With thirty-two molecules associated with the unit cube, the first reflections observed from the (100) and (110) faces correspond with the fourth order. Third order reflections from planes having indices that are all odd are found in the Laue photographs. Plane 100: A=Mg 16cos2 nu +16cos2 π n (u+1)}+O term. n=2 A =Mg(32 cos4 Tu}+0{32 cos4 π v)=0 when u =},v=†. 100 Plane 110: A=Mg Scos2 # nu+8+8cos2 πn (u+1)+8cos n}+O term. π This term also equals zero when u=1, and v=3. Plane 111: = 3 A=Mg Scos6 nu+24cos2nu +0 a similar term in v. The problem in this case is to determine whether there are values for u and v such that A, for n=1 and n = 2, is practically zero; the intensity of reflection when n must be appreciably less than when n=4. An approximate solution can be given graphically; a more exact one could, however, only be made if quantitative measurements of scattering were available. The intensity of reflection (or the amplitude) for all values of u and v when n has a particular value can be represented by a three dimensional figure. Certain "iso-u's" of such a figure obtained when n=1 are given in figure 3. The curves enclosing region n=1 of figure 4 are obtained by plotting those values of u and v which give a certain small amplitude (as may be determined with the aid of figure 3) on either side of zero (arbitrarily chosen for this representation as +50 and -50). All points lying within this region then will satisfy the experimental requirement that no first order is observable. The regions n = 2 similarly enclose all values of u and v for which the second order will be negligible. The condition that the amplitude shall be very large in the fourth order is fulfilled within the areas defined by the curves n=4. These three conditions are satisfied only in the regions about u 1/4 or 34 and v14 or 34. It will be observed that when u 14 and v 344 the arrangement is identical with that of (c); small deviations from these values could not, however, be detected by the experimental means available. The arrangement that would result if u and v were both nearly equal to 14 (or 34) is scarcely feasible from a physical standpoint. Thus (j) furnishes a possible arrangement for the atoms in magnesium oxide. Possible arrangement (k). This must be treated in a similar fashion to the preceding. Thus the reflection term from the (100) face is A=Mg Scos2 nu +Scos π n (1+2u)+8cos πn (§ —Qu) B=0. When n = 1, 2 and 3, A=0 for all values of u and v. Plane (110). A=Mg 8+8cos4 # nu+Scos n+8cos πn (1−4u)} B=0. +0 a similar term in v}. When n=1 or 3, A=0. For n=2: A=Mg 16+cos8 u}+0{16+16cos8 π v}. Plane (111). A=Mg 4cos6 π nu +12cos2 π nu +12sin2 π nu-4sin6 B=—A. For the present qualitative uses it may, therefore, be neglected. It can be shown by a treatment similar to that applied to (j) that when u1 = and u2 =5% (for these particular values of u, the thirty-two equivalent positions each reduce to sixteen) and v=78, there is complete agreement with experiment. Except for the fact that the element whose parameters are represented by u, and u will be of two sorts (all of the atoms of the other kind will be alike), this particular arrangement is simply a twice-scale (c) grouping. If, however, u and had values close to 1% and 7%, the differences in the reflections would be so slight as to escape detection. Arrangement (k) thus becomes a possibility. Grouping (c), the "sodium chloride arrangement" has now been shown to be the only simple structure which explains the experimental data, if the arrangement of the atoms in magnesium oxide is really holohedral. The tetartohedral grouping (f), however, can be made to fit the observations for certain values of its parameters u and v. Of the various ways having thirty-two molecules in the unit cube, both (j) and (k) are possible. All three of the structures with variable parameters, however, are in agreement with experiment only when u and v have such values that the resulting arrangements approximate very closely to the "sodium chloride" grouping. The nature of the forces between the atoms of magnesium oxide. Magnesium oxide has just been shown to have probably the same structure as rock salt, (c). Some information concerning the possible nature of the binding forces between its atoms in the light of the existing ideas on the forces of chemical combination can be obtained from its analogies with sodium chloride and the other alkali halides. Two kinds of unions