PEOCEEDINGS OF SECTION G (l.). 637 



ment expressed in figures. The graphic method has, therefore, much 

 to recommend it. At the same time it must never be lost sight of 

 that absolute accuracy is only attained in figures — the primary and 

 most minute form of statistical expression. Nor should the object of 

 the graphic method be ever forgotten, viz., that of supplying the 

 imagination with an easier means of approximately gauging differences. 

 Any graphic method that does not achieve this object is useless. 



For graphic presentation there are three primary means available, 

 viz., linear, square, and cubic measure. Linear presentation is not 

 only the simplest, but, in view of the object just referred to, also the 

 most effective. There is no gauge which the eye, as well as the mind, 

 takes in and accurately appreciates more easily than length, so long as 

 it comes well under the direct survey of the eye. It requires very 

 little training to approximately realise at a glance that a line 4in. long 

 is double the length of one 2in. long ; yet if the former were to represent 

 £17,986,384 and the latter £8,993,192, only a person accustomed to 

 dealing with figures would easily draw a similar inference from these 

 arithmetical symbols. The method of graphic presentation by straight 

 linear measure is often abandoned for that of circular measure. I 

 doubt whether the natural aptitude of eye and mind can as readily 

 appreciate proportions when thus represented, and as a test submit a 

 very simple example for comparison. (See diagram No, 1.) Coming 

 to square measure, the task required of our perceptive sense becomes 

 at once far more complicated. It is true that if we wish to compare 

 two areas, one of 600,000 acres, the other of 300,000 acres, nature's 

 own method is to show us the difference in square measure ; and this 

 has led many writers to suppose that it is also the method that would 

 appeal most vividly to the imagination. Nothing is, however, less 

 true, for in reality the appeal is an extremely vague one. To put this 

 to the test, draw two separate squares — one on the base lin., the other 

 on the base -7 of an inch — and ask several untrained persons their 

 opinion as to the respective areas of the squares, without allowing 

 them to take measurements. Very few will conclude that the one is 

 as nearly as possible twice the size of the other. (See diagram No. 2.) 

 It becomes then apparent that the squares do not elucidate the pro- 

 portions they represent more clearly than do the figures. 



If this be the difficulty with the simplest form of square measure, 

 it stands to reason that cubic measure adds to it very considerably. 

 Of late years this form of graphic presentation appears to have become 

 very popular. Modern magazines and even statistical year books 

 teem with pictures of similar but unequal objects, purporting to con- 

 vey impressions of quantitative proportions. The untrained reader 

 simply sees, say, a gigantic soldier representing the Russian army 

 next to a pigmy as the symbol of that of Switzerland. More than this 

 he sees not, and cannot see. Leaving alone altogether the question 

 of relative military efficiency, even of the numerical proportions he 

 knows nothing more than that Russia must have several times more 

 soldiers than Switzerland. But the trained mathematician himself 

 is here in the dark, for first of all he does not as a rule know whether 



