By this the difficult concept of continuity is evoked in our experience. The transition from the light of day to the darkness of evening proceeds _continuously_, that is, at no point of the whole transition do we notice that the state just passed is different from the present one, while the difference over a wider extent of the experience is unmistakable. If we wish to bring vividly to our minds the contradiction to other habits of thought which this involves, we need only to represent to ourselves the following instance. I will compare the thing A at a certain time with the thing B, which is so constructed that though objectively different from A, the difference has not yet reached the threshold. From experience, therefore, I must take A to be equal to B. Then I compare B with a thing C, which is objectively different from B in the same way as A is from B, though here, too, the difference is still within the threshold, though very near it. I shall also have to take B as equal to C. But now if I compare A directly with C, the sum of the two differences oversteps the threshold value, and I find that A is different from C. This, then, is a contradiction of the fundamental principle that if A = B and B = C, A = C. This principle is valid for _counted_ things, which, in consequence, are discontinuous, but not for continuous things susceptible by our senses. If in spite of this it is applied to continuous things or _magnitudes_ in the narrower sense, we must bear in mind that it is just as much a case of an _extrapolation to the non-existing ideal instance_ (p. 46) as in the case of the other general principles, which, though they are derived from experience, nevertheless, for practical purposes, transcend experience in their use. The examples cited above prove also that these relations are by no means confined to the judgments we derive on the basis of immediate sensations. When by means of the scale we compare three weights, the differences of which lie within the limit of its sensitiveness but approach closely to it, we can arrive in a purely empirical and objective way also at the contradiction A = B, B = C, but A [Not=] C. In weight and measurement, therefore, we hold fast to the principle that the relations cited have no claim to validity outside the limit of their possible errors. Accordingly, though the non-equation of A [Not=] C can be observed, the difference of both values cannot be greater than at utmost the sum of the two threshold values.