" Rings and Brushes ' ? in a Sjoath Hemitrope . 5G1 



the crystal or crystalline mass, by means of external pres- 

 sure, it is called secondary. Closely related to the cleavage- 

 direction in their connexion with the cohesion of the 

 molecules of a crystal, are the Gliding planes (Grr. Gleit- 

 flachen) or directions parallel lo which a slipping of the 

 molecules may take place under the application of an 

 external force. This molecular slipping may be attended 

 bv a rotation through 1^0° of the molecules and the resulting 

 twin formed. 



According to the mineralogists, Iceland-spar belongs to 

 a class of crystals which always produce twinning lamellae, 

 that is, one twinning plane in the case of this crystal is 

 always followed by another at a very short distance so that 

 a thin layer of similarly oriented molecules is formed. These 

 are found abundantly in nature and, moreover, the pressure 

 upon the cleavage-fragment of Iceland-spar results in the 

 formation of a number of thin laminae in twinning position 

 to the parent mass. Secondary twinning lamellae are often 

 observed in natural cleavage masses of calcite. 



The explanation of the mechanism of formation of twin 

 crystals is rather difficult. Lord Kelvin*, however, has 

 touched upon the problem. He has given a very lucid 

 exposition of the whole process of crystal-building from a 

 solution. In the particular class of crystals producing twins, 

 he considers the constituent molecules symmetrical on the 

 two sides of a plane passing through itself and also on 

 the two sides of a plane perpendicular to this plane, that is 

 to say, his crystalline molecules are egg-shaped. A real 

 crystal which is growing by addition to a face would give 

 layer after layer regularly. But, if by some change in 

 internal circumstances, the molecules that would go to the 

 formation of a layer are all oriented to 180° with respect to 

 the molecules that formed the previous layer, a twinning 

 plane is formed, and if the remaining layers form in the 

 same way as the last mentioned one, then we shall get a 

 crystal having two different parts separated by a twin-plane 

 between. If, again, the process of: orientation continues 

 only to some layers and then, due to the re-establishment of 

 the initial conditions, the layers form as at the start, we shall 

 get two portions to the two sides with similarly oriented 

 molecules, enclosing a thin layer in which the molecules are 

 turned through 180°. The case will resemble that of Iceland- 

 spar. But the main difficulty in the explanation is to under- 

 stand what is that change in the circumstances that causes the 

 crystalline molecules to turn through 180° in the process of 



* Baltimore Lectures, p. (529, Art. 37-39. 

 Phil, Mag, S. 6. Vol. 43. No. 255. March 1922. 2 



