The study of this attribute of sensations has led to _the discovery of a psychological law_, which has much practical importance. Suppose that we are working with intensities of noise, the noise made by the drop of an ivory ball upon an ebony block. Suppose that, by varying the height from which the ball falls, we have found a series of intensities of sensation _a_, _b_, _c_, _d_, _e_, which may be represented by the numbers 1, 2, 3, 4, 5; a series, that is, in which the difference between the two noises _a_ and _b_ is equal in sensation to the difference between _b_ and _c_, or between _c_ and _d_, or between _d_ and _e_. That sounds a little difficult; but the series may really be established without much trouble. Now, what about the stimuli, the heights of fall? Must the ball drop twice as far for _b_ as for _a_, three times as far for _c_ as for _a_, and so on? No: _equal differences in intensity of sensation do not correspond with equal differences in intensity of stimulus. Equal differences in intensity of sensation correspond rather with_ =relatively= _equal difference in the intensity of stimulus_. In other words, the sensation-series 1 2 3 4 5 corresponds with a stimulus-series of the type 1 2 4 8 16; or, mathematically expressed, _an arithmetical series of intensities of sensation is correlated with a geometrical series of intensities of stimulus_. In the instance given, the exponent of the geometrical series is 2; but that is only an imaginary instance; in the case of =noise= the actual exponent is 4/3, so that the sensation-series 1 2 3 4 5 corresponds with the stimulus series 1 4/3 16/9 64/27 256/81; or, if we take units of some sort, such as millimetres of height of fall, the sensation-series 1 2 3 4 5 corresponds with the stimulus-series 81 108 144 192 256. This law of correlation was first formulated by the German physiologist E. H. Weber in 1834 as follows: “in comparing objects and observing the distinction between them, we perceive, not the difference between the objects, but the ratio of this difference to the magnitude of the objects compared.” Weber speaks of objects, because he was thinking of experiments that he had made with weights; he should have said sensations. His law holds, over a middle range of intensities of sensation, for =lights=, =sounds=, =pressures=, =various kinæsthetic complexes=, and =odours=. Its validity in the fields of taste and temperature is doubtful.