1890.] and Crystallization. So 



the fact that hexagonal forms lend themselves to the production of 

 approximately globular masses with a minimum total surface, will 

 increase the tendency to the development of hexagonal forms. 

 We may still however get rhombohedral forms in some cases. It 

 has been shown that if the molecular ellipsoids be oblate sphe- 

 roids with their principal diameters in ratio of V2 : 1, and they be 

 arranged so that each be touched by four others in the plane of its 

 priucipal circular section and by four others in each of two other 

 planes parallel to the first, the crystal will have cubical symmetry, 

 and if we suppose the system uniformly strained in the direction 

 of one of the diagonals of the cubes the spheroids will be deformed 

 into ellipsoids and the crystal will have rhombohedral symmetry. 

 In this case the alternations of twins will not be equally probable 

 and the rhombohedral forms will generally predominate. Formula; 

 are given for calculating the relative probability of different forms 

 when the angular element of the crystal is known, and their appli- 

 cation shown by examples. 



(2) On the Curvature of Prismatic Images, and on Amici's 

 Prism Telescope. By J. Larmor, M.A., St John's College. 



It is well known that, in homogeneous light, a prism acts as a 

 telescope in magnifying transversely the dimensions of objects in 

 the field of view, while their longitudinal dimensions remain un- 

 changed. In fact an incident parallel beam emerges as a parallel 

 beam, so that the prism forms a telescopic system ; and the trans- 

 verse magnification along any ray is, by the general law applicable 

 to such systems, equal to the inverse ratio of the breadths of these 

 incident and emergent pencils. 



These considerations apply equally to any battery of prisms. 



As a single prism has a position of minimum dispersion which 

 is different from the position of minimum deviation, it follows that 

 two prisms, of the same kind of glass, may be combined in opposing 

 fashion so as to form an achromatic pair, while some deviation 

 remains, and therefore also some magnification. By combining in 

 perpendicular planes two such achromatic doublets, of equal magni- 

 fying power, Amici long ago succeeded in producing a telescope 

 which magnified equally (about 4 times) in all directions, was 

 made of the same kind of glass throughout and yet achromatic, 

 and, according to Sir John Herschel's experience of it (Encyc. 

 Metrop. 'Light,' § 453), gave images of remarkable perfection. 



The image of a straight-edge or slit, seen through a prism with- 

 out a collimator, is a curved arch or bow : and it has been pointed 

 out by Sir Howard Grubb that when the prism is rotated the 

 curvature of this arch is proportional to the dispersion of the 



