260 
Mr Levy on the Modes of ‘ Notation 
'n 1 n /f -f- vJ 
U‘ 
l ,, n' n !U 4- 
■ , or n" — 
n'" -f n J 4- I 
Therefore, in the present case, 
> .4.2 
±jh 
* J 3 p n -f 1 
fa H-yi 
By means of this equation, and the one before mentioned, 
Zl . — g it will be easy to find the values of — and — , 
x-i—yx x—y *1 *1 
in terms of the other quantities, or inversely the values of 
^ and in terms of w and x 19 z 1 . They will be found re- 
spectively, 
|/j _ (y — ((» + l)z — — g) 
*1 _ ((« + l)« — x — y) ( 2 z — x — y) 
x x _ (x — y)((n + l)z — x— y)j— (x — z) (nx+ny — 2z) 
%i~ ((ra + 1) x— y) \%z — x — y) 
x (()»-}- 1) + ( n + 1 )_y_i + ) ( z i — Xi) | 
z ~ (nz l + x x +y i ) (x x —y x ) 
y _ ((n + 1)3?! + (»+ l);y, + 2z,) {y x — z t ) j 
-* — <»«i + ^1 +%) (4 — ^1) 
These formulae apply only to the case when the faces of the 
.rhomboid a n , forming the superior solid angle, are situated above 
or below the faces forming the superior solid angle of the pri- 
mitive, which is the case when n is positive and greater than 1, or 
negative and greater than z. But, in every other case, it will be 
necessary to use other formulae, because then the angle (i • i) of 
the dodecaedron with respect to the primitive, corresponds to 
the angle { i : i) of the same dodecaedron with respect to the 
111. 
rhomboid a . If — , — , — , still represent the indices of the 
*1 Vi *1 
dodecaedron relative to the rhomboid a * V it is easy to perceive 
that the equations which express their relations to x 9 and z , 
making due attention to the above remark, will be 
