ON THE METHODS OF STUDY OF THE CROWNS OF THE 
HUMAN TEETH, INCLUDING THEIR VARIATIONS. 
BY HARRISON ALLEN, M.D., PHILADELPHIA, PA. 
[Reprinted from the Dental Cosmos for June, 1888.] 
The mammalian tooth has been described almost entirely as a 
topographical area. It possesses " hills," " valleys," " islands," and 
"boundaries." Lyddeker describes the teeth of the rhinoceros with 
the terms "crochet," "costa," "valley," and " collis or hill." Fred. 
Cuvier treats all depressions as the essential elements, and to a 
great extent ignores the cusps,-a disposition that is still followed 
by writers who state that the lower human molar is distinguished 
by a cruciform sulcus. Salter (" Dental Pathology and Surgery," 
London, 1875, p. 28), in speaking of a deformed tooth, says it is 
" bulged in forming a pit." Even so careful a writer as Prof. Flower 
("Encyclo. Britannica," art. "Horse") describes the incisor of the 
horse as undergoing " an involution of the external surface of the 
tooth by which what should properly be the apex is carried deeply 
into the interior of the crown, forming a fossa or pit." In this ac- 
count the morphological integer is a space which performs a definite 
action. The fact that two cusps exist, and that the "pit" is simply 
the interval between them, is not alluded to. I have undertaken 
elsewhere (Dental Cosmos, 1874, xvi, 617) to show the importance of 
describing the cusps of teeth only, and of ignoring the forms of the 
interspaces. 
Apart from the insistence that the cusp is the dental integer, each 
mammalian tooth can be studied from as many as six different points 
of view. That these are not too minutely considered will be evi- 
dent from the following statements. The illustrations will be taken, 
for the most part, from the human subject. 
(1) The study of the size of the tooth when taken in connection 
with the development of the skin is of importance. In the human 
subject hirsute states of skin are associated with small brachyodont 
teeth. The small size of the teeth of the sloth cannot be separated 2 
from an excessively dense hairy growth. The subject requires 
careful elucidation, for if it be accepted that a connection exists 
between the skin and the teeth, other states besides mere hairiness 
enter into the problem if we are to form conclusions from groups so 
far removed from one another as are the Sirenia, the Cetacea, and 
the Edentata. 
(2) The study of the anterior and posterior borders,-the "yokes " 
of the tooth,-the " yokes " especially of the premolars and molars, is 
of great morphological importance. The " yokes" are best developed 
in the teeth of the mandible. The anterior " yoke" has a distinct his- 
tory from the posterior, and is infrequently the seat of development 
of a separate cusp. The posterior "yoke" often furnishes a sep- 
arate cusp. The yoked cusps are always placed in the lin'es of the 
greatest impact, being commonly on the outer side of the tooth and 
passing thence to the middle of the center of the posterior border 
but never to the inner. Their position thus becomes to the observer 
a delicate test of the directions of attrition-movements on the crown. 
I have found it convenient to represent the positions of the "yokes " 
in strict connection with the true cusps, and in enumerating them 
to regard them as parts of fractions. Thus the first molar of the 
right side of the lower jaw in fifty-two examples of human teeth 
exhibited three cusps on the outer and two on the inner side,-the 
tooth of course having five cusps. The formula | expresses the 
number and positions of the cusps if we arbitrarily accept the 
numerator as representing the outer and the denominator as the 
inner part of the tooth. 
The formula represents that the posterior "yoke" is not on 
either the outer or the inner border of the tooth, but in a position 
midway between them. The formula | expresses the fact that the 
posterior " yoke " is absent. 
In 50 examples the first molar yielded the following expression : 
present 34 times. 
fo present 4 times. 
■| present 9 times. 
| present 3 times. 
In 56 examples of the second molar the following was met with : 
| present 5 times. 
fo present 14 times. 
■J present 32 times. 
present 5 times. 
In 30 examples of the third molars the following was seen : 
| present 6 times. 
