=Weber's Law.=--I said that the intensity of the sensation increases by slower steps than those by which its exciting cause increases. If there were no threshold, and if every equal increment in the outer stimulus produced an equal increment in the sensation's intensity, a simple straight line would represent graphically the 'curve' of the relation between the two things. Let the horizontal line stand for the scale of intensities of the objective stimulus, so that at 0 it has no intensity, at 1 intensity 1, and so forth. Let the verticals dropped from the slanting line stand for the sensations aroused. At 0 there will be no sensation; at 1 there will be a sensation represented by the length of the vertical _S_¹--1, at 2 the sensation will be represented by _S_²--2, and so on. The line of _S_'s will rise evenly because by the hypothesis the verticals (or sensations) increase at the same rate as the horizontals (or stimuli) to which they severally correspond. But in Nature, as aforesaid, they increase at a slower rate. If each step forward in the horizontal direction be equal to the last, then each step upward in the vertical direction will have to be somewhat shorter than the last; the line of sensations will be convex on top instead of straight. [Illustration: FIG. 2.] Fig. 2 represents this actual state of things, 0 being the zero-point of the stimulus, and conscious sensation, represented by the curved line, not beginning until the 'threshold' is reached, at which the stimulus has the value 3. From here onwards the sensation increases, but it increases less at each step, until at last, the 'acme' being reached, the sensation-line grows flat. The exact law of retardation is called _Weber's law_, from the fact that he first observed it in the case of weights. I will quote Wundt's account of the law and of the facts on which it is based. "Every one knows that in the stilly night we hear things unnoticed in the noise of day. The gentle ticking of the clock, the air circulating through the chimney, the cracking of the chairs in the room, and a thousand other slight noises, impress themselves upon our ear. It is equally well known that in the confused hubbub of the streets, or the clamor of a railway, we may lose not only what our neighbor says to us, but even not hear the sound of our own voice. The stars which are brightest at night are invisible by day; and although we see the moon then, she is far paler than at night. Every one who has had to deal with weights knows that if to a pound in the hand a second pound be added, the difference is immediately felt; whilst if it be added to a hundredweight, we are not aware of the difference at all....