1819.]- Hatiy on the Measuring of the Angles of Crystals. 417 
pyramid of quartz between the perpendicular drawn from the 
centre of the base on one of the sides, and the length of the 
axis; it is very probable that after having considered it, he 
should find a small correction to make in it in order to transform 
it into another ratio much more simple. It would be necessary 
merely to add a single unity to the last figure of the term / 149, 
and then the ratio, by dividing both terms by 30, would become 
that of “5 to V 8, which is precisely that to which I arrived. 
I would answer that the great precision of the instrument which 
I employed does not allow me to alter it. He might ask me to 
how much the difference of the inclination * of the faces of the 
pyramid given by that ratio and by that resulting from the ratio 
7 5 to / 8 would amount. If I should tell him that it amounted 
to 4’, I doubt whether he would not be tempted to throw it rather 
upon the observation than to ascribe it to nature. 
Oxide of Tin. 
In the determinations which Mr. Phillips has published of 
the crystalline forms relative to the mineral substances, which 
have been the subject of the preceding articles, he has merely 
given the inclination of the faces of the primitive form: I have 
deduced from these inclinations those of the faces produced in 
the secondary forms by virtue of the laws of decrement, and I 
have compared with them those which I deduced from the ratio 
adopted between the principal dimensions of the primitive solid, 
as being a limit, the choice of which is pointed out by the cha- 
racter of simplicity. Mr. Phillips has been much move ditfuse 
with respect to oxide of tin. He has measured immediately the 
different inclinations of the faces which terminate the secondary 
forms; so that here I shall have it my power to compare him 
with himself; and what will, I hope, render this comparison 
more instructive and more interesting, a part of these inclinations 
are independent of the primitive angles, and are derived solely 
from the laws of decrement whose existence cannot be called in 
question. cM; 
The primitive form of oxide of tin, as I have given it in my 
Tableau Comparatif, is an octahedron (ig. 2), in which the 
common base of the two pyramids’ of which it is composed is a 
square. The ratio which | have adopted between its principal 
dimensions is such that the oblique edge 0 s (fig. 3) of the 
pyramid, and the demi-diagonal b ¢ of its base, are to each other 
as the numbers 7 to 3, which gives »/ 40 for the value of the 
*. We might have taken for the fundamental angle that which is derived from 
this inclination, as well as that between the faces of the rhomboté,-and, in that 
case, the instrument to agree with itself must have given immediately the angle 
183° 44! 46”. 
Vou. XIII. N° VI. JD) 
