On the Humite of Monte Somma. 179 
this angle is 124° 16’; in figure II, 122° 27’; in figure III, 125° 
144’. 'The whole range of difference is only 2° 46’.* Taking these 
planes as homologous, the difference in the dimensions of the three 
types is small, not exceeding what in other species is known 
to be produced by small variations in composition dependent on 
isomorphous substitutions. Moreover, the symbols of the planes, 
on this plan, have greater simplicity, while affording, of course, 
the same angles as in Scacchi’s method. 
Ve may consider the fundamental octahedron as belonging 
to the r series (instead of the m series); and then taking @? in 
figures [ and IIf and i in figure Il,as the form 4: @: 1 the axes 
for the three forms will be as follows :— 
a b Cc 
i agg age Ge . , 18588: 1 : 0:4629 
wr ihe : ; : . 1:4536 : 1: 0:4629 
“Hl, ; : , . 13115: 1: 0-4629 
It will be observed that 
@ in figure I is one third of 4°0764 (a of type I.) 
a II is one half of 29090 (a of type IL) 
a “ IIL is one fourth of 52480 (a of type IIL.) - 
Also ¢ in each, is one half of ¢ in the types I, IL, Il, which is 
Owing to our taking as the zone of the fundamental form, the 
r series instead of the m series,—the axes c in these rah having 
the relation of 2: 1, 
From the above, the vertical axes in these forms is obseowed to 
vary nearly as 136: 145: 131, not a large variation. This ratio 
. JS equivalent to 
14 :.15.: 134, 
which corresponds to the ratio 7: 5: 9 between Scacchi’s verti- 
a axes, as will be deduced by taking into view the ratio which 
Sists ‘between a in each of the three types o . Scacchi, an 
‘th @ in our fundamental forms as above given. A, 
e have repeated the three figures of Humite, (see figs. 
B, C,) with a new lettering, the euclisgrohie piers. being 
(Scat re ee ad ee 
* In Scacchi’s method of viewing the crystals, se OEY referred to oe xf 
type, have the following symbols:—7i2 in fig. | =1:« :# ; ¢ in fig. 
#* in fig. UT,=1:«:4. In the author's Sod, Oa ie tawaiei: a; 6 
(equivalent to 1 : ). 
is litem as ; follow 
Since £0764 : 2°9090::7:5, pe £0764=3X1 ‘8588 and pe rr ‘4536 nearly, 
 Therefi fore, 8X 18588 : diol deag dt 27: 
13588 : 14586 7:2%723X5 pelts 16 
y the same Process the other ratios are obtained. 
jetta oS 
gee de 
