Of the fourth dimension we can discover some facts by analogy. We can count the edges of its typical figure, and apply thought to determining some of its conditions. But a more interesting subject of research is the inquiry into the light thrown by the theory of four dimensions on the determination of certain atoms in chemistry, that are known to be distinct elements, but could only be determined actually in another dimension.[31] “In chemistry, the molecules of a compound body are said to consist of the atoms of the elements which are contained in the body, and these are supposed to be situated at certain distances from one another and to be held in their relative positions by certain forces. At first the centres of the atoms were conceived to lie in one and the same plane. But Wislicenus was led by researches in paralactic acid to explain the differences of isomeric molecules of the same structural formulæ by the different positions of the atoms in _space_. In fact, four points can always be so arranged in space that every two of them may have any distance from each other; and the change of one of the six distances does not necessarily involve the alteration of any other. “But suppose our molecule consists of five atoms? Four of these may be so placed that the distance between any two of them can be made what we please. But it is no longer possible to give the fifth atom a position such that each of the four distances by which it is separated from the other atoms may be what we please. On the contrary, the fourth distance is dependent on the three remaining distances, for the space of experience has only three dimensions. If, therefore, I have a molecule which consists of five atoms, I cannot alter the distance between two of them without at least altering some second distance. But if we imagine the centres of the atoms placed in a four-dimensioned space, this can be done; all the ten distances which may be conceived to exist between the five points will then be independent of one another. To reach the same result in the case of six atoms we must assume a five-dimensional space, and so on.”[32] Here we see that if chemistry as a science is bound to take account of all its facts, the scientist is confronted with a problem of dimensions that is really a problem of Infinity applied not, as in the other cases quoted, to number, but to space.