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 sufficiently 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 holding 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 comparison. For mere length we lay the two things alongside; so for an angle. For number, 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 compared 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 juxtaposition of angles. A circle and an oval are represented by the alternatives of curvature and diameters: in the one, the curvature uniform 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 conceptions are still the same—lineal size, number, angular size, curvature—but the mode of guiding the attention may be various. Sometimes there is a strong and overpowering similarity, with a small and unconspicuous difference; as in our ciphers (compare 3 and 5), and in the letters of our alphabet (C, G), and still more in the Hebrew alphabet. 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-
