And now we can represent the third variable in a precisely similar way. We can take the conclusion as the third variable, going through its four phases from the ground plane upwards. Each of the small cubes at the base of the whole cube has this true about it, whatever else may be the case, that the conclusion is, in it, in the mood A. Thus, to recapitulate, the first wall of sixteen small cubes, the first of the four walls which, proceeding from left to right, build up the whole cube, is characterised in each part of it by this, that the major premiss is in the mood A. The next wall denotes that the major premiss is in the mood E, and so on. Proceeding from the front to the back the first wall presents a region in every part of which the minor premiss is in the mood A. The second wall is a region throughout which the minor premiss is in the mood E, and so on. In the layers, from the bottom upwards, the conclusion goes through its various moods beginning with A in the lowest, E in the second, I in the third, O in the fourth. In the general case, in which the variables represented in the poiograph pass through a wide range of values, the planes from which we measure their degrees of variation in our representation are taken to be indefinitely extended. In this case, however, all we are concerned with is the finite region. We have now to represent, by some limitation of the complex we have obtained, the fact that not every combination of premisses justifies any kind of conclusion. This can be simply effected by marking the regions in which the premisses, being such as are defined by the positions, a conclusion which is valid is found. Taking the conjunction of the major premiss, all M is P, and the minor, all S is M, we conclude that all S is P. Hence, that region must be marked in which we have the conjunction of major premiss in mood A; minor premiss, mood A; conclusion, mood A. This is the cube occupying the lowest left-hand corner of the large cube. [Illustration: Fig. 53.] Proceeding in this way, we find that the regions which must be marked are those shown in fig. 53. To discuss the case shown in the marked cube which appears at the top of fig. 53. Here the major premiss is in the second wall to the right—it is in the mood E and is of the type no M is P. The minor premiss is in the mood characterised by the third wall from the front. It is of the type some S is M. From these premisses we draw the conclusion that some S is not P, a conclusion in the mood O. Now the mood O of the conclusion is represented in the top layer. Hence we see that the marking is correct in this respect. [Illustration: Fig. 54.]