‘ 
1878. | 259 {Frazer. 
not every man to get his own crystallographic formula, at least that of his 
race to be expressed. 
It must be borne in mind too that the planes here shown are not abso- 
lutely correct, but simply an arbitrary series laid on by that most difficult 
of all persons to calculate exactitudes from — a skillful artist. 
In spite of this (and to give the names rather of the things each indi- 
vidual most nearly resembles than what it actually is, and thus aid the 
student in deriving and placing them), the following attempt was made : 
Even with the most symmetrical human face a slight consideration will 
convince one that the Triclinic System or the System of Pinacoids is the 
only one which will serve to represent all the planes; nevertheless the zone 
of macrodemes require a monoclinic habit : and even this fails in many cases 
owing to a lack of parallel pairs: so that one is obliged to introduce the 
somewhat crystallographically confusing notion of a single plane. 
Yet the general parameter relations of such a plane and the position 
which it occupies above, below ; in front, in rear ; right, or left ; being indi- 
cated by P-, P., -P, .P for the front (when necessary, adding for the rear 
P’, P,, /P, ,P) its actual position on the model may be sufficiently well 
known. 
Not that this is not found in nature for some calamine and tourmalines 
have the peculiarity of being asymmetrical or hemimorphic; and instances 
of a lower termination of one basal plane and an upper one of a pyramid 
are not rare. 
Assuming the upper trapezoid on the model to be the basal plane or 0P 
of some triclinic prototype, the following represent some of the principal 
forins represented : 
PoE Mages cee ee anh nae ate vies upper forehead. | 
fil Lill Oe 2 eee ie ie ek Se middle frontal. 
1 § (OV Peo TS ec So le ae eg bridge of nose. Zone 
TAB Gos acre sas ....-middle of upper lip. } of 
s Pp C2) GW ei ere OIOOL Ob ociCieenac - upper chin. Macrodomes. 
TREE Osh a Corte ae orisha nia oes oe ei middle chin. | 
COs tanta wine wien o1a Semiae -.-.-under chin. | 
0 P Top of head and plane of nostrils.... Basal Pinacoid. 
o — o Front and back of neck............ Macropinacoid. 
« P o Side planes of neck...... Waar slats Brachypinacoid. 
1111) Sure Ae ce EO erie upper skull (4 planes). 
TPS aorsre cracls sides serksisina upper skull (4 planes). 
q’P: ..side frontals and lower occiput (4 planes). 
r'P- ..side occiput and middle cheeks (4 planes). 
t'P: ..side skull front and above ears (2 planes). 
Nlew yn da emosnce coke cheeks beside nose (2 planes). J 
Pyramids. 
* Represented also in two occipital planes, 3 in all. 
+ Represented also in one occipital plane, 2 in all. 
