148 
remaining three at the corners of a lower triangle alter- 
nate with the first. These positions are here assumed 
only for the sake of the symmetry that then appears with 
reference to the position 1. A very small change of 
positions will suffice to make the same symmetrical ar- 
‘rangement with reference to any of the 
other positions 2, 3, 4, 5, 6, 7; and itis 
assumed that so much motion may take 
place that only one form of the mole- 
cule MAB, is possible. Under such 
conditions the prediction of isomeric 
forms is largely guess work; but the 
following, which include most of the 
forms actually found, seem probable: 
iybsen i) Ay 13). Mvii BA, 
(2) ABA. (3) i BA. 3), 
3 (ABA, 
5. Oktavalent atoms,—Cube. 
az ar 
Mv (A,B, 
(3) 4 AB.AB 
(ABs 
7 
vill ( OBE f AB; C. 
MM RTS IAN ABC, BC, 
(3) / ABLABAB. syst) PoC IC. 
ae 4 ABC,BC 
(7) ABC_B 
INC, 18. C. 
ACB, 
(A.B, AB, C, 
| A BAB, IB CBC. 
Msi | ABA B AB, C, BC 
‘ A NIB, NIB, A AB, C, BC 
(| AS AA AB, CB 
| A,B,A INKOL IB, Ce 
[ABs west LUSCS IICIIC 
he ABC BAC 
(C3) | wea 
AC, BL CB 
wen ( ABC, NC, 18, C8 
: AC,BC, AC, BCBCB 
(3) ABB. AC OE, 
No BNC LAMB IC: 
AN, WORO, iN, B, CBC, 
MBC IBC: MBC BR, 
A WC, IC NCIC, 18, 
| A, BC.B AN, 18, ©, 18C 
A. CB, EG ASG By XC 
A CHOC. A, BCBCBC 
CS BEI A, CRE, C 
A, CB, AS BC, By C 
ABC, ABC, A, CB, CBC 
AC, ABCBB AB, AC, 
Mei 4 AC, ACB, Mii ACB, ACBC 
(22) NIB, (CNC. (24 ACB, ABC, 
INC ARN ABCBACBC 
AC, BAC, B ABCBABC, 
ABCBAC, AC, BAB, C 
ACB, AC, ACB, AC, B 
ACBCABC, AC, BACB, 
ABC, BC, A ABC, AB, C 
ABC, BCA AB, CACB, 
ABCA AB, ©, A 
ABC,BA. AB, CBC, A 
i AB, GC, BCA 
UAB Ce BVA, 
SCIENCE, 
Vol. XXIII. No. 580 
The possible isomers of more complex molecules of 
this class are very numerous. But there is no advantage 
in writing them out since they are not found in practice. 
When divalent or trivalent atoms or groups replace two 
or three monovalent atoms in the preceding formule, the 
possible forms are in all probability restricted to those in 
which the replaced atoms are adjacent to one another. 
The molecule PY NO, for example, is of the form 
Mv A, B,, but only one of the three isomeric forms given 
in the table is in this case possible. 
If there were examples of still higher valence there 
would be no regular arrangement possible until twelve 
atoms were arranged about the central atom, and these 
tweive would crowd one another or be necessarily so much 
closer to one another than to the central atom that the 
form would be unstable. The same cause of instability 
would of course prevent the formation of molecules in 
which more than twelve atoms are grouped about one. 
We have then a plausible reason why valence should not 
exceed the number eight. 
A possible explanation of the fact that elements having 
odd valence remain odd and those having even valence 
remain eyen may be found in the supposition that atoms 
whose valence is even are symmetrical while those having 
odd valence are asymmetrical,—that is to say, the latter 
have their centre of attractive force for other atoms not 
coincident with their centre of gravity; and on the 
farther supposition that in order to form a stable com- 
pound the atoms must form a more or less symmetrical 
arrangement about the central atom. An atom having 
odd valence will then attract one other atom and form 
with it a symmetrical molecule. A farther addition of 
one atom destroys the symmetry. The addition of a 
third restores it. So that if symmetry is a necessary 
condition of stability the valence must increase by twos. 
On this hypothesis the stereochemical structure of mole- 
cules whose central atom has odd valence will be entirely 
different from what is represented in the preceding 
diagrams. The anomaly of chlorine, whose most stable 
oxygen-acid (per-chloric acid) is the one whose molecule 
appears most irregular in the above diagrams, disappears, 
and the arrangement required for the molecule of per- 
chloric acid is perfectly regular. The arrangements for 
the odd valences, in fact, become the same as for the even 
valences of the next higher order with the omission of 
one point whose place is supposed to be (in part) oc- 
cupied by the asymmetry of the central atom. In some 
cases the number of_isomers possible on this theory 
differs from the number given in the preceding table. 
Such cases may decide which (if either) of the views 
here presented is preferable. 
BOOK-REVIEWS. 
Investigations on Microscopic Foams and on Protoplasm: 
Experiments and Observations directed towards a solution 
of the question of the physical conditions of the phenomena 
of life. By O. Biitschli, Professor of Zoology in the 
University of Heidelberg. Authorized Translation, 
by E. A. Minchin, B.A. (Oxon.), Fellow of Merton 
College, Oxford. London, Adamand Charles Black, 
1894. 1vol., 8vo, xvi, 379 p-, with xii plates. 
‘Tus is an attempt to determine the character of pro- 
toplasm, by analogical reasoning from the microscopical 
appearance and behavior, in water, of drops of oil con- 
taining soluble substances, such as salt or sugar, which, 
by their attraction for the water, cause it to enter into: 
the oil and produce a solution which fills and expands the 
cavities previously occupied by the salt or other substance,, 
thus converting the oil into a fine froth. 
