418 Haiiy on the Measuring of the Angles of Crystals. [Junx, 
demi-diagonal 6 c of its base, and ./ 20 for that of the perpendi- 
cular drawn from the centre upon one of the sides.* 
Among the different angles which the faces of the crystals of 
oxide of tin make with each other, there is one which particu- 
larly fixed the attention of Mr. Phillips; that, namely, which 
measures the incidence of s or g (fig. 4) in the variety which 1 
have called bisserdectmale. He was desirous to compare this 
incidence, such as my theory indicates, with that which the 
reflecting goniometer would have given: and as the instrument 
which he possessed was only graduated to 5’, he borrowed one 
of Mr. Carey, which was graduated to half minutes. The 
angle measured by this instrument was 133° 32’ 30%. Accord- 
ing to my theory, it is 133° 29’ 29%. Difference 3’. 
Mr. Phillips having determined all the other angles by his 
ordinary goniometer, I have chosen the one just mentioned in 
preference, to deduce from it geometrically these same angles, 
and to compare them with those which Mr. Phillips obtained by 
mechanical measurement. The ratio which I have employed is 
that of cr toc s (fig. 3), between the perpendicular drawn from 
the centre of the base of the pyramid a fs 6, and one of the 
sides such as a 6. I have found that in order to answer the 
end proposed, we mustmakec r = / 702, andcs = W317, 
Here a remark occurs analogous to that which I made with 
respect to quartz. If we multiply by 2 the two terms of the ratio, 
we obtain / 1404 and W/W 634. Taking away from both sides 
the last cypher, and then dividing by 7, we have cr: cs:: 
a 20:3. Now this is the ratio which I adopted. 
I shall now go over the different faces of the same variety, 
and make a comparison of the results obtained by the different 
methods respecting their incidences. I shall divide them mto 
two series, one of which will comprehend the terminal faces 
P, § (fig. 4), and the other the lateral faces g, 7,1. 
Terminal Faces.—We have here three kinds of results to com- 
pare; namely, 1. Those to which the theory conducts us; 
2. Those determined by Mr. Phillips by means of the reflecting 
goniometer ; 3. Those which he ought to have obtained in order 
to agree with himself; that is to say, those to which we are led 
by calculating from his own data. I shall denote these three 
results by the letters T, G, C. 
Incidence of P on P’”—T, 67° 42’ 32”; C, 67° 48’ 4”; G, 
67° 50’. Diff. with T, 7’ 28” ; and with C,.1’ 56”. 
Incidence of P on P’—T, 133° 36’ 18”; C, 133° 32’ 38”. 
Diff. between T and C, 3’ 40”.—Mr. Phillips has not given the 
measure of this incidence. ; 
_* It results from this determination, that the half of the square 40 of the demi- 
diagonal 5 c is equal to the sum7 + 3 of the lines} sand ¢ ». 
