milarly, for a ketohexose, which contains three asymmetric carbon atoms,
there are eight possible arrangements. Three sugars of this type are known,
only one (fructose) being common in plants; the others are of only
theoretical interest.

FOOTNOTES:

[1] It is assumed that the reader, or student, is familiar with the
theoretical and experimental evidence in support of the existence of the
so-called "asymmetric" carbon atom and its relation to the effect of the
compound which contains it, when in solution, in rotating the plane of
polarized light. For purposes of review, or of study of this most
interesting and important phenomenon, the reader is referred to any
standard text-book on Organic Chemistry.

[2] Attention should be called, at this point, to the fact that such
formulas as these cannot possibly accurately represent the actual
arrangement of the constituent groups of a carbohydrate molecule around an
asymmetric carbon atom. The limitations of a plane-surface formula prevent
any illustration of the three-dimension relationships in space.
Furthermore, there are certain facts in connection with the birotation
phenomenon and the relation of the molecular configuration to biochemical
properties (which see) that cannot be explained on the basis of the
open-chain arrangement represented by the Fischer formulas used here. A
closed-ring arrangement, showing the aldehyde oxygen as linked by its two
bonds to the first and the fourth carbon atoms of the chain, thus forming a
closed-ring of four carbon and one oxygen atoms, instead of being attached
by both bonds to a single carbon atom, as in the above formulas, is
undoubtedly a more nearly accurate representation of the actual linkage in
the molecule than are the open-chain formulas used above.

The differences in conception embodied by these two types of formulas may
be shown by the following formulas for glucose:

CH_{2}OH CH_{2}OH
| |
CHOH CHOH
| |
CHOH CH-CHOH ------O-------
| | | | |
CHOH O | or CH_{2}OH.CHOH.CH.CHOH.CHOH.CHOH
| | |
CHOH CH-CHOH
| |
CHO OH

Fischer's Closed-ring formulas
formula

It will be observed that in the closed-ring formula there are five
asymmetric carbon atoms, and the asymmetry of