1820.] Philosophical Transactions for \^20, Part 1. 387 



tion produced by ordinary means, he has not ciioien to explain the mode of con- 

 struction he adopted, and has merely referred to a certain artist living at that time 

 in Paris, who was in possession of his secret, and skilful in applying it to the 

 construction of micrometers. 



As I have reason to think that the method to which he alludes in his memoir has 

 never yet been described, I desie;ii, in the present communication, to explain a 

 combination which I have found advantageous, and which 1 think must be the 

 game as that of M. Rochon. 



I shall hope to render the principles of this construction intelligible to every one 

 acquainted with the original observation of Huygens on the properties of polarised 

 light, and to enable any competent artist to cut wedges from hexagonal prisms of 

 rock crystal , in the positions requisite to produce, by their combination, the double 

 effect to which I allude. 



There are three principal directions in which a crystal may be cut specifically 

 different from each other, which require to be distinctly understood. 



In the first place, let us suppose a pri.-niatic crystal to be placed with its axis in 

 a vertical position, and a portion to be cut offfrom the base by a plane surface at 

 right angles to the axis, and sufficient to form a wedge of 20 degrees, by giving it 

 a second surface duly inclined to the former. For distinction, this may be called 

 the horizontal wedge. 



Next, let the crystal be bisected vertically by a plane passing through two oppo- 

 site edges of the prism, in order to make two other wedges which are to be cut in 

 different directions from the two portions, and to have each the same angle of 20 

 degrees. 



Let one of the halves thus obtained be slit in a plane which meets the surface of 

 bisection in one of the edges of the origiual prism, and consequently in a line pa- 

 rallel to the axis. The wedge thus formed may be called a lateral wedge. 



Let the remaining half be cut by another plane not vertical, but inclined to the 

 vertical plane at an angle of 20°, and meeting it in a line parallel to the base, or 

 at right angles to the axis. This may be called a vertical we Age. 



We have thus three wedges cut in different directions at right angles to each other, 

 and, accordingly, having theiraxes of crystallization differently placed in each. 



lu the first, or horizontal wedge, the axis is at right angles to Ihe first surface. 

 In the second, or lateral wedge, the axis is parallel in the first surface, and parallel 

 -to its acute edge. In the third, or vertical wedge, the axis is also in the first sur- 

 face, but it is at right angles to the acute edge. 



An object seen through the first wedge in the direction of the axis docs not 

 appear double ; but since r.iys transmitted through the second or third pass at 

 right angles to the axis, both of these wedges give two images of any object seen 

 through them. 



There are obviously three modes in which these wedges may be combined in 

 pairs, by placing two of them together with their acute edges 

 in opposite directions. The first pair may be represented by 

 L H; the second by V H; the third by V L. In the two 

 first cases, the separation of the images will be the same, since 

 the angles of all the wedges are supposed to be made equal, 

 the compound medium will be comprised under parallel surfaces, so that a ray 

 ordinarily refracted by both, emerges in its original direction; but sine (he 

 extraordinary ray is made to deviate about IT from the ordinary course by „^^ 

 wedge which refracts doubly , this difference is not corrected by the horizontal wed ^^ 

 so that an object seen through either of the combinations L H or V H, appea 

 doubled to the umount of IT, 



The third combination, consisting of the vertical and lateral wedges combined, 

 as in the former cases, with their acute edges in opposite directions, produces an 

 effect perfectly distinct from either of the former combinations ; for by reason of 

 the transverse position of their axes of crystallization, the separation of the two 

 images becomes exactly doubled. The consequence of that position is, that the 

 pencil ordinarily refracted by the first wedge is refracted extraordinaiily by the 

 second, and that which has been refracted extraordinarily by the first sufliis a 

 similar interchange, and is now ordinarily refracted, so lliat neither of the divided 

 pencils returns to its true place ; and since one falls as much short of the mean as 

 the other exceeds the truth, they emerge ultimately separated twice the usual dif- 

 ference betweeu the ordinary and estraordinary refi;actipns, and thus present two 



2 B 2 " 



