Weber's Law (according to Oxford's Dictionary of Psychology)

by Corry Shores
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[The following is summary; my commentary is in brackets.]

Bergson refers to Weber's Law in Time and Free Will

(Essai sur les données immédiates de la conscience).

We begin by holding a kilogram of weight. We slowly add very small increments of weight until we first feel a difference. We find that when we start with 1 kg, we first feel a difference as soon as 0.02 kg is added.

Then, we begin with 10 kg. After a gradual increase, we first notice a difference of weight when 0.2 kg is added.

We begin with 100 kg. We feel the first difference when 2 kg is added.

1 : 0.02

10 : 0.2

100 : 2

We notice that in each case, the ratio of the smallest sensible difference to the original weight is 1/50. More precisely, when Weber conducted this experiment, he found it to be 1/51. So no matter the starting weight, the constant ratio of the smallest-perceptible-difference to beginning weight is nearly always 1/51 for everybody.

Weber found the ratios to be consistent also for the other senses, although each sense has its own unique ratio. For discriminating changes of brightness: 1/62. Changes of pitch: 1/333. Sound-volume changes: 1/11.

We will designate E to stand for the quantity of stimulus that we begin sensing. We will gradually increase or decrease the original stimulus amount. ΔE will stand for the smallest amount of alteration needed for us to first feel a difference. We found that for each type of sensation, there was a constant ratio of smallest-detected-change to original-stimulus-quantity. So we will abbreviate "constant" with "const." Now, we can formulate the ratio:

Image From:

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:

http://www.archive.org/details/timeandfreewill00pogsgoog

Material from:

Colman, Andrew. "Weber's Law." A Dictionary of Psychology. Oxford: Oxford University Press, 2001.

Article available online at:

http://www.encyclopedia.com/doc/1O87-Weberslaw.html

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