480 REPORT — 1902. 



work : he will preserve a proper balance between experimental work, 

 didactic teaching, and numerical exercise work. 



Use of squared paper . — The use of squared paper by merchants and 

 others to show at a glance the rise and fall of prices, of temperature, of 

 the tide, etc. The use of squared paper should be illustrated by the 

 working of many kinds of exercises, but it should be pointed out that 

 there is a general idea underlying them all. The following may be men- 

 tioned : — 



Plotting of statistics of any kind whatsoever of general or special 

 interest ; what such curves teach ; rates of increase. 



Interpolation, or the finding of probable intermediate values ; probable 

 errors of observation ; forming complete price-lists by manufacturers j 

 finding an average value ; areas and volumes as explained above. 



The plotting of simple graphs ; determination of maximum and 

 minimum values ; the solution of equations. Very clear notions of what 

 we mean by the roots of equations may be obtained by the use of squared 

 paper. 



Determination of laws which exist between obsei'ved quantities, 

 especially of linear laws. 



Corrections for errors of observation when the plotted quantities are 

 the results of experiment. 



Geometry. — A knowledge of the properties of straight lines, parallel 

 lines, right angles, and angles of 30°, 45°, and 60°, obtained by using and 

 testing straight-edges and squares ; dividing lines into parts in given pro- 

 portions, and other experimental illustrations of the Sixth Book of Euclid ; 

 the definitions of the sine, cosine, and tangent of an angle, and the deter- 

 mination of their values by graphical methods ; setting out of angles by 

 means of a protractor, when they are given in degrees or radians, also (for 

 acute angles) by construction when the value of the sine, cosine, or tangent 

 is given ; use of tables of sines, cosines, and tangents ; the solution of a 

 I'ight-angled triangle by calculation and by drawing to scale ; the con- 

 struction of any triangle from given data ; determination of the area of 

 a triangle. The more important propositions of Euclid may be illustrated! 

 by actual drawing. If the proposition is about angles, these may be 

 measured in degrees by means of a protractor, or by the use of a table of 

 chords ; if it refers to the equality of lines, areas, or ratios, lengths may 

 be measured by a decimal scale, and the necessary calculations made 

 arithmetically. This combination of drawing and arithmetical calcula- 

 tion may be freely used to illustrate the truth of a pi'oposition. A good 

 teacher will occasionally introduce demonstrative proof as well as mere 

 measurement. 



Defining the position of a point in space by its distances from three 

 co-ordinate planes. What is meant by the projection of a point, line, oi* 

 a plane figure, on a plane % Simple models may be constructed by the 

 student to illustrate the projections of points, lines, and planes. 



The distinction between a scalar quantity and a vector quantity ; 

 addition and subtraction of vectors ; experimental illustrations, such as 

 the verification by the student himself of the triangle and polygon of 

 forces, using strings, pulleys, and weights. 



