168 THE AMERICAN MONTHLY [June, 



the specially interesting intermediate case where n 

 equals beta, the sum of 2 Ha and 2 Ho will be exactly 

 180°, and sin Va equals sin Ha and sin Vo equals sin 

 Ho, when also Va equals Ha and Vo equals Ho. 



From the above theoretical consideration one can im- 

 mediately deduce the course to be taken to render the 

 immersion liquid exactly equal to the beta index of the 

 crystal ; if the measured values of 2 Ha and 2 Ho add 

 up to over 180° a liquid of higher refraction must be ob- 

 tained, and vice versa if the sum is less than 180°. There 

 are, however, several different ways of determining the 

 closeness of approximation of the indices without going 

 to the trouble of actually making preliminary measure- 

 ments. In the first place the crystal will disappear in 

 the liquid, that is to say, will be invisible, provided that 

 it is colorless, when its refractive power is equal to that 

 of the surrounding medium, especially when the line of 

 the observer's vision lies in the plane of the optic axes. 

 This is very beautifully observed when calcite is im- 

 mersed in monobromnapthaline, and particularly when 

 it is arranged so that the observer looks along the direc- 

 tion of the vertical axis of the crystal; under these con- 

 ditions the latter is completely invisible. In the sec- 

 ond place, instead of hyperbolic curves passing through 

 the positions occupied by the optic axes ; the brushes 

 will take the form of almost straight lines when the re- 

 fraction of crystal and liquid is about the same. 



In chosing crystals for observation by the new method, 

 Prof. Klein recommends that individuals or fragments 

 should be selected which are equally thick in two per- 

 pendicular directions in the plane of the optic axes, that 

 is, such as are almost cylindrical in appearance, and not 

 too thick to prevent the interference figures being ob- 

 served. When immersed in the liquid, it is as if at each 

 moment, and for every position during rotation of the 



