are the globular form of the cranium, united as it is with the prolate
spheroidal form produced by the parts which constitute the face, and the
approximation of the profile to the vertical; for in none of the lower
animals does the skull present so near a resemblance to a combination
of these geometric forms, nor the plane of the face to this direction.
We also find that although these peculiar characteristics are variously
modified among the numerous races of mankind, yet one law appears to
govern the beauty of the whole. The highest and most cultivated of these
races, however, present only an approximation to the perfect development
of those distinguishing marks of humanity; and therefore the beauty of
form and proportion which in nature characterises the human head and
countenance, exhibits only a partial development of the harmonic law of
visible beauty. On the other hand, we find that, in their sculpture, the
ancient Greeks surpassed ordinary nature, and produced in their beau
ideal a species of beauty free from the imperfections and peculiarities
that constitute the individuality by which the countenances of men are
distinguished from each other. It may be requisite here to remark, that
this species of beauty is independent of the more intellectual quality
of expression. For as Sir Charles Bell has said, “Beauty of countenance
may be defined in words, as well as demonstrated in art. A face may
be beautiful in sleep, and a statue without expression may be highly
beautiful. But it will be said there is expression in the sleeping figure
or in the statue. Is it not rather that we see in these the capacity
for expression?—that our minds are active in imagining what may be the
motions of these features when awake or animated? Thus, we speak of an
expressive face before we have seen a movement grave or cheerful, or any
indication in the features of what prevails in the heart.”
This capacity for expression certainly enhances our admiration of the
human countenance; but it is more a concomitant of the primary cause of
its beauty than the cause itself. This cause rests on that simple and
secure basis—the harmonic law of nature; for the nearer the countenance
approximates to an harmonious combination of the most perfect figures in
geometry, or rather the more its general form and the relation of its
individual parts are arranged in obedience to that law, the higher its
degree of beauty, and the greater its capacity for the expression of the
passions.
Various attempts have been made to define geometrically the difference
between the ordinary and the ideal beauty of the human head and
countenance, the most prominent of which is that of Camper. He traced,
upon a profile of the skull, a line in a horizontal direction, passing
through the foramen of the ear and the exterior margin of the sockets of
the front teeth of the upper jaw, upon which he raised an oblique line,
tangential to the margin of these sockets, and to the most prominent part
of the forehead. Agreeably to the obliquity of this line, he determined
the relative proportion of the areas occupied by the brain and by the
face, and hence inferred the degree of intellect. When he applied this
measurement to the heads of the antique statues, he found the angle much
greater than in ordinary nature; but that this simple fact afforded no
rule for the reproduction of the ideal beauty of ancient Greek art, is
very evident from the heads and countenances by which his treatise is
illustrated. Sir Charles Bell justly remarks, that although, by Camper’s
method, the forehead may be thrown forward, yet, while the features
of common nature are preserved, we refuse to acknowledge a similarity
to the beautiful forms of the antique marbles. “It is true,” he says,
“that, by advancing the forehead, it is raised, the face is shortened,
and the eye brought to the centre of the head. But with all this, there
is much wanting—that which measurement, or a mere line, will not shew
us.”—“The truth is, that we are more moved by the features than by the
form of the whole head. Unless there be a conformity in every feature to
the general shape of the head, throwing the forehead forward on the face
produces deformity; and the question returns with full force—How is it
that we are led to concede that the antique head of the Apollo, or of the
Jupiter, is beautiful when the facial line makes a hundred degrees with
the horizontal line? In other words—How do we admit that to be beautiful
which is not natural? Simply for the same reason that, if we discover a
broken portion of an antique, a nose, or a chin of marble, we can say,
without deliberation—This must have belonged to a work of antiquity;
which proves that the character is distinguishable in every part—in each
feature, as well as in the whole head.”
