_Turn now to the case of finding the unknown means to a distinctly conceived end._ The end here stands in the place of _a_, _b_, _c_, in the diagram. It is the starting-point of the irradiations of suggestion; and here, as in that case, what the voluntary attention does is only to dismiss some of the suggestions as irrelevant, and hold fast to others which are felt to be more pertinent--let these be symbolized by _l_, _m_, _n_. These latter at last accumulate sufficiently to discharge all together into _Z_, the excitement of which process is, in the mental sphere, equivalent to the solution of our problem. The only difference between this and the previous case is that in this one there need be no original sub-excitement in _Z_, coöperating from the very first. In the solving of a problem, all that we are aware of in advance seems to be its _relations_. It must be a cause, or it must be an effect, or it must contain an attribute, or it must be a means, or what not. We know, in short, a lot _about_ it, whilst as yet we have no _acquaintance_ with it. Our perception that one of the objects which turn up is, at last, our _quæsitum_, is due to our recognition that its relations are identical with those we had in mind, and this may be a rather slow act of judgment. Every one knows that an object may be for some time present to his mind before its relations to other matters are perceived. Just so the relations may be there before the object is. From the guessing of newspaper enigmas to the plotting of the policy of an empire there is no other process than this. We must trust to the laws of cerebral nature to present us spontaneously with the appropriate idea, but we must know it for the right one when it comes.