essential requisite, that P=o when two groups are identical, is fulfilled; and that if two groups, 93 and 94, e.g., change places, the sign of P is simply reversed, its numerical value remaining the

same.

From this view the following novel and essential consequences result. If the groups are in the following order:

94 93 92 > 919

and the substance is, say, right-handed, then when 9, is replaced by smaller and smaller groups, we may expect:

1. Diminution of the right rotation for g,>93; 2. Inactivity when g1=93;

3. Left rotation, increasing to a maximum and then diminishing, when g>94>92 ;

4. Inactivity when 94-92;

=

5. Right rotation, increasing to a maximum, and then diminishing, when g1> 94>91 ;

2

6. Inactivity when g1=g;

7. Left rotation, increasing, when g1 91. Thus, when one of the groups gradually passes from the maximum to the minimum the sign of the rotation will change four times.

Let us consider first the derivatives of active amylalcohol, C2H,(=29) CH2.CH.CH2OH. The substances are arranged in the order of the magnitude of the radical replacing CH2OH, and it is seen that, in general, increase of the largest group leaves the sign of the rotation unaltered:

givceric, and valerianic acids as have been investigated yields the same result, namely, that the weight of the groups acts in the sense demanded by Guye's fundamental conception, but not strictly according to the formula chosen by him as a first approximation.3

In the glyceric acid derivatives, CH2OHCHOHCO,X, the rotation is seen to rise as the largest group, COX, becomes larger.

The case of tartaric acid is somewhat more complicated. In the first place there are two asymmetric carbon atoms, but these being perfectly identical we may confine ourselves to the consideration of one. But, further, in the derivatives there are always two groups which alter. If we set out the groups thus:

H=1<0H=17 <CO2H=45<CHOHCO2H=75, we see that, in the esters in which carboxyl hydro1 Frankland and MacGregor, Chem. Soc. J. Trans. 1893, 524. 2 Guye, Compt. Rend. 116, 1454. Is the decrease of rotation with the group-weight due to the increased formation of the racemoïd form on distillation, caused by the higher boiling-point?

In confirmation of this see Walden, Zeitschr. physik. Chem. 15, 638; I. Welt, Compt. Rend. 119, 885; Ann. Chim. Phys. [7], 6, 115 ; Ph. A. Guye and L. Chavanne, Compt. Rend. 119, 906; 120, 452. Compare J. W. Walker, J. Chem. Soc. 67, 914, and Purdie and Williamson, l.c. p. 957.

gen is replaced, the two largest groups increase, and therefore the rotation; in those in which hydroxyl hydrogen undergoes substitution, OH=17 increases, and also the largest group: a change of sign is therefore to be expected, and at increase in the numerical value.

the same time an Both occur; only

the change of sign does not exactly correspond with the equality of the group-weights.

Further, we must emphasise the fact that, in isomeric compounds, groups of equal weight do not correspond to equal rotations. Among glyceric esters, propyl- and iso-propyl, butyl- and iso-butyl have not the same action; with tartaric acid the case is the same, but not with valerianic acid. But whether in the first two cases the difference is as great as the figures indicate is uncertain, as it is doubtful how far they can be compared. Thus Freundler found that ethylic diacetyl tartrate rotates, in alcohol, +1.02 instead of +5.

Finally, it is a striking fact, in agreement with Guye's conception, that the very high rotations are observed among compounds of high molecular weight. One example of this is seen in methylic benzoyl tartrate, -88.8°. Then we have the small rotation of 2° for lactic acid, as compared with -21° for oxybutyric, and -11° for leucic acid, 71° for tropaic acid, -156° for mandelic acid, and 135° for isopropylphenylglycollic acid. Perhaps in the last the effect of ring formation is superadded. It is a fact that the highest known rotations are found among the alkaloids and santonine derivatives (over

300° for quinidine, 700° for santonine), where several rings and high molecular weight coexist. Of course, the converse of this rule does not hold. Even when the molecular weight is high, identity among the groups annihilates the rotation, and similarity among the groups perhaps reduces it to small proportions.

VI. MORE COMPLICATED CASES

Several asymmetric groups in one molecule.-So far we have dealt chiefly with the simplest cases, with a single asymmetric carbon atom. It remains to add a few words on more complicated compounds, which may throw some light on the subject. In the first place we may consider the idea expressed in my former pamphlet that when there are several asymmetric carbon atoms their action is to be added or subtracted. Thus for the four pentose types, COH(CHOH),CH,OH, we should have the following

and since the sum of No. 2, No. 3, and No. 4 is equal to ABC, the rotation of arabinose (probably the highest) should be equal to the rotations of xylose, ribose, and the expected fourth type 2 taken together.

For the asymmetric compounds of the saccharic acid group a similar conclusion may be drawn. The four active types would have the following rotations:

See Preface.

Discovered since, and called lyxose.