iia 
Mr, Whewell on calculating 
or if = 3 = i-,r = y, 
the symbol of which is (^ ; g ; r). 
Draw y O, a: M parallel to PQ, meeting hx and Ay. Then 
^ r\ xy.x'? nc.ha nha 
^ ~ xQ kc k 
AO=Ao: — X 0 = ;za(i — yj 
A M = : 
n. ivi — ^ Q 
na . n c 
n k 
k^h' 
Similarly if x N be parallel to PR, AN = 
Hence the equation to the plane x M N is 
na, k J nc * ^ I } nc 
orp-^ + CP — ^l) T+ (P — ^)t—P 
and the equations to planes pqr and PQR 
/>T+9t + ‘/T=i; 
c 
are 
n 
t>^ A- (i) — A- (i) 
\ z 
and their symbols are (p; q\r), {p\p — q; p — r) . 
Also the edges Ay, A z are symmetrical ; and hence we have 
two other co-existent planes {p; r; q)(^p — r; p — q). 
These are included in the formula |(/> ; q,r)(^p; p — q,p — r)| 
The solid angles at y and z are also symmetrical ; and a 
plane being supposed to be formed at y as before, we must 
have a co-existent plane at z. Let p' q' r' be a plane cutting 
off the angle y, and b being the edge of a molecule in the 
direction y z, let yp\ y q\ yr' = hh, kc, I c respectively, and 
let z P', z Q', z R' =yp', y (f^yr' respectively. Then p' cf r' 
