1819.] Haiiy on the Measuring of the Angles of Crystals. 421 
goniometer differ more, especially the second, from the first 
result than all those hitherto mentioned. This is what should 
not have been expected; for, according to Mr. Phillips, the 
crystals of the distique variety on which he operated united at 
once the merit of singular beauty and of very small size, a condi- 
tion so important for the precision of measurements that the 
same gentleman afterwards states, that crystals of a certain size, 
even those whose faces appear most smooth and level, presented 
very sensible differences in the determination of their angles ; 
while, on the contrary, those of small size give uniform results. 
Hence he concludes that they are the only ones which can be 
depended on when precision is wanted. 
{ shail add here a consideration which flows naturally from 
what has preceded. The table of angles determined by Mr. 
Phillips on the different varieties of oxide of tin, by means of the 
reflecting goniometer, notwithstanding the superiority of that 
instrument over the common goniometer and the dexterity of the 
experimenter, presents a series of results which are really only 
approximations, which, having been determined independently, 
have no bond of union, and some of which even contradict 
others ; far from agreeing with the simple laws of structure, 
they would tend to transform them into so many. anomalies. 
If we supposed, for example, that the incidence of 7 on 7’ on the 
two sides of g (fig. 4) was exactly 143° 10’, as Mr. Phillips indi- 
eates the two sides adjacent to the right angle in the measuring 
triangle would be to each other (confining ourselves to five 
figures) as 94878 : 31393, and the corresponding number of 
ranges subtracted would have the same ratio. Substitute for 
these two series the numbers 3 and 1, to which they are nearly 
proportional, and you have a simple law, which is that of nature. 
This example shows of how much consequence it is to the pro- 
gress of the sciences to join theory with observation in order to 
regulate it, to remove the want of connexion, which would 
otherwise subsist between the results, and to compose a whole 
all the parts of which harmonize with each other. 
Sulphate of Lead. 
The description which I am going to give of the crystals of 
sulphate of lead is derived from observations made since the 
publication of my Tableau Comparatif. The examination of the 
new crystals sent me from England during that interval has 
enabled me to discover a considerable error contained in my 
former determination.* But the most decisive observations 
on the subject were obtained from a very interesting set 
* This error, amounting to about 8°, was owing to the extreme rarity of crys- 
tals of sulphate of lead at the time of my determination. To measure the primitive 
angles, I made use of a small fragment, in which the natural joints brought into 
view by mechanical division had an unequal tissye which céncealed their true 
Jnclipations, 
