Of a very large number of crystals of the red oxide of copper in my possession, some hundreds of which were selected on account of their extraordinary brilliancy, solely with the view of subjecting them to the reflecting goniometer, I have not been able to find a single crystal of which the primitive planes are adapted to its use.
The attempt to measure the angles formed by the meeting of the primitive planes of the red oxide of copper, may reasonably be supposed to have been made only for the sake of corroborating the results of calculation. These results cannot perhaps be doubted, when it is considered that the primitive crystal of this substance is the regular octahedron, which is often found to pass into the cube; for the angles of the one being known with certainty, it follows that those of the other may be calculated with precision. This observation will apply to all those substances which have for their primitive crystals, either of those solids, or the rhomboidal dodecahedron, the regular tetrahedron, or the hexahedral prism.
But there are many forms of primitive crystals, included under the term parallelepiped (amongst which are those of quartz and the sulphate of barytes,) as well as several varieties of the octahedron, both acute and obtuse, which do not, with the same case, seem susceptible of equal certainty in the determination of the value of their angles. I am induced to believe that many, if not most, of these, which have already been given by Haüy, will be found to demand revision.
As it may be expected that reasonable cause should be shewn for doubting authority so eminent, I shall briefly subjoin the reasons that have principally led me to adopt this opinion.
The first step towards ascertaining the value of the several angles at which the numerous planes of crystals meet each other, is altogether