Dr Oken says upon this subject:[17]—“The face is beautiful whose nose is
parallel to the spine. No human face has grown into this estate; but
every nose makes an acute angle with the spine. The facial angle is, as
is well known, 80°. What, as yet, no man has remarked, and what is not to
be remarked, either, without our view of the cranial signification, the
old masters have felt through inspiration. They have not only made the
facial angle a right angle, but have even stepped beyond this—the Romans
going up to 96°, the Greeks even to 100°. Whence comes it that this
unnatural face of the Grecian works of art is still more beautiful than
that of the Roman, when the latter comes nearer to nature? The reason
thereof resides in the fact of the Grecian artistic face representing
nature’s design more than that of the Roman; for, in the former, the nose
is placed quite perpendicular, or parallel to the spinal cord, and thus
returns whither it has been derived.”
Other various and conflicting opinions upon this subject have been
given to the world; but we find that the principle from which arose
the ideal beauty of the head and countenance, as represented in works
of ancient Greek art, is still a matter of dispute. When, however, we
examine carefully a fine specimen, we find its beauty and grandeur to
depend more upon the degree of harmony amongst its parts, as to their
relative proportions and mode of arrangement, than upon their excellence
taken individually. It is, therefore, clear that those (and they are
many) who attribute the beauty of ancient Greek sculpture merely to a
selection of parts from various models, must be in error. No assemblage
of parts from ordinary nature could have produced its principal
characteristic, the excess in the angle of the facial line, much less
could it have led to that exquisite harmony of parts by which it is so
eminently distinguished; neither can we reasonably agree with Dr Oken and
others, who assert that it was produced by an exclusive degree of the
inspiration of genius amongst the Greek people during a certain period.
That the inspiration of genius, combined with a careful study of nature,
were essential elements in the production of the great works which have
been handed down to us, no one will deny; but these elements have existed
in all ages, whilst the ideal head belongs exclusively to the Greeks
during the period in which the schools of Pythagoras and Plato were open.
Is it not, therefore, reasonable to suppose, that, besides genius and the
study of nature, another element was employed in the production of this
excellence, and that this element arose from the precise mathematical
doctrines taught in the schools of these philosophers?
An application of the great harmonic law seems to prove that there is no
object in nature in which the science of beauty is more clearly developed
than in the human head and countenance, nor to the representations of
which the same science is more easily applied; and it is to the mode
in which this is done that the varieties of sex and character may be
imparted to works of art. Having gone into full detail, and given ample
illustrations in a former work,[18] it is unnecessary for me to enter
upon that part of the subject in this _résumé_; but only to shew the
typical structure of beauty by which this noble work of creation is
distinguished.
The angles which govern the form and proportions of the human head and
countenance are, with the right angle, a series of seven, which, from the
simplicity of their ratios to each other, are calculated to produce the
most perfect concord. It consists of the right angle and its following
parts—
Tonic. Dominant. Mediant. Subtonic.
(¹⁄₂) (¹⁄₃) (¹⁄₅) (¹⁄₇)
(¹⁄₄) (¹⁄₆)
These angles, and the figures which belong to them, are thus arranged:—
[Sidenote: Plate IX.]
The vertical line A B (Plate IX. fig. 2) represents the full length of
the head and face. Taking this line as the greater axis of an ellipse of
(¹⁄₃), such an ellipse is described around it. Through A the lines A G,
A K, A L, A M, and A N, are drawn on each side of the line A B, making,
with the vertical, respectively the angles of (¹⁄₃), (¹⁄₄), (¹⁄₅), (¹⁄₆),
and (¹⁄₇). Through the points G, K, L, M, and N, where these straight
lines meet the curved line of the ellipse, horizontal lines are drawn
by which the following isosceles triangles are formed, A G G, A K K, A
L L, A M M, and A N N. From the centre X of the equilateral triangle
A G G the curvilinear figure of (¹⁄₂), viz., the circle, is described
circumscribing that triangle.
The curvilinear plane figures of (¹⁄₂) and (¹⁄₃), respectively, represent
the solid bodies of which they are sections, viz., a sphere and a prolate
spheroid. These bodies, from the manner in which they are here placed,
are partially amalgamated, as shewn in figures 1 and 3 of the same plate,
thus representing the form of the human head and countenance, both in
their external appearance and osseous structure, more correctly than they
could be represented by any other geometrical figures. Thus, the angles
of (¹⁄₂) and (¹⁄₃) determine the typical form.
