The analogy, however, has in some way to be brought in, and to this the rest of the proof is devoted. In order to consider how this is done, we must first consider the nature of the analogy itself. Kant speaks of 'a conception-of-the-understanding of the reciprocal sequence of the determinations of things which coexist externally to one another'; and he says that 'that relation of substances in which the one contains determinations, the ground of which is contained in the other substance, is the relation of influence'. His meaning can be illustrated thus. Suppose two bodies, A, a lump of ice, and B, a fire, close together, yet at such a distance that they can be observed in succession. Suppose that A passes through changes of temperature a_{ 1} a_{ 2} a_{ 3} ... in certain times, the changes ending in states [alpha]_{ 1} [alpha]_{ 2} [alpha]_{ 3} ..., and that B passes through changes of temperature b_{ 1} b_{ 2} b_{ 3} ... in the same times, the changes ending in states [beta]_{ 1} [beta]_{ 2} [beta]_{ 3}. Suppose also, as we must, that A and B interact, i. e. that A in passing through its changes conditions the changes through which B passes, and therefore also the states in which B ends, and vice versa, so that a_{ 2} and [alpha]_{ 2} will be the outcome not of a_{ 1} and [alpha]_{ 1} alone, but of a_{ 1} and [alpha]_{ 1}, and b_{ 1} and [beta]_{ 1} jointly. Then we can say (1) that A and B are in the relation of influence, and also of interaction or reciprocal influence, in the sense that they _mutually_ (not alternately) determine one another's states. Again, if we first perceive A in the state [alpha]_1 by a perception A_{ 1}, then B in the state [beta]_{ 2} by a perception B_{ 2}, then A in the state [alpha]_{ 3} by a perception A_{ 3} and so on, we can speak (2) of a reciprocal sequence of perceptions, in the sense of a sequence of perceptions in which alternately a perception of B follows a perception of A and a perception of A follows a perception of B; for first a perception of B, viz. B_{ 2}, follows a perception of A, viz. A_{ 1}, and then a perception of A, viz. A_{ 3}, follows a perception of B, viz. B_{ 2}. We can also speak (3) of a reciprocal sequence of the determinations of two things in the sense of a necessary succession of states which _alternately_ are states of A and of B; for [alpha]_{ 1}, which is perceived first, can be said to contribute to determine [beta]_{ 2}, which is perceived next, and [beta]_{ 2} can be said to contribute to determine [alpha]_{ 3}, which is perceived next, and so on; and this reciprocal sequence can be said to be involved in the very nature of interaction. Further, it can be said (4) that if we perceive A and B alternately, and so only in the states [alpha]_{ 1} [alpha]_{ 3} ... [beta]_{ 2} [beta]_{ 4} ... respectively, we can only fill in the blanks, i. e. discover the states [alpha]_{ 2} [alpha]_{ 4} ... [beta]_{ 1} [beta]_{ 3} ... _coexistent_ with [beta]_{ 2} [beta]_{ 4} ... and [alpha]_{ 1} [alpha]_{ 3} ... respectively, if we presuppose the thought of interaction. For it is only possible to use the observed states as a clue to the unobserved states, if we presuppose that the observed states are members of a necessary succession of which the unobserved states are also members and therefore have partially determined and been determined by the observed states. Hence it may be said that the determination of the unobserved states coexistent with the observed states presupposes the thought of interaction.