Instead of placing the plates so that their nodal lines coincide, set these lines at right angles to each other. That is to say, push A over A′, Fig. 70. In these figures the letter P means positive, indicating, in the section where it occurs, a motion of the plate upward; while N means negative, indicating, where it occurs, a motion downward. You have now before you a kind of check pattern, as shown in the third square, consisting of a square _s_ in the middle, a smaller square _b_ at each corner, and four rectangles at the middle portions of the four sides. Let the plates vibrate, and let the vibrations of their corresponding sections be concurrent, as indicated by the letters P and N; and then suppose the vibrations of one of them transferred to the other. What must result? A moment’s reflection will show you that the big middle square _s_ will vibrate with augmented energy; the same is true of the four smaller squares _b_, _b_, _b_, _b_, at the four corners; but you will at once convince yourselves that the vibrations in the four rectangles are in opposition, and that where their amplitudes are equal they will destroy each other. The middle point of each side of the plate of glass would therefore be a point of rest; the points where the nodal lines of the two plates cross each other would also be points of rest. Draw a line through every three of these points and you will obtain a second square inscribed in the first. The sides of this square are lines of no motion. [Illustration: FIG. 70.] We have thus far been theorizing. Let us now clip a square plate of glass at a point near the centre of one of its edges, and draw the bow across the adjacent corner of the plate. When the glass is homogeneous, a close approximation to this inscribed square is obtained. The reason is that when the plate is agitated in this manner the two sets of vibrations which we have been considering actually coexist in the plate, and produce the figure due to their combination. Again, place the squares of glass one upon the other exactly as in the last case; but now, instead of supposing them to concur in their vibrations, let their corresponding sections oppose each other: that is, let A cover A′, Fig. 71. Then it is manifest that on superposing the vibrations the middle point of our middle square must be a point of rest; for here the vibrations are equal and opposite. The intersections of the nodal lines are also points of rest, and so also is every corner of the plate itself, for here the added vibrations are also equal and opposite. We have thus fixed four points of rest on each diagonal of the square. Draw the diagonals, and they will represent the nodal lines consequent on the superposition of the two vibrations. [Illustration: FIG. 71.]