Haüy; and 3′.30″. more than the latter. It may therefore be presumed that the value of other angles connected with this, as obtained by the reflecting goniometer, differ from those given by Haüy, both in the Traité and in the Tableau. I am perfectly aware that it becomes me to speak with great deference on this subject. I offer only the results of a mechanical attempt to ascertain the angles of this substance, being incapable of verifying or of detecting their fallacy by a recourse to calculation.
The angle formed by the meeting of the planes PP of the primitive crystal, fig. 18. Pl. 15. is given by Haüy as 67° 42′; by the reflecting goniometer, I have uniformly obtained from clear reflections, an incidence of 67°.50′. making a difference of 8 minutes.
The incidences subjoined, are, for the most part, the result of many perfect agreements of each, on different crystals. In no instance has an average result been noticed. All are not to be relied on with equal confidence. The plane forming the 9th modification of the primitive octahedron is always so striated, and those of the 3d and 10th, are always so dull, that the incidences of those planes with any other in the subsequent series can only be considered as approximations.
| Incidence of | P on P fig. 18. Pl. 15 | 67°. | 50′ | |
| ────────── | P of either pyramid on its opposed plane over the apex | 112°. | 10′ | |
| ────────── | 1 on P fig. 21. Pl. 16 | 113°. | 25′. | ? |
| ────────── | 1 on 1 fig. 21 | 90° | ||
| ────────── | 1 on 2 fig. 26 | 133°. | 32′. | 30″ |
| ────────── | 2 on P fig. 26 | 150°. | 45′. | |
| ────────── | 2 on 2 of either pyramid over the intervening edges, fig. 27 | 121° | 40′. | |
| ────────── | 2 on its opposed plane 2, overt the apex, fig. 27 | 92°. | 55′. | |
| ────────── | 2 on 2 over the plane 1, fig. 27 | 87° | 5′. | |
| ────────── | 3 on 2 fig. 33 | 136°. | 35′. | ? |
| ────────── | 4 on P fig. 39. Pl. 17 | 123°. | 55' | |
| ────────── | 5 on 1 fig. 49 | 161°. | 35′. |
