124 
Mr. Whewell on calculating 
rs 
By these formulce we may determine the arrangement of 
any set or sets of secondary faces. Thus if we have a symbol 
(/>, q, r) in which p q, q > r; we have 6 faces. The expres- 
sion for r sin. ^ is the same for all : hence they are all at the 
same distance from the summit B. And cos. x will be greater 
as 2^—^ — r is, or as sp — (^ + ^+^) is so. Consequently 
the values of cos. x taken in order of magnitude will corre- 
spond to [p\ q\ r){c[ ;p \ r)(r \ p \ q). The other three values 
be the same, viz. {p;r; q) (q;r;p) (r; q;p); and indicate 
longitudes on the other side of A x. 
The arrangement of the planes is represented in fig. 22. 
It is to be observed that as the order of the Jirst index 
is p, q, r, beginning from x, the order of the second index is 
/>, g, r beginning from y, and of the third p, q, r, beginning 
from z. 
44. (2) In the Prism. Let the line IF, fig. 21, parallel to 
A z, be taken for the axis of the ellipsoid ; and let the posi- 
tion of P be determined by (x) the longitude which is measured 
by the angle between the planes FID and FIP ; and by (x 
the latitude, the angle PIN. 
It is evident that tan. x will be greater as ^ is greater. 
Let (^ ; g ; r) be the symbol of the plane, and its equation will 
greater ; because a and b are constant for the same substance. 
Also sin, [X is greater as PN is greater ; that is, as ^ 
And the values of lO, ON, NP, will be 
p a 
qb 
r c 
IS SO. 
