SS2 M. Levy on the Determinatmi of Seconda/ry Faces in 
7 ) 
that of 3 and 4. From these two equations, the values of ^ 
and ^ are readily found. 
f _J Y -1_ L_ Y_1 
i^g ^2PiXw3|>4 ^^ 4 ^ 3 ) 
By writing in this formula m for w, and reciprocally, the va- 
lue of ^ is obtained. 
JP 5 
Vpi« 
If the two faces 1 and 2 are supposed to be parallel to a dia- 
gonal of the primitive — to a 5, for instance, then the new face 5 
will be parallel to the same diagonal. In that case, = Wi, 
the values of — and^-^ become both the same. 
and m, 
m 
and, by reduction, equal to 
(wg ^4-- mg 714) 
/ l__ J-L + ("-i- 
mi, have entirely disappeared from this 
formula ; and it should be so, since the condition of being pa- 
rallel to a diagonal of the primitive, does not depend upon any 
secondary plane. If the two faces 1 and S are parallel to an 
edge, to oc, for instance, then 5 is parallel to the same \ Pi and 
^3 are infinite. The values of ^ and ^ become so too, 
when the infinite is substituted for and p^ in the general for- 
mula. But if, before making the substitution, we divide the 
one value by the other, we then get 

Pa Pr. ^4 
m, 
n. 
m^p^ 
1 • 
m4^g 
These three formulae, the first principally, are not very simple 5 
but it must be observed, that the problem has been resolved in 
the greatest degree of generality. In most cases that occur, they 
