Bartow—A Mechanical Cause of Homogeneity of Crystals. 627 
entire system as composed of but two individuals which inter- 
penetrate one another. 
If instead of the surfaces of movement meeting in an axis, as 
in the case above given, they are parallel to one another, it is 
evident that the same cause will lead to the production of parallel 
twinning, ¢.e., the kind of twinning called “ polysynthetic.” <A 
good deal of the latter twinning may be expected to be of the 
symmetrical (‘‘ mirror-image ”’) form, and when the closest-packed 
arrangement is an enantiomorph, this will of course result in the 
alternation of right-handed and left-handed forms for the parallel 
layers. 
If the dimorphous change of an assemblage does not take 
place everywhere throughout it at the same instant, this alone may 
suffice to produce twinning, without the intervention of any external 
restraining influence on change of form. Tor if, at a certain 
instant, part only is prepared to distort, the inflexibility of the 
remainder may make it easier for the distorting portion to change 
its form in twinned blocks in the way described rather than as a 
_ single individual. The nature of the external form of an assemblage 
subjected to a dimorphous change gradually asserting itself from 
without would evidently be an important factor in determining 
where the separating surfaces of the different blocks should 
come. 
If a dimorphous change involves no appreciable alteration in the 
situations of the principal singular points’ of a homogeneous as- 
semblage, but only some slight changes in the distances between 
the ball-centres, while leaving the general distribution of them 
much the same, then the assemblage can undergo change while 
continuing solid,’ passing from one system of symmetry to the other 
without any material change of volume or of shape; and, since the 
transition is not accompanied by any appreciable general distortion, 
it may extend itself gradually, and not affect the whole mass at 
once. 
1 Singular points in a homogeneous structure are points which occupy specially 
symmetrical situations, and so form point-systems containing fewer points than 
ordinarily ; they lie on axes of rotation or on planes of symmetry, or on both. Comp. 
Zeitschr. f. Kryst., 23, p. 60. 
2 See note 1, p. 530. 
