1819.] Haiiy on the Measuring of the Angles of Crystals. 413 
ArTICLE II. 
Observations on the Measuring of the Angles of Crystals. 
By M. Hauy.* 
WueEn I composed, 20 years ago, my Traité de Mineralogie, 
my collection, which was not very far from its commencement, 
was affected by the rarity of regular and well-defined crystals 
among us. It was almost solely with these feeble means that 1 
undertook to apply my theory to all the varieties hitherto 
described, adding those that were new to myself. It is well 
known that the study of such bodies requires a copious collec- 
tion in order to be able to find crystals free from those accidental 
circumstances which alter the level of the surface and occasion 
perceptible differences between their inclinations and those 
derived from invariable laws of structure. These accidental 
deviations occasioned some of the inaccuracies into which I fell, 
notwithstanding all my care, and which I should have avoided had 1 
been possessed of different crystals of the same variety to verify 
my observations. Other inaccuracies were occasioned by imper- 
fections of which I was aware, without being able to extricate 
myself from the uncertainties to which they gave rise. In such 
cases I took care to mention that I did not guarantee the accu- 
ie of the measurements.+ 
such is the fate of works which constitute the foundation of a 
great system, especially those which result from a multitude of 
delicate researches. Some of them indeed exhibit the requisite 
degree of accuracy, but others still leave uncertainties to be 
cleared up, by the investigation of objects which admit more 
decisive conclusions. 
The great increase of my collection since the publication of 
my treatise, has put it in my power to correct many of my old 
determinations. Some of these corrections have been consigned 
in my Tableau Comparatif; and since the publication of that 
book, I have continued to occupy myself with the same subject, 
proposing to insert the new results which I have obtained in the 
second edition of my Traité de Mineralogie, which I am prepar- 
ing for the press. 
_ I had no ether instrument for the determination of the angles 
but the goniometer invented by M. Carangeot, by means of 
which one can scarcely hope to come nearer the truth than 
* Translated from the Journal de Physique, 1xxxvii. 233. (October, 1818.) 
+ When treating of the crystals of oxide of tin (Traité de Mineralogie, iv. 153), 
I employed considerations derived from the law of symmetry, which led me to 
infer a difference between the primitive form of this mineral and the cube, frum 
which it does not deviate far. But the only crystals which I had (they were 
_ macles) did not enable me to verify my notions, I pointed out the difference in 
iny Tableau Comparatif, pp. 284 and 285. 
