Bartow—A Mechanical Cause of Homogeneity of Crystals. 575 
in extremely fine needles which bend themselves somewhat 
vigorously, and then, while strong evidences of tension, sometimes 
resulting in rupture, show themselves, straighten themselves out. 
The larger crystals show brilliantly the progress of the formation 
of branches; directly they impinge on any obstacle, however in- 
significant, brush-like radiations are formed at the place.? 
Tetragonal well formed crystals of cromfordite (phosgenite) 
are sometimes met with which have a spiral twist.’ 
Dimorphism, Trimorphism, &c. 
The relative situations taken up by the ball centres of a mixed 
assemblage as the result of closest-packing depend, as we have 
seen, on what sizes are brought together.* It is evident, therefore, 
that where there is more than one kind of ball, if a change of con- 
ditions occurs which alters the sizes of balls of different kinds 
differently, the alteration produced may conceivably be such that 
closest-packing is no longer attained in the type of arrangement 
which originally gave it. And where this is the case, if the 
change be made gradually, it will be found that immediately a 
critical point is passed at which the type of arrangement origin- 
ally presented ceases to be the closest-packed equilibrium-arrange- 
ment, the assemblage will cease to approximate to this original 
type of arrangement, and will commence approximating to some 
other different type, viz. to that which after the critical point is 
passed becomes the one which now gives closest-packing. When- 
ever a critical point of this kind is passed, an assemblage will, 
therefore, take up a new type of arrangement, and if both before 
and after the critical point is passed, the same bodies constitute 
one homogeneous assemblage, the two assemblages thus presented 
will be dimorphous assemblages. 
At the critical point exactly the assemblage will of course be 
equally disposed to take up either arrangement, and consequently 
10. Lehmann, ‘‘ Ueber das Wachstum &c.,”’ pp. 479-481. 
2 There is an exceptionally fine specimen in the British Museum, London. 
3 But see note 1, p. 546. Some effect in determining the nature of the arrange 
ment is also traceable to the linkage; and this applies to all linked assemblages 
whether they consist of a single kind of ball or of more than one kind. 
SCIEN. PROC. R.D.S., VOL. VIII., PART VI. 2U 
