426 Haiiy on the Measuring of the Angles of Crystals, (Jun, 
same property; because the line drawn from the upper extre- 
mity of the edge, on which their base originates, to the lower 
extremity. of the opposite edge, is perpendicular to both, as I 
have explained in my Memoir on the Law of Symmetry. 
The ratios of which we are speaking appear at intervals in the 
series of those which the different angles give that divide the 
circumference. ‘They take place at the parts in which their 
component parts are susceptible of division by a common factor,, 
which reduces their value, and frees them from the complication 
in which they were enveloped. The intervals which, separate 
‘these ratios answer to the differences in the corresponding 
angles, which vary more or less, sometimes the fourth of a 
degree, sometimes half a degree, or more. When the crystals 
on which we operate have a form not very determinate, it is 
ossible that an approaching ratio may be taken for the true one. 
This of necessity happened to me more than once when I was 
composing the geometrical part of my Treatise. I have corrected, 
as I have already said, a part of my old determinations, among 
which there are some that relate to the angles taken by Mr. 
Phillips, to which they approach much more nearly at. present 
than they did formerly. 
Admitting then that I have obtained, with respect to all the 
other species, ratios in which accuracy agrees as nearly as possi- 
ble with simplicity, as, I think, has been the case in particular 
with regard to quartz, oxide of tin, and sulphate of lead, I 
consider myself as entitled to say, that these ratios are sufficient 
to determine without any ambiguity the laws of decrement, on 
which depend the secondary forms belonging to each species ; 
for the difference in the inclination of the faces that would be 
produced by mistaking one law for another, would be much 
greater than what could exist between the angles as given by my 
ratio and by the reflecting goniometer. There is even in the 
results derived from both a convergence worthy of being 
remarked and very favourable to the theory. | It consists in this, 
that the differences between the primitive angles become much 
less in the inclinations of the secondary faces; so that some- 
times they approach so near that all difference vanishes. [I shall 
take as an example the angles of the primitive rhomboid of 
calcareous spar. According to the measures of Wollaston and 
Malus, the angle which any face of the rhomboid forms with a 
parallel to the axis is 134° 37’ instead of 135° which I had indi- 
cated, from the condition that when the axis of the rhomboid was 
situated vertically, each of its faces was equally inclined to a 
vertical and a horizontal plane. If we set out from the two pre- 
ceding measures, we find for the great angle which the faces of 
the rhomboid make with each other on the one side 105° 5’, 
on the other 104° 28’, which is a difference of 37’. But this 
difference diminishes in passing into the results of the decre- 
ments which produce the secondary forms ; so that in the metas- 
~~. 
