258 
Mr Levy on the Modes of Notation 
Art. V . — On the Modes of Notation erf Weiss , Mohs , and 
Mail y. By M. Levy, M. A. &c. Communicated by the 
Author. (Continued from page 185.) 
The next question to solve, is to determine the laws of decre- 
ments, by which the hypothetical forms which have just been con- 
sidered may be derived from the adopted primitive rhomboid. 
This may be effected without difficulty, by means of the formu- 
lae I have demonstrated in one of the preceding numbers of the 
Philosophical Journal of Edinburgh, to discover from certain 
parallelisms of edges, the indices of a secondary plane. To find 
the law, for instance, from which may be derived the rhomboid, 
the superior edges of which correspond to the lines da , dc of 
the dodecaedron, it will be sufficient to find the indices of a 
plane parallel to the diagonal mn of the primitive Fig. 2, and 
also to the intersection da of two faces of the dodecaedron. 
Now, the formula above mentioned, in the case where the se- 
condary plane, whose indices are required, is parallel to one of 
the diagonals of the primitive, is 
1 
1 
m 4 
m 5 n 4 
n 5 ( 1 
1 ^ 
( 1 - 1 
f 4 
P s nJ 
\m 5 P 4 P 5 m 4 / 
In the present case we 
have — 
m 5 
111 
— 2 , — = y. Substituting these values, the formula gives, 
n, P /> 
yx — xz 
x 
— ^ = 7-5 — - f ~ r = — T- 11 ; and therefore the 
n 5 (yZ — z' 2 ) — (xy — xz) y + z — x 
rhomboid assumed as a hypothetical primitive form, may be de- 
rived from the primitive rhomboid by a decrement of z — x 
00 
rows in breadth on the superior angle. If the quantity 
y+*' 
x 
X 
was negative, it would result of a decrement by 
-(y + z — x) 
x 
rows 
in breadth on the inferior angle. In the same manner, it 
