Crystals requiring neither Measurement nor Calculatmi ^35 
also, by Fig. 107. parallel to the intersection of the two planes 
of the fifth modification, replacing the angles aoc^ oed, Fig. 4. 
Here the third formula must be used, and the following values 
substituted in it, 
n^~l. 
m^=z^ JP4 .=^ n^zzil. 
Then, ^ = 2. 
Therefore, the third modification is the result of a decrement 
by two rows in breadth on the edges of the cube, 
Siwth Modyication. — Fig. 107. shews that one plane of this 
modification is parallel to the intersection of the plane of the 
fifth parallel to the diagonal ac, and the plane of the second mo- 
dification w'hich replaces the edge oc, and also to the line of in- 
tersection of the face of the octohedron which replaces the angle 
o, and the plane of the third which replaces the edge oc. There- 
fore, here 
p^-=:9, z=z 1 . 
m^ — 1 n^—l =: 00 . 
W 5 = 1 = 1 . 
— 2 W4 = 1 ^4 =: 00. 
These values being put in the first formula, give = 2, 
the same values when substituted in give ^ = 3. Therc- 
^5 ^5 
fore, p^ 2. The planes of the sixth modifica- 
tion may be consequently considered as the result of an inter- 
mediary decrement by six rows parallel to qc, three parallel to 
oa^ and two parallel to oh. 
As to the fourth modification, there are not sufficient data to 
determine it, no other parallelism being observable than those of 
the planes of this modification with the edges of the octohedron. 
The indices of the five others being now known, nothing is 
easier than to calculate the incidence of any two of their planes. 
I shall now examine Mr Phillips’ paper on the Oxide of Tin. 
Its raerit is so well; known, that I think it almost useless to say, 
that the remarks I am going to make upon it will in no way 
diminish its value, which principally consists in having measured 
