218 



SCIENCE 



[N. S. Vol. XXXII. No. 815 



If its form be that of a prolate spheroid 

 with its poles equidistant from three of the 

 axes, then those axes will be drawn as it were 

 toward the poles and the lengths of these 

 axes will be greater than of the other three. If 

 the poles are midway between four of the 

 axes, they will be similarly drawn together 

 and elongated. If the molecule is an oblate 

 spheroid, corresponding axes will be repelled 

 and shortened. These eases wiU readily be 

 seen to belong to the hexagonal, or rhombo- 

 hedral, and the tetragonal systems ; in the first 

 two, with the vertical axis longer than the 

 lateral, and in the last two, with the vertical 

 shorter. 



Some of the variations will not be regular 

 or symmetrical, yet they may all be shown to 

 correspond to some one of the six recognized 

 crystallographic systems. The following table 

 will indicate the possible variations and the 

 systems into which they would fall, and also 

 some other points. It is to be taken as sug- 

 gestive rather than exhaustive. 



Concerning hemihedral forms, we seem to 

 obtain no more light from this conception than 

 from the older view. 



The apparent advantages resulting from 

 this discussion may be briefly stated as fol- 

 lows: 



1. It aiiords a rational explanation of the 

 various phenomena and characteristics of 

 crystals. Given equal and similar particles 

 and simple attractions for each other, which 

 attraction follows the laws conceived to gov- 

 ern gravitation, with the time and freedom 

 for adjustment of particles in the most com- 

 pact form, and crystals with constant angles 

 and similar cleavage along similar planes, will 

 necessarily result. 



2. This recognition of the fundamental re- 

 lation of the rhombic dodecahedron, which 

 rests on mathematical principles, explains, 

 also, why the kinds of symmetry found in 

 crystals are only the two-, three-, four- and 

 six-fold, for these are factors of twelve. We 

 find why no five-, seven- or other fold wiU oc- 

 cur. 



J. E. Todd 

 Lawkence, Kan., 

 June 16, 1910 



THE TWENTY-SECOND ANNUAL MEETING 



OF THE GEOLOGICAL SOCIETY OF 



AMERICA. II 



The Upper Cayugan of Maryland: T. PooLE May- 



NAKD, Atlanta, Ga. (Introduced by W. B. 



Clark.) 



The Upper Cayugan of Maryland occurs in two 

 well-defined areas in the western part of the state, 

 the Hancock and Cumberland areas, and crosses 

 the state in a northeast-southwest direction, fol- 

 lowing the general trend of the Appalachians. 

 The rocks constituting the Upper Cayugan con- 

 sist, usually, of argillaceous, thin-bedded lime- 

 stones at the bottom, passing gradually into the 

 heavier bedded limestones of the Lower Helder- 

 berg. These limestones lie between the Salina 

 below and the Coeymans above and have an aver- 

 age thickness of one hundred and ten feet. There 

 is only a gradual change in lithology from the 

 Salina to the Coeymans and no well-defined lith- 

 ological break exists. The upper and lower limits 

 of the rocks constituting the Upper Cayugan are 

 determined on paleontological grounds. These 

 rocks, while equivalent in Maryland to the Man- 

 lius and Cobleskill of New York, can not be sub- 

 divided in Maryland on either paleontological or 

 lithological grounds. The Rondout is absent in 

 Maryland, while the fauna of the Cobleskill and 

 Manlius are not distinct and separate as they are 

 in New York, but they intermingle, typical New 

 York Manlius and Cobleskill forms occurring to- 

 gether. They are also associated with forms 

 occurring in the Upper Decker Ferry of New 

 Jersey. 



Discussed by A. W. Grabau. 



Sfratigraphic Relations of the Livingston Beds 



of Central Montana: R. W. Stone and W. R. 



Calvert, Washington, D. C. ( Introduced by 



M. R. Campbell.) 



The Livingston formation occurring at Living- 

 ston, Montana, has been described as resting un- 

 conformably on the Laramie and overlain by the 

 Fort Union formation. Its age has been consid- 

 ered to be post-Laramie and it has been correlated 

 with the Denver formation of Colorado, partly on 

 lithologic similarity, both formations being com- 

 posed largely of tufaceous beds. This paper 

 showed that the Laramie of the Livingston and 

 Little Belt Mountains folios of the Geologic Atlas 

 of the United States is Eagle, or at least lower 

 Montana, and that there is no unconformity be- 

 tween it and the overlying Livingston beds in the 

 area under discussion. It .showed also that on the 

 west and south sides of the Crazy Mountains about 

 7.000 feet of sediments, mainly andesitic tuffs. 



