We are now, therefore, in a position to approach the question of true isomorphism, and as leading up to the fuller treatment of the subject in Chapter X. we may conclude this chapter by referring first to one important investigation in which the necessity for extreme accuracy of measurement and perfection of material was fully appreciated. This was an admirable research carried out in the years 1887 and 1888 by H. A. Miers[10] on the red silver minerals, proustite, sulpharsenite of silver, Ag_{3}AsS_{3}, and pyrargyrite, the analogous sulphantimonite of silver, Ag_{3}SbS_{3}, which afforded a further indication of the existence of real small differences of angle between the members of truly isomorphous series. These two minerals form exceptionally beautiful crystals belonging to the trigonal system, the hexagonal prism being always a prominent form, terminated by the primary and other rhombohedra, scalenohedra and various pyramidal forms, many of the crystals being exceedingly rich in faces. When the crystals are freshly obtained from the dark recesses of the silver mine they are very lustrous and transparent, but they are gradually affected by light, like many silver compounds, and require to be stored in the dark in order to preserve their transparency. A magnificent crystal of proustite from Chili is one of the finest objects in the British Museum at South Kensington, but is rarely seen on account of the necessity for preservation from light. Pyrargyrite is generally dark grey in appearance, and affords a reddish-purple “streak” (colour of the powder on scratching or pulverising). Proustite, however, possesses a beautiful scarlet-vermilion colour, and affords a very bright red streak. Now these two beautiful minerals are obviously analogous compounds of the same metal, silver, with the sulpho-acid of two elements, arsenic and antimony, belonging strictly to the same family group, the nitrogen-phosphorus group, of the periodic classification of the elements according to Mendeleéff. Consequently, they should be perfectly isomorphous. Miers has shown in a most complete manner that they are so, that they occur in very perfect crystals of similar habit belonging to the same class of the trigonal system, the ditrigonal polar class, both minerals being hemimorphic, that is, showing different forms at the two terminations, in accordance with the symmetry of the polar class of the trigonal system. But the angles of the two substances were not found to be identical, although constant for each compound within one minute of arc, there being slight but very real differences, which are very well typified by the principal angle in each case, that of the primary rhombohedron. In the case of proustite it is 72° 12′, while the rhombohedron angle of pyrargyrite is 71° 22′.