Exposition and illustration in teaching . 374 EXPOSITION AND ILLUSTRATION IN TEACHING form of illustration is at present rather in favour. Acircle is taken to represent some total, and is dividedup into various sectors, each representing a specificpart of this total. But here, again, it is very difficult toestimate the areas of the sectors. The usual way is tomake an estimate of the relative areas of the varioussectors by comparing the parts of the circumference cutoff by the including radii. Considerable skill in estimat-ing angular measurement may be acquired by a studyof the face of the clo
Exposition and illustration in teaching . 374 EXPOSITION AND ILLUSTRATION IN TEACHING form of illustration is at present rather in favour. Acircle is taken to represent some total, and is dividedup into various sectors, each representing a specificpart of this total. But here, again, it is very difficult toestimate the areas of the sectors. The usual way is tomake an estimate of the relative areas of the varioussectors by comparing the parts of the circumference cutoff by the including radii. Considerable skill in estimat-ing angular measurement may be acquired by a studyof the face of the clock and the different positions ofthe hands. Limiting himself to the positions of thetwelve hours, the student assumes the unit of the houras equivalent to 30°, and by estimating the positionof the radii in relation to the fixed points of the hours,he can make a fair guess at the number of degreesincluded, and therefore of the proportion of the areaof the circle included in a given sector. The two following diagrams were published in an. official document to illustrate certain quantitativerelations. One would have thought that the percent- THE DIAGRAM 375 ages required no help, but somehow the drawings wereassumed to make the matter clearer, till one of the offi-cials, who had trained his eye on the clock-facestandard, chanced to see them, and declared after amoments inspection that both were incorrect (a) tothe extent of two-thirds of an hour { 10°) and (6)to the extent of one-third of an hour { 5°). Onmeasurement, the reader will find that the estimate isalmost exactly right, so skilful is it possible to becomeat estimating angular measurement by reference to afixed standard. It is true that this is not quite anestimate of areas, but rather of positions on a estimate of the included area is really an inferencefrom the angular measurement. This last fact hasprobably something to do with the popularity of thecircular form of quantitative illustration. Somet
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