exceptions certainly exist, reliance cannot be placed but on crystals so small, or rather so minute, as that it may reasonably be doubted whether it be possible for the most skilful hand to obtain with accuracy the admeasurement of the angles formed by the meeting of their facets by means of the common goniometer. The larger crystals are certainly best adapted to the use of this latter instrument, and hence, as I conceive, must have arisen, at least in part, the differences in the results obtained by it, and by the reflecting goniometer.
The admeasurement of the angle formed by the meeting of the planes 1 and 2 Fig. 27, Pl. 16. is prominently noticed by Haüy. This angle is first given in his Traité as 135°, and secondly in his Tableau as 133° 29′; the value of almost if not of every other angle in any degree connected with this, likewise differs very materially. These circumstances induce the supposition that having assumed the value to be first 135° and afterwards 133° 29′, the rest were arrived at by calculation in both instances, and if so, were, of course, dependent on the truth and accuracy of this single determination. It is not therefore surprising that they should be made to differ so essentially in the two works.
In attempting the admeasurement of the angle above noticed, viz. that of 1 on 2 fig. 27. Pl. 16. the reflecting goniometer I first employed, being graduated only to 5 minutes, never satisfactorily gave an incidence of 133, 30, or 133. 35, but generally approached as nearly to the one as to the other. This caused the suspicion that the true value lay somewhere between them, and induced the wish for a goniometer more highly divided; and I have obtained one graduated to half a minute, from Mr. Carey, whose ingenuity led him to add to it some apparatus with a view to precision in its use. By this instrument, I have repeatedly found the angle in question to be 133°.32′. 30″.—being 1°.27′.30″. less than the former determination of