178 On the Humite of Monte Somma. 
for figure III, 9. By keeping this in view, the general symbols 
are easily deduced and need not be here repeated : (e.g., for r in 
fig. III, the special symbol is 1:15: 'y, and hence the general 
symbol will be 1: '§ : 18; for m?* the special symbol is 1: 4 
: 3, and therefore the general symbol is 1: 5, : ;'s). 
The following are some of the angles obtained by M. Scacchi, 
calculating from the dimensions of the common type. 
Type I, (fig. 1.) —A on ¢ 138° 38’, on i? 124° 16’, on 73 102° 48’. 
A on r 135° 52’, on r? 129° 30’, on vr? 121° 44’, on r* 112° 24’, on 
r5 101° 39’. 
A on n 116° 34’, on n2 99° 28’. 
A on e 140° 49’, on e? 134° 28’, on e? 126° 21’, on e* 116° 08’, on 
0 se 
B on o 144° 14’, on 0? 114° 50’. 
Type Il, (fig. II.) —A on ¢ 122° 27’, 
A on r 135° 17', on r? 125° 48’, on r3 113° 24’, on r+ 98° 19’. 
A on » 125°, on n? 103° 8’, 
A on m 114° 55’, on m? 95° 19’, 
A on e 135° 51’, on e? 108° 58’. 
Type Ill, (fig. IlIl.)—A on ¢ 136° 40’, on i2 125° 144’, on 13 109° 27’. 
A on 7 140° 15’, on r2136° 11’, on r2131° 24’, on r+ 125° 48’, on r3 
119° 17’, on 7®111° 50’, on 77 103° 31’, on r® 94° 35’. 
A. on n 132° 13’, on n2 122° 57, on n® 111° 15’, on n* 97° 23. 
A on m'114° 55’, on m2 92° 57°. 
A on ¢ 143° 10’, on e? 133° 39’, on e2 119° 47’, on e* 100° 48’. 
Passing by, for the present, other details in the admirable paper 
of M. Scacchi, we proceed to a few remarks on another mode of 
viewing these crystals and to some deductions therefrom. 
The difficulty in referring the three dissimilar types to a com- 
mon fundamental form or to forms approximately identical, arises 
from the fact that the three crystals have no planes in common 
that can be referred to such a form. The planes of the series 7; 
referred to acommon type for all the crystals, are all different im 
symbol on one erystal, from what they are on either of the others; 
and so with the other series. For example, in the series e, fot 
figure I, the planes are 1: 3, 1; 4). $22 4, 12 $5 toe ogee 
» 1:3, 1:33 for igure I, 1:7, 1:4,1:3, 1:4. The planes 
here are not identical in any’ one instanee, neither have they 
a simple relation. And again we observe that planes which 
have nearly the same inclination towards A, are still different 
nes. 
We observe that the inclinations of A on ¢ in figures i and Ul 
and on @in figure IL, differ but little from one another. In figure 
