202 SCHOOL SCIENCE AND MATHEMATICS

voted in the above list? If so write their numbers under one ofthe following heads:

a. Experiments that have always been there, you don’t know quitewhy.

&. Experiments that teach principles which the average citizenshould know.

c. Experiments that teach principles which none but an expertphysicist cares to know�physics curios, as it were. ,

d. Experiments that interest and stimulate the curiosity of thestudents.

e. Experiments that stimulate the student to investigate furtheron his own account.

f. Experiments given for other reasons together with their justi-fication.

Answers should be addressed to C. R. Mann, Ryerson Labora-tory, University of Chicago. They should be sent in not laterthan March 15, at which time the results will be tabulated. Thosewho send answers will receive the tabulated results togetherwith further questions which the results may suggest. We sin-cerely hope that everyone will join in this move and add his votefor the purpose of helping each other in making our truly greatsubject inspiring to the youth of this country.

C. R. MANN^ University of Chicago.C. H. SMITH, Hyde Park High School, Chicago.C. F. ADAMS, Central High School, Detroit.

REPORT OF THE COMMITTEE ON "A STRAIGHT LINE IS THESHORTEST DISTANCE OR PATH BETWEEN

TWO POINTS."

[At the meeting of the Mathematical Section of the Associationof Ohio Teachers of Mathematics and Science, March 25, 1905,Professor Halsted read a paper on "How to Teach RationalGeometry." At the conclusion of this paper the following resolu-tion was offered: Resolved, That in,, teaching demonstrativegeometry we will not use the phrase "A straight ’line is the short-est distance or path between two points;" or the phrase ^Theshortest distance between two points is measured on the straightline joining them." This resolution was referred to a committee,elected by the Section, with instruction to report at the nextmeeting. This committee, composed of Professor Halsted, Pres-ident Howe and Professor Wilson, reported at the meeting of theSection, December 28, 1905, as below: The report was adopted.]

A STRAIGHT LINE 203

Your committee beg leave to report as follows:(1) We believe that it is self-evident that one side of a triangle

is less than the sum of the other two; however Euclid 1: 20 showsthat it is not necessary to make this assumption.

(2) That the shortest course from one point to another inEuclidean space lies along a straight line is a proposition whichin ultimate analysis involves concepts not contemplated in itsoriginal statement as an assumption of elementary demonstrativegeometry. Consequently the ground is left in better shape forfuture progress if this proposition is not assumed in ElementaryGeometry.

(3) Both clearness and simplicity demand that the most funda-mental of distinguishing properties shall be chosen as the basis ofa definition. The fundamental notion in a straight line is quali-tative, thus the mind first grasps and most easily comprehends it,and such is certainly the property on which the definition shouldrest. � The fact that the notion of a minimum is somewhat com-plex in itself, and that in some cases of discontinuity or hyper-space the notion of minimum length is inapplicable to the straightline makes it desirable to avoid the idea of a minimum in defininga straight line or in a fundamental assumption. The particularway in which the qualitative property shall be used in the defini-tion of a straight line is a matter open to individual choice.

[Signed] G. B. HALSTED, Chairman,C. S. HOWE,W. H. WILSON.