330 SECOND REPORT— 1832. 
in the spirit and according to the method of his master; as 
has another distinguished mineralogist from the same school, 
Mr. Haidinger. 
Mr. Brooke has, in a great measure, employed the formulas of 
spherical trigonometry, in which he has been followed by others. 
This method has the great advantage of enabling us immedi¬ 
ately to perform all our calculations by the help of logarith¬ 
mic Tables. 
The most scientific mode of treating the subject, which con¬ 
sists in reasoning by means of the equations to the planes accord¬ 
ing to the methods of analytical geometry, was employed from 
the first by Weiss. It has been adopted by Mr. Levy, and by 
a number of German writers, as G. Rose, Kupffer, Kohler. 
Naumann in his Principles of Crystallography, published 
in 1826, employed processes much resembling those of Mohs : 
but in a much enlarged and improved work on the subject 
which appeared in 1830, he states, with great candour, that at 
the former period “ he was not acquainted with the great ad¬ 
vantages of an analytical-geometrical mode of treating the sub¬ 
ject,” and that he has now “ arrived at the conviction that this 
is and must be the simplest and most natural of all methods.” 
This is a conviction which will probably be more widely diffused 
as the subject is more studied. M. Naumann has by this 
method calculated all the formulae which are likely to be needed 
in a very clear and complete manner, and has exhibited the re¬ 
sults of the most common combinations in a tabular form. 
Ratzeberg has published a similar synoptical Table, with 
figures of the crystalline forms and their combinations accord¬ 
ing to the method of Weiss ; a very convenient mode of pre¬ 
senting the subject. 
Geometrical truth has generally several aspects, each of which 
by constant contemplation appears to the individual reasoner to 
become the most luminous possible; and this is especially the 
case with regard to a system of truths so complex and multiplied 
as those which the solid geometry of crystals offers to our no¬ 
tice. It is not surprising, therefore, that other authors besides 
those above mentioned, should have taken other views of the 
best mode of treating the subject, and should have brought for¬ 
wards these as considerable discoveries. Thus Mr. Grassmann 
(Stettin 1829,) published a Treatise “ On Physical Crystallo- 
nomy,” in which he develops the connexion of forms by means 
of “ a mathematical discipline hitherto never pursued.” He 
determines the position of a plane by means of a “ radius con¬ 
structor or line perpendicular to it, and assuming three fun¬ 
damental radii of this kind, he deduces the number and mutual 
relation of the others by the combination of the relations of 
