of IVemf Muhs, and Hau^. Ti 
dary rhomboid with the axis, or with a plane perpendicular ta 
it, will be known. It must only be observed in making use of 
it, that when one of the faces of the secondary rhomboid is pa- 
rallel either to EL or EM ; that is, when the planes of the se- 
condary rhomboid are situated above the edges of the primitive, 
tan a') — 90°) should be preceded \vith the sign minus. 
With this alteration, according as the values of n deduced will 
be positive either greater or less than 1 , or negative either less or 
greater than S, we shall have respectively one of the four cases 
mentioned. Whenw =:l, the secondary rhomboid becomes a 
plane perpendicular to the axis, when n — — % a six-sided 
prism. 
I± is now easy to obtain a formula giving the value of n in 
function of the two angles (P, P), (a”, a”) of the two rhomboids 
for we have found generally. 
COS' 
tan2 ((P,a') — 90°) = 
tan^ ((tt”, a') — 90°) = 
4 cos^ 
cos^ 
(P> P) 
a 
(a«, a") 
a 
: we shall have also 
. - a”) 
4cos^ 
and, by substitu- 
ting these values in the proportion (^A). 
COS' 
(a”, a”) 
2 
COS' 
(P, P) 
COS'^ 
(a% a”) 
COS" 
(P, P) 
(n + Sf; (n-l)» (B). 
a proportion, by means of which we easily find the value of 
~ ^ ^ by the use of logarithms, and subsequently that of n, 
— 1 ® 
This formula leads to some curious remarks. If we call q the 
quotient of the first term by the second, we shall have 
f t f y or = ± V?, and consequently two 
{n — 1)^ ^ n — 1 
different values of n. Therefore a secondary rhomboid of a 
given angle (a”, a”) may be derived in two different ways from 
the primitive ; and if we call n' the index corresponding to the 