■|o present 6 times. 
present 13 times. 
| present 5 times. 3 
On the left side the results were so similar that they need not 
be separately tabulated. If the shifting of the cusp from the outer 
side to the center of the posterior border be accepted as a test of 
the position of the greatest impact, it follows that this method of 
studying teeth presents a means of determining that the lateral 
impact is greater in the first molar than in the second, that the pos- 
terior impact is greater in the second than in either the first or the 
third, and that in the third it is indifferent.* 
(3) The foregoing considerations are closely related to the manner 
in which the teeth were worn. I have found it a useful method of 
studying the effects of attrition to observe that the type will pre- 
sent the greatest attrition on the outer border, and the or | type 
will show a distinct disposition to posterior wear,-a fact not men- 
tioned by Topinard ("Anthropology," Eng. Trans., p. 138), who as- 
sumes that the " wear " is always on the outer side. 
If attempts be made to correlate the manner of wearing down of 
the crowns of the molars in man with those of the shapes of the 
condyloid processes and of the glenoid fossae (points which have been 
especially elucidated in quadrupeds by Profs. Cope and Ryder), great 
difficulty will be experienced. After making many observations of 
human crania, I am compelled to acknowledge that, with our present 
means of study, no coordination can be established. 
(4) In every mammalian tooth a disposition exists for the main 
cusp to be duplicated by a second placed to its inner side. It is 
constantly seen that the second cusp is the smaller and is at first 
placed in line with the main cusp. In states of specialization the inner 
cusp in many groups becomes larger than the external, and passes 
backward so as to encroach upon the privileges of a second pair. 
In this manner two lines of changes are detected by which complex 
forms of teeth are evolved from the simple ones,-viz., a duplication 
of the initial cusp on an interior line, and a development of the 
duplicated part posteriorly. As in the case of the "yoke," it is the 
hinder part of the cusp which gains. This variety of tooth-struc- 
ture, while best presented in the tertiary mammals, particularly as 
studied by Cope (see Hayden's " Geological Survey of the Territo- 
ries," iii, 1884), is also seen in the variations of the molars of the 
human subject. 
(5) Yet another method of study of the teeth pertains to the rela- 
tive size of the members of the same series. Thus the comparisons 
of the sizes of the incisors and molars are of first importance. That 
*In "Anthropologia," p. 434, it is stated on the authority of Hamy that in 59 
first mandibular molars 29 were pentacuspid, and in 50 second molars but 10 were 
pentacuspid-the remainder being quadricuspid. The relative positions of the 
cusps are not given. 4 
the first molar should be greatly larger than the second, while the 
third proves to be as large if not larger than the first, forms a 
heterodont series which is opposed to the gradual loss 
before backward. The abrupt is also the unusual, and the breaks 
or " faults " in the series are indicative of vital failure in more than 
one direction. 
(6) The order of congenital loss or excess constitutes the last 
method which will be here named. I need only allude to the 
labors of W. Turner, Spence Bates, W. H. Flower, and lately of 
Schlosser, in this connection. A true method would compel an 
acknowledgment that the missing factors in the dental formula of 
each and every species should be carefully considered by the odonto- 
logist. In a word, that the determination of the missing teeth in the 
formula would be a part of his method of study. 
Series of forms which are constant in one group but variable in 
another closely-allied one are always to be carefully observed. The 
rugae of the mouth in the human subject may be named in this con- 
nection. The dispositions of these folds are variable on the two sides, 
-i. e., the right and the left,-each being disposed in its own way to 
adapt the folds to the conformation of its own parts. The entire 
series would appear to be in coordination to the disposition of the 
facial bones to grow downward rather than forward, and to the fact 
that the involution of the sacs of the permanent incisors takes place 
on the palatal side of the deciduous teeth and creates elements of 
variation in the anterior portion of the hard palate as contrasted 
to the posterior part. The lateral incisors in a normal condition 
always enter the dental arch from the palatal aspect, and this en- 
trance most probably is a disturbing element in the arrangement 
of the rugae, especially at or near the premaxilla.