216 SCIENCE PROGRESS. 



cut at right angles to the lamellae, and therefore suitable for 

 measurement. In his latest work he goes farther, and 

 shows that sections not lying in any determinate zone may 

 often be utilised to give trustworthy conclusions. 



To be able to determine the orientation of any ran- 

 dom section of a crystal in a rock-slice, and to deduce 

 the important optical constants of the mineral from it, 

 would, of course, be of the highest importance both for the 

 felspars and for other minerals; but this is a problem which 

 still awaits complete solution in a practical form. Lane 

 (17) has given formulae which may be useful in particular 

 cases, when the section shows the traces of known crystallo- 

 graphic planes (crystal-faces, cleavages, twin-planes, etc.). 

 For instance, in a twinned augite, he measures the angles 

 between the cleavage-traces and the twin-line, the extinc- 

 tion-positions of the two individuals of the twin, and their 

 relative retardations, and (using convergent light) the 

 direction in which the hyperbolas close into a cross ; from 

 these data can be calculated the orientation of the section, 

 the positions of the optic axes, etc. 



Recurring to the felspars, we may note another con- 

 tribution of Michel Levy (iS). In 1S90 he pointed out 

 how among the random sections of felspar-crystals in a 

 rock-slice it is often possible to verify, by tests which he 

 notes, that some one of them is cut, with sufficiently close 

 approximation, parallel to the brachypinacoid. If such a 

 crystal be found, we can adapt to it the measurements of 

 Schuster, and its extinction-angle will at once enable us to 

 refer it to its place in the series of felspars. 



In his most recent memoir, already alluded to (16), the 

 same author has gone a long way towards solving in its 

 entirety the problem of discriminating the various felspars 

 in rock-slices, though it may be doubted w T hether some of 

 the considerations involved are of ready enough application 

 to come into general use. Here, for the first time, we 

 have all the leading properties of double refraction in the 

 felspars worked out from the most trustworthy numerical 

 data, and graphically exhibited for seven typical varieties 

 in as many coloured plates of stereographic projections. 



