a mechanical operation dependent on the skilful use of the goniometer; and for this purpose doubtless brilliant and well defined crystals have been selected. Having arrived at the admeasurement of some one prominent angle, by means of the goniometer in common use, it can scarcely be doubted that its value has been assumed as a basis on which to calculate the rest. This, there is reason to believe, was the process adopted by Haüy in regard to his determination of the angles of the primitive crystal of the sulphate of barytes, which he has given to seconds, and which the common goniometer will not indicate. It must be obvious that the perfect fidelity of this preliminary mechanical determination is most essential.
It is no trivial argument against the accuracy of this practice, that those who are the most skilful in the use of the common goniometer, have differed in the results obtained from the same substances. But, even were it possible to depend upon the accuracy of the instrument, and upon the skill of the hand using it, there seems much reason for doubting whether the planes of such crystals as are best adapted to its use can be relied on. I allude of course to such as are of considerable dimension. These, when submitted to the reflecting goniometer, rarely agree with each other; and the measurements they afford almost always differ very considerably from those obtained upon small crystals; which much more frequently give similar results, but which are too minute, as it seems to me, for the accurate use of the common goniometer.
The difficulties already described as having attended my numerous attempts to verify the admeasurements of Haüy. in regard to the primitive crystals of quartz and the sulphate of barytes, belong not to the crystals of these two substances only. I have found these difficulties to exist in different degrees in respect to more than
