Weiss, Mohs, and Haiiy. 
IS 
tan^((P, «') — 90“) = 
sin^((P, a') — 90“) 
cos"((P, a') — 90°) 
-co.i.2|S.> 
4 cos^ ’ 
a formula which may easily be calculated by logarithms. The 
(p p\ 
quantity — cos 3 -- ^ will always be positive ; for the three 
equal angles (P, P) of the summit of the rhomboid are together 
greater than two right angles, and less than six, consequently 
3(P, P) 
is greater than one right angle, and less than two, and 
/ 
— cos 3 
(p, p) 
IS positive. 
1 shall first consider the rhomboid derived from the primitive, 
and the problem I propose to resolve in this and the following 
cases, is the inverse of the one solved by Plaliy in his Treatise 
on Crystallography. There he gives formulae to calculate the 
incidences of the faces of a secondary form with one another, or 
with the planes of another modification, supposing that their in- 
dices are known; so that in each particular case where the pa- 
rallelism of the edges is not sufficient to determine d priori the 
indices of the modification in contemplation, he is obliged to try 
in his formulas the substitution of different numbers, till he finds 
tliat the incidences calculated are equal or nearly equal to those 
which have been observed. This method is uncertain, and may 
in many cases be very laborious. I shall endeavour, as I have 
already stated, to give formulae to obtain the indices of secon- 
dary planes from the immediate data of observation. 
Let ABCD, Plate III. Fig. 1. be the principal section of the 
primitive, that is, its intersection with a plane passing through 
the axis of the rhomboid, two oblique diagonals, AC, BD, and 
the two corresponding superior edges AD, CB. Let E be the 
middle point of AC, and draw a line parallel to the face of the 
secondary rhomboid. This line will be in one of the four posi- 
tions EF, EL, EM, EN. In the two first cases, the secondary 
rhomboid is said to be the result of a decrement on the superior 
angle of the primitive. The only distinction between the two 
cases is, that, when the face of a secondary rhomboid is parallel 
3 
