There are two forms of sugar found in honey, dextrose and levulose.  They are similar in chemical constitution, but the one is the reverse of the other when examined by polarized light—­that is, they rotate the plane of polarization of a ray of light in opposite ways.  If their atoms are conceived to have the power of motion in the fourth dimension, it would be easy to understand why they differ.  Certain snails present the same characteristics as these two forms of sugar.  Some are coiled to the right and others to the left; and it is remarkable that, like dextrose and levulose, their juices are optically the reverse of each other when studied by polarized light.

Revolution in the fourth dimension would also explain the change in a body from producing a right-handed, to producing a left-handed, polarization of light.

ISOMERISM

In chemistry the molecules of a compound are assumed to consist of the atoms of the elements contained in the compound.  These atoms are supposed to be at certain distances from one another.  It sometimes happens that two compound substances differ in their chemical or physical properties, or both, even though they have like chemical elements in the same proportion.  This phenomenon is called isomerism, and the generally accepted explanation is that the atoms in isomeric molecules are differently arranged, or grouped, in space.  It is difficult to imagine how atoms, alike in number, nature, and relative proportion, can be so grouped as somehow to produce compounds with different properties, particularly as in three-dimensional space four is the greatest number of points whose mutual distances, six in number, are all independent of each other.  In four-dimensional space, however, the ten equal distances between any two of five points are geometrically independent, thus greatly augmenting the number and variety of possible arrangements of atoms.

This just escapes being the kind of proof demanded by science.  If the independence of all the possible distances between the atoms of a molecule is absolutely required by theoretical chemical research, then science is really compelled, in dealing with molecules of more than four atoms, to make use of the idea of a space of more than three dimensions.

THE ORBITAL MOTION OF SPHERES:  CELL SUB-DIVISION

There is in nature another representation of hyper-dimensionality which, though difficult to demonstrate, is too interesting and significant to be omitted here.