414 Haiiy on the Measuring of the Angles of Crystals. (Jus, 
within half a degree, or the third of a degree when the crystal 
measured possesses every desirable perfection. But the method 
which I had adopted, and which I shall immediately explain, 
seemed to put it in my power to dispense with a greater degree 
of precision, by giving me a means of knowing from theory the 
term at which I ought to stop, amid the various results which I 
obtained sometimes on one side, and sometimes on another. 
As the sciences advance, those who cultivate them invent new 
methods of determining with more precision the quantities which 
serve as data for the solution of problems. The repeating circle 
of Borda furnished one of these methods to astronomy and 
geodesy. Malus employed it to measure, by means of the angles 
of incidence and reflexion of light, the angles of different natural 
bodies, which he wished to employ for the development of his 
beautiful theory of double refraction. Dr. Wollaston, to whom 
the sciences lie under so many obligations, has contrived another 
very ingenious instrument, founded on the same _ principle 
expressly, for the use of crystallography. The smallness of the 
size, far from being a reason for excluding crystals, is, in his 
mstrument, rather a motive of preference. ‘This is a prerogative 
which this distinguished philosopher enjoys to be able to employ 
the method furnished: by physics and chemistry to determine at 
one time the angles, at another the constituents of a substance, 
almost too small to be perceived, and which seems to borrow 
from the extreme dexterity of the hand who performs the expe- 
riment what it wants in bulk and weight. ae an 
Mr. Phillips, who has successfully practised the art of hand- 
ling this instrument, has published in the Transactions of the 
Geological Society of London, the results of his measurement of 
the angles of a variety of crystals ; and without comparing them 
with those which I have obtained, it is merely necessary to con- 
sider the way in which the instrument is constructed and 
graduated to be entitled to conclude that the ordinary goniometer 
is unable to contend with it, and that we have no reason to 
hesitate about the choice whenever we wish to obtain the requi- 
site precision in the measurement of the angles of crystals. 
The results of Mr. Phillips, who had no knowledge of most of 
the rectifications which I have made of my old measurements, 
point. out very sensible differences with several of those, which 
seem to complete the proof of the pre-eminence of the reflecting 
goniometer. And the kind of disgrace into which they have 
a tendency to bring the one of which I made use may even be a 
reason for doubting if my theory be as well proved as I believed 
it to be, and whether it ought-not even to be rejected, as not 
being able to exhibit in its applications that accuracy which 
constitutes the essence of every theory. 
I propose, therefore, to show, that my theory, in the state 
into which it has been brought by the new attempts which I 
have made to complete it, cannot leave any doubt respecting 
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