Here is the list of countries to which SCHOOL SCIENCE AND MATHEMATICS goes each month: Every State in the United States, every Province in Canada, Mexico, Cuba, Porto Rico, Brazil, Argentine, Chile, Peru, Ecuador; nearly every country in Europe (before the war every country); Egypt, Liberia, Cape Colony, The Transvaal, Persia, Ceylon, India, China, Korea, Japan, Philippines, New Zealand, Australia and Hawaii. The only Journal in the English language devoted primarily to the needs of Science and Mathematics teachers in High Schools. Remember this when deciding upon your subscription list of periodicals for Science and Mathematics. This Journal is the only Journal whose pages are devoted to all phases of progressive Secondary Science and Mathematics Teaching. Be a partner in this enterprise by investing $2.50 with it each. year. Those teaching these subjects in Secondary Schools who wish to be progressive should be subscribers to this Journal. During the last ten years it has accomplished more in placing Science and Mathematics teaching on its present high plane than any other agency. Wide awake Mathematics teachers should have it to keep abreast of the times. Progressive Science teachers should read it to keep themselves alive in their subjects. The best instructors in any subject are those broad enough in their pedagogical views to have a knowledge of what those in other subjects are doing. SCHOOL SCIENCE AND MATHEMATICS is the only Journal through which you can receive this knowledge. School Science and Mathematics 2059 East 72nd Place CHICAGO, ILL. Please mention School Science and Mathematics when answering Advertisements. It should be used primarily for potentials only, or for very small currents of the order of a few milliamperes. The cells will, however, deliver about 1-10 ampere, but for a short time only, the voltage soon dropping off. Cells constructed of sheet lead and formed as these should be charged regularly once per week whether they are used or not. For convenient charging the trays should be mounted in a cupboard as described, where the individual trays may be returned for charging. If preferred, the cupboard may be replaced by three cabinets of 1,000 volts each mounted on rubber tired castors, thus making the battery available in different rooms. DUST SPIRAL NEAR FLAGSTAFF, ARIZONA. Heard At 1:15 or 1:20 p. m., on June 19, 1920, the writer's attention was attracted by a peculiar sound suggesting an automobile motor. out of doors, the sound resembled the tearing of coarse paper. Above the forest, due west of the Fort Valley Experiment Station, nine miles northwest of Flagstaff, a column of tawny dust, the color of the dry soil at that time, was seen traveling in an easterly direction, though with minor deviations, and forming a somewhat undulating band in the general direction of the sun. From below it appeared to be a nearly vertical spiral so close to the sun that the upper part could be seen only with great difficulty. The column was intermittent, sometimes almost wholly disappearing, at which time the characteristic noise subsided also. The height was difficult to estimate; perhaps 500 feet, perhaps 1,000. When about 500 feet west of the west fence of the station grounds it broke off to the southeast downhill, and whirled around near the back corral. It oscillated on this flat for a time, apparently moving first southeast, then northwest, possibly in a circle, or in other directions. At one time it seemed to be starting to move north or northeast directly toward the station buildings. The basal diameter, judged from a distance of about 300 feet, was from 10 to 15 feet. Leaves and trash were included in the swirl for a height of not less than 5 or 10 feet, resulting in a dense blackish cloud to this height. Had the whirl been observed from above, its rotation would have appeared counterclockwise. When south of the observer the column still seemed to lie in the general direction of the sun, although probably mainly ahead of the position of the ground end. The spiral died out on a rocky point about 500 feet south of the back corral at about 1:25 p. m., the upper part of the dust column floating for some time after the ground swirl had disappeared. The wind about noon had been variable-northwest, north, northeast, and east. The northwest and east winds are less common here than those from other directions. At about 1:25 p. m., there was almost no wind on the station grounds. The day was clear and hot with a maximum shade temperature of 81° at 2 p. m., and 80° at the time of the phenomenon.