EDUCATION AS A SCIENCE. 427 



demonstration will certainly compel attention and end in the feeling 

 of difference, but the cost is too great to be often repeated. 



4. The great practical aid to the discovery and the retention of 

 difference is immediate succession or, what comes to the same thing, 

 close juxtaposition. A rapid transition makes evident a difference 

 that would not be felt after an interval, still less if anything else 

 were allowed to occupy the mind in the mean time. This fact is suffi- 

 ciently obvious, and is turned to account in easy cases, but is far 

 from thoroughly worked out by the teacher and the expositor. Any 

 trifling diversion will suffice to blind us to its importance. 



We compare two notes by sounding them in close succession ; two 

 shades of color by placing them side by side ; two weights by hold- 

 ing them in the two hands, and attending to the two feelings by 

 turns. These are the plain instances. The comparison of forms leads 

 to complications, and we cease to attempt the same kind of compari- 

 son. For mere length we lay the two things alongside ; so for an 

 angle. For nuitibei*, we can place two groups in contiguous rows 

 three by the side of four or five and observe the surplus. 



Mere size is an affair of simple juxtaposition. Form, irrespective 

 of size, is less approachable. A triangle and a quadrangle are com- 

 pared by counting the sides, and resolving the difference of form 

 into the simpler element of difference of number. A right-angled, 

 an acute-angled, an isosceles triangle, must be compared by the juxta 

 position of angles. A circle and an oval are represented by the alter- 

 natives of curvature and diameters : in the one, the curvature uni- 

 form and the diameters equal ; in the other, the curvature varying 

 and the diameters unequal. The difference between a close and an 

 open curve is palpable enough. 



The geometrical forms are thus resolvable into very simple bases 

 of comparison ; and the teacher must analyze them in the manner now 

 stated. For the irregular and capricious forms, the elementary con- 

 ceptions are still the same lineal size, number, angular size, curva- 

 ture but the mode of guiding the attention may be various. Some- 

 times there is a strong and overpowering similarity, with a small and 

 unconspicuous diflerence; as in our ciphers (compare 3 and 5), and in 

 the letters of our alphabet (C, G), and still more in the Hebrew alpha- 

 bet. For such comparisons, the difference, such as it is, needs to be 

 very clearly drawn or even exaggerated. Another method is to have 

 models of the same size to lay over one another, so as to bring out 

 the difference through the juxtaposition. By an express effort, the 

 teacher calls on the learner to view, with single-minded attention, the 

 differing circumstance, and afterward to reproduce it by his own 

 hand. An express lesson consists in asking the pupil what are the 

 ciphers, or the letters, that are nearly alike, and what are the points 

 of difference. 



The higher arts of comparison to impress difference are best illus- 



