478 REPORT— 1902. 



APPENDIX. 



Two Suggested Schedtiles of Experimental Geometry. 



{Scheme sub7nitted by Mr. Eggae, chiefly Geometrical, on Euclidean Lines.) 



Accurate measurements of lines, angles, areas, and (if possible) volumes, 

 should precede any formal definitions. The following suggestions are 

 intended for the earliest stages. 



Instruments. — Hard pencil, compasses, dividers, straight-edge gra- 

 duated in inches and tenths, and in centimetres and millimetres ; protractor 

 (if rectangular, its connection with the division of the circle should be 

 carefully pointed out) ; set-squares (45° and 60°) ; notebook of squared 

 paper ; tracing paper ; scissors and loose paper for cutting out and 

 folding. 



It is important that careful draughtmanship and the use of properly 

 adjusted instruments should be insisted on. All constructions should be 

 drawn in fine pencil lines. Inaccurate work, or work done with soft or 

 blunt pencils, should receive very little credit. 



Processes. — Test of a straight line ; intersection of two lines ; notion 

 (not definition) of a point ; measurement of a length ; estimation of the 

 second place of decimals of inches or centimetres ; use of set-squares for 

 drawing parallel lines ; construction and measurement of angles from 

 0° to 360° by the use of a protractor ; limits of error in setting off angles ; 

 test of a right angle ; test for accuracy of set-squares : their use in 

 drawing perpendiculars. 



The drawing of parallels and perpendiculars by the aid of compasses ; 

 the bisection of angles and straight lines ; construction of triangles from 

 given dimensions ; the fundauiental properties of triangles verified and 

 illustrated by drawing ; similar triangles ; the division of lines into equal 

 parts and into parts in given proportion ; test of equality of angles by 

 the superposition of the angles of similar (not equal) triangles by means 

 of tracing paper. 



The construction of rectangles, parallelograms, and quadrilaterals, 

 from adequate data ; notion of a tangent line ; construction of tangents 

 to circles, using drawing-office methods ; notion of a locus ; construction 

 of circles satisfying given conditions ; verification of the properties of 

 circles. 



Measurement of area ; use of squared paper ; area of an irregular 

 figure found by counting the number of squares. 



Illustrations of propositions relating to the areas of squares, rect- 

 angles, parallelograms, and triangles. Calculation of these areas from 

 given dimensions {e.g., base and altitude), and verification by squared 

 paper. 



The length of the circumference of a circle determined experimentally 

 {e.g., by rolling a coin with an ink mark on its rim down an inclined 

 sheet of paper, or by wrapping a strip of paper tightly round a cylinder, 

 pricking the paper where it overlaps, unwrapping and measuring the 

 distance between the two marks) ; the area of a circle determined by 

 squared paper. 



The area of a rectangular sheet of paper can be calculated from 

 measurements in inches and in centimetres, and hence the number of 