-Monthly Weather Review, GEOMETRY. By John C. Stone and the late James F. HIGHER ARITHMETIC. James F. Millis. By John C. Stone and the late JUNIOR HIGH SCHOOL MATHEMATICS. By John C. THE FIRST YEAR OF SCIENCE. By John C. Hessler. Two. ELEMENTS OF PHYSICAL GEOGRAPHY. Edition. By Thomas C. Hopkins. Benj. H. Sanborn Co. Revised Chicago New York Boston "School Science and Mathematics" bears the same relation to progressive Science and Mathematics Teaching as does the "Iron Age" to the Hardware business. No up-to-date Hardware merchant does without this trade Journal. Every Science and Mathematics teacher should be a subscriber to the professional trade Journal, "School Science and Mathematics." Dependable and worth while BIOLOGICAL SUPPLIES OF YEARS Large stock of material in Zoology, Botany, Life Histories and For the student, the class room, the museum. New Zoological and Life History Catalogs. Catalogs free, Zoology, Life Histories, Botany, Microscope slides. Supply Department MARINE BIOLOGICAL LABORATORY Woods Hole, Mass. Please mention School Science and Mathematics when answering Advertisements. PROBLEM DEPARTMENT. Hyde Park High School, Chicago. This department aims to provide problems of varying degrees of difficulty which will interest anyone engaged in the study of mathematics. All readers are invited to propose problems and solve problems here proposed. Problems and solutions will be credited to their authors. Each solution, or proposed problem, sent to the Editor should have the author's name introducing the problem or solution as on the following pages. The Editor of the department desires to serve its readers by making it interesting and helpful to them. If you have any suggestion to make, mail it to him. Address all communications to J. A. Nyberg, 1039 E. Marquette Road, Chicago. LATE SOLUTIONS. 733. Smith D. Turner, Andover, Mass. SOLUTION OF PROBLEMS. 736. Proposed by J. T. Crawford, University of Toronto, Canada. A geometric and a harmonic progression have the same pth, qth, and rth terms, a, b, and c, respectively. Prove a(b-c)log a+b(c-a)log b+c(a−b)log c = 0. Solution by L. R. Kellam, Culver Mil. Acad., Culver, Ind. From the G. P. we derive a = ARP-1, b = AR-1, c-ART-1 or RP-q = a/b and Rab/c. Then (p-q) log R=log a log b, (q-r) log R=log b-log c, or (1) (p −q) / (q−r) = (log a −log b) / (log b −log c). From the H. P. we derive 1/a = x+(p−1)d, 1/b=x+(q−1)d, 1/c= x+(r-1)d, and from these equations derive (2) (p-q)/ (q − r) = (b-a)/a(c-b). Combining equations (1) and (2), we get the desired result. =c Also solved by T. E. N. Eaton, Redlands, Calif.,; J. B. Faught, Yankton College, So. Dak.; J. F. Howard, Brackenridge H. S., San Antonio, Texas; Edna E. Kramer, student, Hunter College, New York; H. Lazott, Worcester, Mass.; and the following pupils of the Redlands H. S., Calif.: Ralph Cope, '23; John Ide, '23; Homer Joy, '25; Reva Rose, '25. The editor feels sure that the readers of the department would like to hear how Mr. Eaton manages to teach progressions and logarithms to a freshman class. Comparing problems 713, 731 and 736, we note that this relation is true for an A. P. and a H. P. only if the qth term is half way between the pth and rth, and that for an A. P. and a G. P., the relation is (b-c)log_a+(c-a)log b+(ab)log c=0. 737. Proposed by Henry L. Wood, Boonton, New Jersey. Without using parallel lines, construct the fourth proportion to three given lines, a, b, c. I. Using the theorem about the segments of two chords in a circle, the problem was solved by J. F. Howard; Hazel C. Jones, Hammond, Ind.; H. Lazott; Isabel McCoy, pupil, North East H. S., Kansas City, Mo.; Edw. A. Ravenscroft, pupil, New Trier Township H. S., Kenilworth, Ill.; Smith D. Turner. Using the theorem about the segments of two secants, by Iram Luelleman, Mattoon, Ill.; G. H. Crandall, Culver Mil. Acad., Ind. Using the theorem about an inscribed triangle, and altitude, and a diameter, by I. Luelleman. Using two similar triangles, by L. R. Kellman; Claude Nunnally, pupil, Chester Agriculture H. S., Va II. Solution by John B. Faught, Yankton College, Yankton, So. Dak. On a line take AB =b, BC=c, so that AC=b+c. On AC as a diameter, draw a circle and erect a perpendicular to AC at B, meeting the circle at D. Then BD2 = bc. From B lay off on the given line BE=a. Draw a circle through D and E having its centre on AC, and call F its intersection with AC. Then BF = x is the required line. For BD2 = ax, and hence ax = bc, or a:bc:x. Similarly solved by F. A. Cadwell, St. Paul, Minn. III. The Proposer has sent in two interesting solutions due to E. Daniele of Pavia, and E. Dubois. Hawkes-Luby-Touton: Plane Geometry Solid Geometry (Just published) McPherson and Henderson: Chemistry and Its Uses Laboratory Practice in Chemistry (Ready in July) Other Standard Texts Millikan and Gale: Practical Physics. Bergen and Caldwell: Botanies. Gruenberg: Elementary Biology. Caldwell and Eikenberry: General Science (Rev.) Waters: Essentials of Agriculture. Leventhal & McCormack's Exercises in Plane Geometry (in Press) A BRIEF, COMPACT AND CONCISE presentation GLOBE BOOK COMPANY, 949 Broadway, New York City Please mention School Science and Mathematics when answering Advertisements. |