each other in C; FE intersects AB in H, and DG intersects AB in K. Prove that CH CK. Geometrical and trigonometrical solutions are desired.

=

SCIENCE QUESTIONS.

Conducted by Franklin T. Jones.

The Warner & Swasey Company, 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, 10109 Wilbur Ave., S. E., Cleveland, Ohio.

Please send examination papers on any subject or from any source to the Editor of this department. He will reciprocate by sending you such collections of questions as may interest you and be at his disposal.

War Questions on Science.

310. What questions on science, new and old, has the war brought to our attention?

'It will be most timely to give general circulation to such questions as

have come to your attention, especially those which have introduced interesting discussions into your classes. Mail them to the Editor now. Would you guess from current questions in science examinations that the past two years represent the most stupendous scientific development ever known?

The following list of questions speaks for itself:

COLLEGE ENTRANCE EXAMINATION Board.

Comprehensive Examination in Physics, Friday, June 21, 1918.

A teacher's certificate covering the laboratory instruction must be presented as a part of the examination unless the laboratory notebook is to be presented at a laboratory examination.

Answer ten numbered questions, distributed as follows: three from Group I, two from Group II, two from Group IV, two from Group V, and one of the remaining questions.

The number in parentheses before each question indicates the number of credits assigned to it.

Show clearly the method by which you obtained your answers to problems and state the units used in each case.

Attach to the answer, in each case, the number and letter used in the printed

1. A wooden cube 5 cm. on an edge weighs 100 g. (a) (3) What is the density of the cube? (b) (3) What force would be required to hold the cube submerged in a liquid having a density of 1.5 g. per cu. cm.? (c) (4) How much of its volume would protrude above the surface if the cube were floated in a liquid having a density of 1.2 g. per cu. cm.?

2. (a) (3) Define work; mechanical advantage of a machine; efficiency of a machine. (b) (7) Two men raise a weight by means of a jackscrew. They push with a force of 100 lbs. each, at opposite ends of a bar 5 ft. long that passes through a hole at the top of the screw. If the pitch of the screw is 1-2 inch and the efficiency of the machine is 30 per cent, how great is the weight?

3. An engine operates a pump which raises water to a height of 50 ft. at the rate of 1,000 gal. per min. (One gallon of water weighs 8.4 lbs.) (a) (3) How much work is done upon the water per second? (b) (7) If the efficiency of the pump is 90 per cent, how many horse-power is the engine developing?

4. A constant force acting on a mass of 40 grams for 5 seconds changes its velocity from 60 cm. per second to 100 cm. per second. What is: (a) (2) the acceleration? (b) (2) the magnitude of the force? (c) (2) the total distance covered in the five seconds? (d) (2) the final momentum? (e) (2) the kinetic energy at the end of the first two seconds?

5. (a) (8) A tank having a volume of 12 cu. ft. contains air under a pressure of 30 lbs. per sq. in. On connecting the tank to an exhausted receptacle the air pressure is reduced to 10 lbs. per sq. in. Find the volume of the receptacle. (b) (2) Describe two phenomena that are caused by surface tension.

GROUP II.

6. (a) (2) Define coefficient of linear expansion. (b) (8) Describe an experimental method of measuring the coefficient of linear expansion of a solid, describing the apparatus used, the measurements made, and the way in which these measurements are used to compute the coefficient.

7. (a) (6) A balloon is filled on a cool night with 20,000 cu. ft. of gas at a temperature of 7° C. under a pressure of 15 lbs. per sq. in. In the sunshine of the day the gas becomes warmed. At what temperature will the pressure reach 16 lbs. per sq. in.? Assume that the gas bag does not stretch and that no gas escapes. (b) (2) Express 9° C. on the Fahrenheit scale. (c) (2) Compare the advantages of mercury and of air as thermometric substances.

8. (a) (2) Name and define a unit quantity of heat. (b) (8) A copper calorimeter of mass 210 g. contains 85 g. of water and 100 g. of lead shot at 15° C. How much boiling water must be added to raise the temperature

of the calorimeter and contents to 25° C.? (Sp. ht. of copper of lead = 0.032.)

GROUP III.

9. (a) (2) What conditions are necessary for the formation of an echo? (b) (2) What is the physical difference between a noise and a musical sound? (c) (2) Why is thunder usually heard some time after a lightning flash is seen? (d) (2) Upon what does the loudness of sound depend? (e) (2) Upon what does the pitch of a sound depend?

GROUP IV.

10. (a) (3) A more sharply defined shadow is cast by an opaque body when the source of light is an arc lamp than when it is a gas jet. Explain by the aid of diagrams. (b) (3) What should be the brightness of a single light in the ceiling 10 ft. from a book to give the same illumination as two candles placed one foot from the book?

