THE VAPJATION OF ANGLES OBSERVED IN CRYSTALS. 467 
action of the solvent, with the original faces, when the latter have been removed by 
the solvent; the refractive indices of solid plates, prisms, or crystals can be measured 
by total reflection or minimum deviation by immersing them in appropriate liquids ; 
and the refractive index of a liquid can similarly be measured by means of a plate or 
prism immersed in it. 
Again, the angles of isomorphous mixtures may be ascertained as the composition 
changes, by measuring a crystal while in a solution of different composition; or 
measurements may be made of a crystal enveloping a similar crystal of a substance 
isomorphous with it by immersing the latter in a solution of the isomorphous 
material; this would render it possible to ascertain the angles between the faces of 
the shell and the corresponding faces of the kernel. Examples of some of these uses 
will be found in the following pages. 
With the object of testing the goniometer, some observations were made upon tlie 
etching of calcite by dilute HCl, and upon the parallel growth of sodium nitrate with 
calcite. Since these are either new, or were new at the time when they were made 
(1893), and were certainly made liy a new method, and since they bear upon the 
subject of vicinal faces, a few of the results of these measurements may be here 
mentioned. 
(a.) Etching of Calcite 'with HCl. 
A cleavage rliomb of calcite immersed in about 50 cub. centims. of water gave the 
following readings for two faces Ri’:— 
~R 211° 52f' 
Hr = 74° 55A. 
_r 136° 57f 
One drop of dilute HCl was added and after the lapse of li hours distinct pits 
were etched on both faces, having at first the form of linear channels parallel to the 
edge R/’, and subsequently assuming a more triangular outline, and faint images 
begin to make their appearance close to those from R and r. After 9 hours the 
following well-defined images were obtained in the zone [Rr] ;— 
211° 51' 
r 136° 57' rr^ = 0° 8'. 
136° 49' 
Another rhomb gave readings ;— 
R 42° 37^' 
Rr = 74° 56A-' before etching. 
r 327° 41' 
3 o 2 
