The faculty of re-solution is possibly much invigorated by mathematical study, and especially by that highest branch of it which, unjustly, and merely on account of its retrograde operations, has been called, as if _par excellence_, analysis. Yet to calculate is not in itself to analyze. A chess-player, for example, does the one, without effort at the other. It follows that the game of chess, in its effects upon mental character, is greatly misunderstood. I am not now writing a treatise, but simply prefacing a somewhat peculiar narrative by observations very much at random; I will, therefore, take occasion to assert that the higher powers of the reflective intellect are more decidedly and more usefully tasked by the unostentatious game of draughts than by all the elaborate frivolity of chess. In this latter, where the pieces have different and _bizarre_ motions, with various and variable values, what is only complex is mistaken (a not unusual error) for what is profound. The _attention_ is here called powerfully into play. If it flag for an instant, an oversight is committed, resulting in injury or defeat. The possible moves being not only manifold, but involute, the chances of such oversights are multiplied; and in nine cases out of ten, it is the more concentrative rather than the more acute player who conquers. In draughts, on the contrary, where the moves are _unique_ and have but little variation, the probabilities of inadvertence are diminished, and the mere attention being left comparatively unemployed, what advantages are obtained by either party are obtained by superior _acumen_. To be less abstract: Let us suppose a game of draughts where the pieces are reduced to four kings, and where, of course, no oversight is to be expected. It is obvious that here the victory can be decided (the players being at all equal) only by some _recherché_ movement, the result of some strong exertion of the intellect. Deprived of ordinary resources, the analyst throws himself into the spirit of his opponent, identifies himself therewith, and not unfrequently sees thus, at a glance, the sole methods (sometimes indeed absurdly simple ones) by which he may seduce into error or hurry into miscalculation.