(c) (4) Explain what is meant by saying that the index of refraction of water is 4/3. Make a careful, fully labeled diagram showing the passage of a ray of light obliquely from air into water.

11. (a) (2) Define principal focus; conjugate foci. A moving-picture machine is to be designed to project the picture on the film upon a screen 60 ft. from the film. If the image on the screen is to be 119 times the linear dimensions of the picture on the film: (b) (2) How far from the film must the projection lens be placed? (c) (4) What must be the focal length of the lens? (d) (2) How many times as intense will be the light passing through the film as that falling on the screen?

12. (a) (4) Make a diagram to show the dispersion of a narrow beam of sunlight by a triangular glass prism. (b) (4) What is the explanation of refraction? of dispersion? (c) (2) Explain carefully why the same blue cloth may seem to be of a different color when viewed by gaslight and by sunlight.

GROUP V.

13. (a) (2) What type of cell is best adapted to the ringing of electric bells? Why? (b) (2) What is meant by the term local action as applied to voltaic cells? (c) (2) How may local action be reduced? (d) (2) What is meant by polarization of cells? (e) (2) How may polarization be reduced?

14. Two resistance coils of 10 and 30 ohms joined in parallel are connected in series with a key, an ammeter of negligible resistance, and a battery whose electromotive force is 21 volts and whose internal resistance is 3 ohms. A voltmeter of high resistance is connected in parallel with the battery. (a) (2) Draw a diagram of the connections. (b) (2) What will be the ammeter and voltmeter readings when the key is open? (c) (6) What will the readings be when the key is closed?

15. (10) Describe the construction and operation of two of the following: electric bell; telegraph key and sounder; telephone receiver. Illustrate by carefully drawn diagrams.

ARTICLES IN CURRENT PERIODICALS.

American Mathematical Monthly, for September; 27 King Street, Oberlin, Ohio: "Definitions of the Discriminant of a Rational Integral Function of One Variable," G. A. Miller; "What is the Origin of the Name 'Rolle's Curve'?" Florian Cajori; "The Mathematics of Aerodynamics," E. B. Wilson.

American Naturalist, for August-September; Garrison, N. Y.; $4.00 per year, 80 cents a copy: "The Relation Between Color and Other Characters in Certain Avena Crosses," H. H. Love and W. T. Craig; "Opisthotonos and Allied Phenomena Among Fossil Vertebrates," Roy L. Moodie; "Cancer's Place in General Biology," W. C. MacCarty; "A Survey of the Hawaiian Coral Reefs," Vaughn MacCaughey. Astrophysical Journal, for September; University of Chicago Press; $5.00 per year, 65 cents a copy: "The Visibility of Radiation," Edward

P. Hyde, W. E. Forsythe, and F. E. Cody; "Studies Based on the Colors and Magnitudes in Stellar Clusters," Harlow Shapley; "The Absorption of Near Infra-Red Radiation by Water-Vapor," W. W. Sleator.

Auk, for October; Cambridge, Mass.; $3.00 per year, 75 cents a copy: "The Nesting Grounds and Nesting Habits of the Spoon-billed Sandpiper," Joseph Dixon; "A Winter Crow Roost," Charles W. Townsend; "The Pterylosis of the Wild Pigeon," Hubert L. Clark; "Sexual Selection and Bird Song," Chauncey J. Hawkins.

Blast Furnace and Steel Plant, for October; Pittsburgh, Pa., $1.00 per year; 15 cents a copy: "Cement Gun Used in Repairing Pit Stacks, Characteristic of Automatic Engine Stops," Walter Greenwood; "Remote Controlled Sub-Station Described," W. T. Snyder; "Standardizing Large Rolling-Mill Motors," K. Pouly; "Electrically Driven Mills at Bethle hem," J. T. Sturtevant.

Condor, for September-October; Hollywood, Calif.; $1.75 per year, 30 cents a copy: "Notes on the Nesting of the Mountain Plover," W. C. Bradbury; "Evidence That Many Birds Remain Mated for Life," F. C. Willard; "Some Ocean Birds from Off the Coast of Washington and Vancouver Island," Stanton Warburton.

Geographical Review, for October; Broadway at 156th Street, New York City; $5.00 per year, 50 cents a copy: "The Geographical Barriers to the Distribution of Big Game Animals in Africa," Edmund Heller. (1 map, 14 photos); "The Outline of New Zealand," C. A. Cotton, (1 map, 7 diagrs., 11 photos); "The Slavs of Southern Hungary," B. C. Wallis. (3 insert maps in color, 1 text map, 1 diagr.); “The Activities of the Canadian Arctic Expedition from October, 1916, to April, 1918," Vilhjalmur Stefansson. (1 insert map.)

