GEOMETRIC RECREATION 731

Objections.I. That the proposition that there is empty space is re-

pugnant to common sense.II. That the proposition, nature abhors a vacuum, and

nevertheless allows it, accuses nature of impotence, whichimplies a contradiction.

III. That numerous experiences, even everyday, show thatnature cannot suffer a vacuum.

IV. That an imperceptible matter, unheard of and un-known, to all the senses, fills such a space.

V. That light being, either an accident or a substance itis not possible for it to exist in a vacuum, being an accident;and it fills that space void in appearance, being a substance.

A GEOMETRIC RECREATION.

BY ISABEL HARRIS,Richmond, Va.

In the Collegiate School for Girls of Richmond, Virginia,a class in plane geometry, consisting of twenty girls, bubblingover with an unusually effervescent enthusiasm, planned thisunique and fascinating modification of the usual contest ingeometry.The members of the class got together and divided them-

selves into two groups and each group selected in an animatedvoting contest one of their number to be captain. These twocaptains with the instructor were asked to form a committeeto draw up the regulations that should govern the contest, andthe following resolutions were submitted to the class:

I. There shall be a series of six contests in Math. IV duringthe months of December, January, February, and March.

II. The class shall be divided into two teams, consistingof a captain and nine members. The names, of the teams shallbe the Pythagoreans and the Platonians.

III. The instructor in mathematics shall referee the contest.IV. Each team shall elect an official score keeper.V. The propositions to be proved shall be selected by the

referee and shall be written on the board one at a time.VI. The first trial of the first proposition shall be decided

by lot and shall thereafter alternate with the two teams.VII.. When a proposition is given by the referee, the captain

shall appoint a member of her team to attack it. If she gives alogical proof, that side scores two points. If she fails to give

732 SCHOOL SCIENCE AND MATHEMATICS

a proof, the captain can call on another member of the sameteam. If she proves the proposition, the team scores one point.If she fails to prove it, the opportunity of proving the propositiongoes to the opposing team. The opposing team proving it scoresone.

VIII. When a member of one team fails to give a correctproof, that member is disqualified for the day.

IX. A member having proved a proposition is not entitledto another trial until all other members have been given anopportunity to attack a proposition.X. An illogical proof detected by the opposing team at

end of proof shall score one-half point for that team.XI. Any interruption of the one proving a proposition,

either by her own team or the opposing team before she hasreached the Q. E. D., shall be considered an ^error" and shallscore one-half point for the opposing side.

XII. At the close of the contest the team having the highestscore shall be guests of honor at a ^feast" given by the losingteam.

..-��.�..-----.-���..�Captain of Platonians.

.��-�.�.----.--..-...�-Captain of Pythagoreans.�-�.�-..--����--..-Referee.

The regulations were received with a suppressed and tenseenthusiasm, and were adopted by a unanimous vote. The con-tests followed in rapid succession and the interest was keptup by a careful selection of original exercises, beginning withsimple propositions and continuing by easy ascents to moredifficult ones. The teams were well matched and the competi-tion was spirited. First one team and then the other was ahead,and the whole school watched with increasingly eager interestthe outcome of each contest. Intercollegiate basket ball gamesand the World Series in baseball were no more discussed androse to no higher point in the scale of school interests thanthe score of the Pythagoreans and the Platonians.The Pythagoreans were the final victors and the Platonians

evolved this clever scheme of giving them a mathematical^feast." Mystic invitations written on paper oiled with Wessonoil to represent parchment and rolled like scrolls, bade theguests to the party. They were greeted at the door by Plato’sominous motto printed in big, bold letters: ^Let no one ignorantof geometry enter here." Guests and hostesses were all seatedat one long table, which was elaborately decorated with vases

GEOMETRIC RECREATION 733

of ^flowersn made by tying various mathematical symbolscut out of pink crepe paper to small bushy branches of shrubs.Over the table were scattered other symbols and the candleshades were decorated with weird and fantastic mathematicalexpressions. On the place cards were drawn familiar geometricfigures. The following menu was served. Since the readercan not have the opportunity of verifying the menu by thecourses served, an interpretation is given below.)

U N �. -

Given:

Quadrilaterals

M E

Proper Fractions(Lettuce)-l

Extracted RootsTriangles

Homogeneous Creamfi 4-32°F+Cake made by Heron’s Formula

Cylinders with II Lines.- Champagne (Imaginary)

HaO (Real)To prove that the Pythagoreans are equal to any occasion.(Hint. Prove by elimination of hypothesis.)

Time Limit oo

InterpretationGiven:

Chicken salad over lettuceSaltines Sandwiches

Saratoga chipsIce cream

and cakeSociety mints

Mr. Evershed thinks that the values of the color indices assigned byProf. N. H. Russell to the sun and Venus (+ .79 m. and + .78 m.) aremutually inconsistent, since they imply that no selective absorptiontakes place in Venus’s atmosphere. Mr. Evershed finds evidence of de-cided selective absorption in the violet, as compared with his cloud spec-tra.�Nature (London), Feb. 19, 1920, p. 675.

U. S. GEOLOGICAL SURVEY ESTABLISHES RESIDENT GE-OLOGIST IN SAN FRANCISCO BRANCH OFFICE.

J. M. Hill of the United States Geological Survey, has been trans-ferred from Washington to the Survey^s office in San Francisco where hewill be associated with Charles G. Yale. Mr. Hill’s field of geologicalstudies will include the Pacific Coast States and to some extent also Ari-zona and Nevada. The desirability of having a geologist attached to theSan Francisco office has long been felt, for many requests for examinationand report are received that can not be met by sending a Federal geol-ogist across the continent.