93 



the other a plate wliich gave rings of the same size as the plate of 

 calcareous spar. But when we combine a system of rings produced 

 by a crystal of zircon, with the system produced by calcareous spar, 

 a different effect is produced ; and the system, instead of being di- 

 minished, is increased, and is equal to that which would have been 

 produced by a thin plate of calcareous spar, whose thickness is equal 

 to the difference of the thicknesses of the plate of calcareous spar 

 employed, and the plate of calcareous spar that would give rings of 

 the same size as those given by the zircon alone. In the section 

 "on crystals with two or more axes of polarization," Dr. Brewster 

 observes that, although M. Biot considered mica as the only mineral 

 possessing the compound structure indicating two axes, he had found 

 the same structure in topaz, nitre, tartrate of potash and soda, sul- 

 phate of potash, acetate of lead, and mother-of-pearl, as early as 1813; 

 and he points out the means of deducing the number of axes in crystals 

 from their primitive forms. Dr. Brewster expresses the general law 

 of the tints for crystals with one or more axes in the following man- 

 ner. The tint produced at any point of the sphere by the joint action 

 of two axes is equal to the diagonal of a parallelogram whose sides 

 represent the tints, and whose angle is double the angle formed by the 

 directions in which the forces are exerted. 



The fourth and fifth sections of this paper relate to the resolution 

 and combination of polarizing forces, and the reduction of all crystals 

 to those with two or more axes ; and to the polarizing structure of 

 crystals that have the cube, the regular octohedron, and the rhom- 

 boidal dodecahedron for their primitive form. The sixth and con- 

 cluding section describes the artificial imitation of all the classes of 

 doubly refracting crystals, by means of plates of glass ; in which the 

 author demonstrates that the polarizing structure depends entirely 

 upon the external form of the plate, and on the mode of aggregation 

 of its particles. When its form is circular, it has only one axis of 

 polarization, which is attractive if the density diminishes towards the 

 centre, and repulsive if it increases towards the centre ; but when 

 its form is rectangular or elliptical, it then has two axes of polari- 

 zation, the strongest of which appears to be attractive, and the weak- 

 est repulsive. The elementary spheroid of crystals with double axes 

 may be supposed, says the author, to be formed by elliptical plates 

 bent into spheroidal strata; and the spheroid itself may be con- 

 structed by spheroidal strata of glass, it then exhibiting all the com- 

 plicated phenomena produced by the simultaneous actions of two 

 unequal axes. 



On the Parallax of certain fixed Stars. By the Rev. John Brinkley, 

 D.D. F.R.S. and Andrews Prof essor of Astronomy in the University 

 of Dublin. Read March 5, 1818. [Phil. Trans. 1818, p. 275.] 



Since the author's former observations on the parallax of a Lyrse, 

 published by the Royal Society in a Letter to Dr. Maskelyne, he (the 

 author) has met with apparent motions in several of the fixed stars, 



