74 Mr Levy on the modes of Notation 
troduced without changing altogether the notation. Indeed, 
unless the advantages of a new method be very obvious, ought 
we not to adopt that of the man to whom we are indebted for 
the science of crystallography ? 
The formulae I am now going to explain, will therefore, I 
trust, be of some use ; and, at all events, it is easy to deduce 
from the results they lead to, the corresponding signs of Profes- 
sors Weiss and Mohs. 
I shall begin with the forms derived from a rhomboid, which 
are so numerous and so interesting. I denote the different parts 
of it in the same manner as Haiiy. I designate by (P, P) the 
incidence of two of the primitive faces meeting in one of the su- 
perior edges by (P, a !) ; the incidence of one of the primitive 
faces with the plane whose sign is a\ and which replaces the 
summit of the rhomboid by a plane perpendicular to the axis. 
The following relation between (P, P) and (P, «'), is imme- 
diately obtained : 
/X \ ^ cos i (P, P) 
cos ((P, a!) — 90°) = 
I shall have occasion to use, in the following investigations, 
the tangent of the angle (P, a') — DO"" ; that is to say, the 
angle of one of the primitive faces with the axis ; and in order 
to obtain for this new trigonometrical line a formula calculable 
by logarithms, I proceed in the following manner : 
sin2((P,«') — 90°) = 
1 — 
cos 
2i(p, P) 
3 — 4 cos^ I (P, P) 
3 
1 — 2 cos (P, P) sin (P, P) — S sin (P, P) cos (P, P) 
3 ~ 3 sin (P, P) 
sin (P, P) — sinS(P, P) 
3 sin (P, P) - 
6si„^cos(i¥l> ^ 
_ 2 cos sin (M) _ cos 
^ ^ consequently, 
. . (P,P) (P,P) 
6 sin cos 
cos 3 
(P, P) 