Journal of Geology, for September-October; University of Chicago Press; $4.00 per year, 65 cents a copy: "Permo-Carboniferous Conditions versus Permo-Carboniferous Time," E. C. Case; "Notes on the Geology of Eastern Guatemala and Northwestern Spanish Honduras," Sidney Powers; "Loess-Depositing Winds in Louisiana," E. V. Emerson; "Description of Some New Species of Devonian Fossils," Clinton R. Stouffer.

National Geographic Magazine, for August; $2.50 per year; Washington, D. C. "Bringing the World to Our Foreign-Language Soldiers," with 4 illustrations, Christina Krysto; "Recent Observations in Albania,' with 22 illustrations, Brig. Gen. George P. Scriven; "The Ukraine, Past and Present," with 14 illustrations, Nevin O. Winter; "The Acorn, a Possibly Neglected Source of Food," with 8 illustrations, C. Hart Merriam; "Our Littlest Ally," with 16 illustrations, Alice Rohe.

Photo-Era, for October; $2.00 per year, 20 cents a copy; Boston, Mass.: "Craft and Art in Amateur Photography," Edouard C. Kopp; "Proe and Kahn on Soft-Focus Lenses," August Krug; "Pictures that Appeal,' H. B. Rudolph; "Pictorial Photography as I See It (In Three PartsPart III)," C. W. Christiansen; "A New Plan for Salon-Hangings," Sigismund Blumann; "Trial-Exposures and Economy," British Journal. Physical Review, for November; $6.00 per year, 60 cents a copy, Ithaca, N. Y. "Note on the Reversal of the Corbino Effect in Iron," Alpheus W. Smith; "The Relation between Certain Galvanomagnetic Phenomena," C. W. Heaps; "The Photoluminescence and Kathodo-Luminescence of Calcite," E. L. Nichols, H. L. Howes and D. T. Wilber; "The Evaporation of Small Spheres," Irving Langmuir; "The Motion of an Electrical Doublet," Leigh Page; "Law of Motion of a Droplet Moving with Variable Velocity in Air," Raymond B. Abbott; "The Specific Heat of Tungsten at Incandescent Temperatures," Paul F. Gaehr.

Fifty cents each will be paid for back numbers Vol. II, No. 3, May, 1902.

PERSONALS.

Mr. James H. Armstrong, for many years principal of one of Chicago's largest high schools, the Englewood, has recently been promoted to Assistant Superintendent in charge of Chicago's high schools. This is a most important position, one which has for many years been vacant to the great detriment of the high schools. No one in Chicago is better qualified in every particular to fill this most important position than Mr. Armstrong. This journal predicts a new era and all-round improvement in these schools under his management.

Mr. Franklin T. Jones, editor of Science Questions' Department in this journal, lately with the Glidden Paint and Varnish Company of Cleveland, has after many years again connected himself with the Warner and Swasey Company of Cleveland. Among other matters Mr. Jones will have charge of the development of an apprentice school into a junior engineering college.

Professor M. E. Grober has been elected to the chair of mathematics in Heidelberg University, Tiffin, Ohio.

Dr. W. O. Mendenhall, who has been professor of mathematics in Earlham College, has been made president of Friends' University, Wichita, Kansas.

Dr. E. L. Packard of the geology department at the Agricultural College of Mississippi has accepted a position in his chosen subject at the University of Oregon.

Dean Albert R. Mann, of the College of Agriculture at Cornell University, has been appointed by Governor Whitman a member of the state food commission.

Dr. Veranus A. Moore, head of the New York State Veterinary College at Cornell University, was elected president of the American Veterinary Medical Association at the Philadelphia meeting.

Professor George F. Freeman, of the College of Agriculture in the University of Arizona, has moved to Cairo, Egypt, where he will be connected with the Société Sultamenne de Agricultur.

Professor O. P. Jenkins, of the geology department of the State College of Washington, has been made geologist to the Arizona State Bureau of Mines, Tucson.

Professor J. W. Young, of Dartmouth College, has been made director of mathematics instruction in war work, given under the management of the Y. M. C. A.

Professor Edwin E. Hill succeeds to the position of director of the Jefferson Physical Laboratory of Harvard University, due to the retirement of Professor W. C. Sabine.

Dr. William P. Brooks has resigned from the position of director of the Massachusetts Agricultural Experiment Station, a position which he has held for nearly thirty years.

A SIMPLE "FALL" APPARATUS.

BY A. H. COOPER,

Grove Park School, Wrexham, Eng.

The need for a simple and direct method of demonstrating to junior students the fact that a freely falling body moves with a constant acceleration, has frequently been felt by teachers of physics.

The apparatus described below has been in use by the writer for some five or six years, and has been of great service in making clear the laws of falling bodies to elen entary students. It possesses the advantages that the whole apparatus is simple; an experiment is quickly performed;