261 
of Weiss, Mohs , and Haiiy. 
ff — g _ »! — ffi „ nd ^ _ . wa-) + z, + .V, 
*—*/ yi — Z\ c ^ + 3/ + 
from which the following values are readily obtained : 
y __ (gi— ^i)(wa? x +.yi+gi) — fa— ^i)<^a , iH-TOy I +.wgi+.y 1 +g t ) 
* (s x + y L — *fi) 4- «/x 4- *i) 
£ _ (ffi — *i) (wa> I +,y I 4- g x ) — (ay— s f ) (ga?i + 4- m*i4-#i 4- * x ) 
* " rf fe + yr-%0i) ( n ^i +yi+ 
y t __ ( z — J/) .(w,4? 4- n y — - %z) — (a? — 3/) (Vi£ 4 - z — x — y) 
z L ~~ (z — x) (nx 4- ny — $2#) 4- (x — ■ ?/) (^3 4- £ — ; ; a? - — ?/) 
^x_ _ ; 4 ; : 1 ; (pc 4-2/ ~ %*) (x +y — nz — z)- 
z L ~ (z — x) (nx 4- ny— 2 z) 4- (x —y) (nz 4- z — x — y) 
Which formulas ought to be used instead of the four preceding, * 
when n is positive and less than 1 , or negative and less than 52. 
If, in the two last formulae, n is supposed to be equal to 
■ — they become 
y± — (2/ — z) (^4-2/4 - 4s ) — (x —y ) (z — %x — %/) 
*1 (c V — z) (x + y 4- 4sz) 4- (v—y) (z — 2x — 2y) 
x L _ (x 4- y — 2z) (2x 4- 2y — z) 
zl ~ (x — z) (x + y 4- 4#) + (x — y) (z — 2x — 2y) 
These formulae, therefore, determine the decrement which 
should take place upon the rhomboid a % or to produce the 
same dodecaedron as that whose sign with respect to the primi- 
tive is ( b * hi> fc). But the rhomboid e ^ measures the same an- 
gle as the primitive, and differs only from it as to its position, 
its oblique diagonals corresponding to the superior edges of the 
primitive, and its superior edges to the oblique diagonals. Con- 
sequently, if a dodecaedron was derived from the primitive by 
an intermediary decrement, the indices of which were — , — — 
oc L y L z L ] 
the ratios between x L y L z t being determined by the two prece- 
ding formulae, it would be equal to the dodecaedron, whose 
sign is (b* b v ¥), but its position with respect to the primitive 
would be different, since it would be situated relatively to the 
rhomboid f4, precisely as the dodecaedron (b* b y Ip) is relative- 
