The grocer needs to be assured of the accuracy of his scales, and the chemist of the high accuracy of his chemical balance; the surveyor needs to know about the errors that may creep into the process of measuring the length of a line or angle. All of them, using instruments to assist in accurate perception of facts, are concerned about the accuracy of their instruments. Now, we all use the senses in perceiving facts, and "errors of sense" therefore concern us {447} all. Some of the errors committed in sense perception can be laid at the door of the senses, and some rather belong in the sphere of perception proper.

If you come out of a cold room into a warm room, the latter seems warmer than it is; and if you come out of a dark room into a light room, the latter seems brighter than it is. These errors, due to adaptation of the temperature sense and of the retina, are properly classed as errors of sense.

If you are taking a child's temperature with a "minute thermometer", it is best to use your watch to tell you when the minute is up, for the minute, when you are simply waiting for it to pass, seems very long. But if you are "working against time", a minute seems short. The professor is shocked when the closing bell rings, and thinks that certainly the hour cannot be up; but some of the students have been consulting their watches for quite a long while, being sure the hour must be nearly over. These are scarcely errors of sense, but they are errors of perception.

Where we tend to err in one certain direction from the truth, as in the examples just cited, psychology speaks of a "constant error", and evidently the knowledge of such constant errors is of importance wherever the facts are of importance. In a court of law, a witness often has to testify regarding the length of time occupied by some event, and a knowledge of the constant errors in time perception would therefore be of considerable legal importance. They would need to be worked out in considerable detail, since they differ according to the desires and attitude of the witness at the time of the event.

Besides constant errors, there are accidental or variable errors, due to slight momentary causes. Both constant and variable errors can be illustrated by a series of shots at a target. The variable error is illustrated by the scatter of {448} the hits, and the constant error by the excess of hits above the bull's-eye, or below, or to the right or left. The constant error can be corrected, once you know what it is; if results show that you tend to shoot too high, you can deliberately aim lower. But the variability of any performance cannot be eliminated except by long practice, and not altogether even then.

Fig. 66.--Constant error and scatter in hitting at a target. The little circle was the target, but the center of the actual distribution of the attempts lies at the cross, which was drawn in afterwards. The constant error could be stated by saying that the center of distribution was so far from the target, and in such and such a direction. The scattering of the attempts can be measured also.

Experimental psychology has taken great pains in measuring the accuracy of different sorts of perception. How small a difference in length can be perceived by the eye, how small a difference of weight by the hand--these are sample problems in this line.

For example, to measure the fineness with which weights can be perceived when "hefted" in the hand, you take two objects that are alike in size and appearance but differing slightly in weight, and endeavor to decide which is the heavier just by lifting them. You try repeatedly and keep track of the number of errors, using this number as a measure of the accuracy of perception. Now, if one weight were twice as heavy as the other (one, for example, weighing 100 grams {449} and the other 200), you would never make an error except through carelessness; but if one were 100 and the other 120 grams, you would make an occasional error, and the number of errors would increase as the difference was decreased; finally, comparing 100 and 101 grams, you would get almost as many wrong as right, so that your perception of that small difference would be extremely unreliable.

The smaller the difference between two stimuli, the more numerous the errors in perceiving it, or, the less perceptible it is, and there is no sharp line between a difference that can be perceived and one that is too small to be perceived. That is the first great result from the study of the perception of small differences.

The second great result is called Weber's law, which can be stated as follows: In the same sort of perception, equal relative (not absolute) differences are equally perceptible. For example, from the preceding table we see that 28 per cent. of errors are made in comparing weights of 100 and 104 grams; then, according to Weber's law, 28 per cent, of errors would also be made in comparing 200 grams with 208, or 500 with 520, or 1000 with 1040 grams, or any pair of weights that stood to each other in the ratio of 100 to 104. Weber's law is only approximately true for the perception of weights, since actually fewer errors are committed in comparing 500 and 520 than in comparing 100 and 104 grams; but the discrepancy is not extremely great here, and in {450} some other kinds of perception, as especially in comparing the brightness of lights or the length of seen lines, the law holds good over a wide range of stimuli and only breaks down near the upper and lower extremes. We are familiar, in ordinary life, with the general truth of Weber's law, since we know that an inch would make a much more perceptible addition to the length of a man's nose than to his height, and we know that turning on a second light when only one is already lit gives a much more noticeable increase in the light than if we add one more light when twenty are already burning.

A third great result of this line of study is that different sorts of perception are very unequal in their fineness and reliability. Perception of brightness is about the keenest, as under favorable conditions a difference of one part in one hundred can here be perceived with very few errors. Visual perception of length of line is good for about one part in fifty, perception of lifted weight for about one part in ten, perception of loudness of sound for about one part in three. But the perception of small differences in the pitch of musical tones is keener still, only that, not following Weber's law in the least, it cannot be expressed in the same way. A person with a good ear for pitch can distinguish with very few errors between two tones that differ by only one vibration per second, and can perceive this same absolute difference equally well, whether the total vibration rate is 200, 400, or 800 vibrations per second.