Bartow—A Mechanical Cause of Homogeneity of Crystals. 557 
_ to indicate that the centres are at different distances from the 
_ plane of the diagram being followed and no attempt being made 
to show the spheres themselves or the way in which they touch one 
another.’ 
We have in this case most of the symmetrical and other con- 
ditions which are met with in quartz-crystals, including a compo- 
sition and grouping which agree with the molecular composition 
of that body, and screw-movement axes which involve a spiral 
arrangement of the parts such as is requisite to account for the 
property of rotation of the plane of polarization. 
Case of bipyramidal hemihedrism. 
Take a stack of close-packed spheres, such as is described on 
page 534 and in fig. 3, and, keeping the spheres which are nearest 
to each hexagonal screw axis in contact both laterally and longi-. 
tudinally, separate the stack into strings of triads of spheres by 
slightly increasing the distances between the axes in a uniform 
manner. 
Orientate all the strings of triads uniformly about the respec- 
tive axes so as to bring some of the separated spheres again into 
contact. Finally, place in each of the largest interstices now left 
between the spheres a sphere of some other radius as large as 
possible. 
It is probable that such a value can be selected for the ratio 
of the sizes of the two kinds of spheres in an assemblage of the 
kind just described as will make it the closest-packed mixed 
arrangement for spheres whose magnitudes bear this proportion. 
The type of homogeneous structure produced in this way is num- 
bered 20a, in my list;? all the centres lie at singular points, the 
more numerous in planes of symmetry and the less numerous on tri- 
gonal axes. The generic symmetry is that of class 11 in Sohncke’s 
list of Krystallklassen. The two kinds of balls are present in the 
numerical proportions 2: 3. 
1 Compare fig. 22, Taf. II. in Sohncke’s Entwickelung einer Theorie der Krystall- 
struktur. 
2 Zeitschr. fiir Kryst., 23, p. 45. 
