[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 the terminal one forms the basis for the explanation of the existence of the so-called [alpha] and [beta] modification of _d_-glucose (see page 46). However, the ordinary aldehyde reactions of the sugars are more clearly indicated by the open-chain formula. Some investigators are inclined to be that sugars actually exist in the open-chain arrangement when in aqueous solution, and in the closed-ring arrangement when in alcoholic solution. The closed-ring formulas will be used in this text in the discussions of the birotation phenomena and of biochemical properties, but for the explanations of the stereo-isomeric forms and similar phenomena, the open-chain formulas are just as useful in conveying an idea of the possibilities of different space relationships, and are so much simpler in appearance and in mechanical preparation, that it seems desirable to use these rather than the more accurate closed-ring formulas. CHEMICAL CONSTITUTION OF MONOSACCHARIDES