between atoms can be explained by the present knowledge of the structure of atoms. (1) The "electro-negative" atoms of a compound may be able to abstract electrons from the "positive" atoms so that the compound becomes an aggregate of charged atoms held together chiefly by the electrostatic attractions between them. Or (2) if extremely electropositive atoms are not involved in the combination, all of the atoms in the compound may strive, without complete success, to acquire electrons in the somewhat inexplicable, but clearly real, attempt to close their clusters of eight outside electrons. Electrons are thus in some way held in common by two atoms-a second sort of bonding which can be called a valency bonding. Partly because of their crystal structures the alkali halides are commonly supposed to be compounds exhibiting the first kind of combination. In sodium chloride each atom, according to arrangement (c), is equally distant from six atoms of the other sort and thus there seems to be no connection between what is commonly called the valence, in the chemical sense, of the atoms, and their locations in space. Similarly the crystal structure of magnesium oxide seems to point to the fact that the oxygen atoms have been able to remove completely the two outside electrons Ralph W. G. Wyckoff, J. Wash. Acad. Sci., 9, 565, 1919. 'J. Stark, Prinzipien der Atomdynamik, III, p. 193. of magnesium so that the compound is an aggregate of doubly charged oxygen and magnesium "ions." The writer wishes to express his thanks to C. J. Ksanda for assistance in carrying out parts of this determination. Summary. An attempt has been made using Laue photographs and X-ray spectrum measurements to get a unique solution for the crystal structure of magnesium oxide. If it possesses holohedral symmetry then the only simple structure which is possible is the "sodium chloride arrangement," (c). Certain cases of grouping, showing tetartohedral symmetry and of the more complicated holohedral arrangements, (j) and (k), each with thirtytwo molecules associated with the unit, are in agreement with the existing experiments. These other possibilities, however, differ but slightly from the "sodium chloride arrangement," and can not be positively treated by the experimental facilities now available. ART. X.-The Mississippian Formations of the HortonWindsor District, Nova Scotia; by WALTER A. BELL. INTRODUCTION. The paleontological writings of Sir William Dawson early determined the Horton-Windsor district as the type area for two Mississippian series of formations, the Horton and the Windsor. Later controversies that arose between paleontologists on the one hand, and structural stratigraphers on the other, involved the correlation of the older or Horton formation, a circumstance that lends additional interest to the Mississippian stratigraphy of this district. Previous work.-Among the previous workers who have written on the geology are such famous names as Sir William Logan, Sir Charles Lyell, and Sir J. W. Dawson. Logan visited the area in 1841, fresh from his geological studies in South Wales, where he had so ably established the true nature of Stigmarian underclays. His discovery in the Horton formation of amphibian footprints (Hylopus logani Dawson), in conjunction with the coal-measure appearance of the Horton strata and of the contained flora, led him to consider these beds of Coal Measures age. The gypsiferous or Windsor series was recognized as stratigraphically younger, and fossils gathered at Windsor and submitted to De Verneuil, Keyserling, and Murchison were first regarded as Permian in age. This correlation, however, was doubted by Sir Charles Lyell as long ago as 1843, and he was the first to assign both the Windsor and Horton beds to the lower Carboniferous, a conclusion soon corroborated by Sir William Dawson. For the next fifty years Dawson contributed various papers dealing with the flora, fauna, and stratigraphical relations of these Mississippian rocks. His observations and conclusions are admirably presented in the various editions of his "Acadian Geology. Later references to the correlation of the Mississippian formations are made by David White, R. Kidston, A. Smith Woodward, L. M. Lambe, H. M. Ami, Charles Schuchert, and J. W. Beede. White (1901) assigned the Horton a Kinderhookian age, with a partial equivalence Published by permission of the Director of the Geological Survey of Canada. |