We see here the vision of the intellect prolonged beyond the boundaries of sense into the region of what might be considered mere imagination. But, unlike other imaginations, we can bring ours to the test of experiment; indeed, so great a mastery have we obtained over these waves, which eye has not seen, nor ear heard, that we can with mathematical certainty cause them to coincide or to interfere, to help each other or to destroy each other, at pleasure. It is perhaps possible to be a little more precise here. Let two stones--with a small distance between them--be dropped into water at the same moment; a system of circular waves will be formed round each stone. Let the distance from one little crest to the next following one be called _the length of the wave_, and now let us inquire what will take place at a point equally distant from the places where the two stones were dropped in. Fixing our attention upon the ridge of the first wave in each case, it is manifest that, as the water propagates both systems with the same velocity, the two foremost ridges will reach the point in question at the same moment; the ridge of one would therefore coincide with the ridge of the other, and the water at this point would be lifted to a height greater than that of either of the previous ridges. [Sidenote: COINCIDENCE AND INTERFERENCE.] Again, supposing that by any means we had it in our power to retard one system of waves so as to cause the first ridge of the one to be exactly one wave length behind the first ridge of the other, when they arrive at the point referred to. It is plain that the first ridge of the retarded system now falls in with the second ridge of the unretarded system, and we have another case of coincidence. A little reflection will show the same to be true when one system is retarded any number of _whole wave-lengths_; the first ridge of the retarded system will always, at the point referred to, coincide with a _ridge_ of the unretarded system.