From each of the points _u_ and _n_, where A M cuts G G on both sides of
A B, a circle is described through the points _p_ and _q_, where A K cuts
G G on both sides of A B, and with the same radius a circle is described
from the point _a_, where K K cuts A B.
The circles _u_ and _n_ determine the position and size of the eyeballs,
and the circle _a_ the width of the nose, as also the horizontal width of
the mouth.
The lines G G and K K also determine the length of the joinings of the
ear to the head. The lines L L and M M determine the vertical width of
the mouth and lips when at perfect repose, and the line N N the superior
edge of the chin. Thus simply are the features arranged and proportioned
on the facial surface.
It must, however, be borne in mind, that in treating simply of the
æsthetic beauty of the human head and countenance, we have only to do
with the external appearance. In this research, therefore, the system
of Dr Camper, Dr Owen, and others, whose investigations were more of
a physiological than an æsthetic character, can be of little service;
because, according to that system, the facial angle is determined by
drawing a line tangential to the exterior margin of the sockets of
the front teeth of the upper jaw, and the most prominent part of the
forehead. Now, as these sockets are, when the skull is naturally clothed,
and the features in repose, entirely concealed by the upper lip, we must
take the prominent part of it, instead of the sockets under it, in order
to determine properly this distinguishing mark of humanity. And I believe
it will be found, that when the head is properly poised, the nearer the
angle which this line makes with the horizontal approaches 90°, the more
symmetrically beautiful will be the general arrangement of the parts (see
line _y z_, figure 3, Plate IX.).
THE SCIENCE OF BEAUTY, AS DEVELOPED IN THE FORM OF THE HUMAN FIGURE.
The manner in which this science is developed in the symmetrical
proportions of the entire human figure, is as remarkable for its
simplicity as it has been shewn to be in those of the head and
countenance. Having gone into very full details, and given ample
illustration in two former works[19] upon this subject, I may here
confine myself to the illustration of one description of figure, and to a
reiteration of some facts stated in these works. These facts are, _1st_,
That on a given line the human figure is developed, as to its principal
points, entirely by lines drawn either from the extremities of this line,
or from some obvious or determined localities. _2d_, That the angles
which these lines make with the given line, are all simple sub-multiples
of some given fundamental angle, or bear to it a proportion expressible
under the most simple relations, such as those which constitute the scale
of music. _3d_, That the contour is resolved into a series of ellipses
of the same simple angles. And, _4th_, That these ellipses, like the
lines, are inclined to the first given line by angles which are simple
sub-multiples of the given fundamental angle. From which four facts,
and agreeably to the hypothesis I have adopted, it results as a natural
consequence that the only effort which the mind exercises through the
eye, in order to put itself in possession of the data for forming its
judgment, is this, that it compares the angles about a point, and thereby
appreciates the simplicity of their relations. In selecting the prominent
features of a figure, the eye is not seeking to compare their relative
distances—it is occupied solely with their relative positions. In tracing
the contour, in like manner, it is not left in vague uncertainty as
to what is the curve which is presented to it; unconsciously it feels
the complete ellipse developed before it; and if that ellipse and its
position are both formed by angles of the same simple relative value as
those which aided its determination of the positions of the prominent
features, it is satisfied, and finds the symmetry perfect.
Müller, and other investigators into the archæology of art, refer to the
great difficulty which exists in discovering the principles which the
ancients followed in regard to the proportions of the human figure, from
the different sexes and characters to which they require to be applied.
But in the system thus founded upon the harmonic law of nature, no such
difficulty is felt, for it is as applicable to the massive proportions
which characterise the ancient representations of the Hercules, as to the
delicate and perfectly symmetrical beauty of the Venus. This change is
effected simply by an increase in the fundamental angle. For instance,
in the construction of a figure of the exact proportions of the Venus,
the right angle is adopted. But in the construction of a figure of the
massive proportions of the Hercules, it is requisite to adopt an angle
which bears to the right angle the ratio of 6:5. The adoption of this
angle I have shewn in another work[20] to produce in the Hercules those
proportions which are so characteristic of physical power. The ellipses
which govern the outline, being also formed upon the same larger class
of angles, give the contour of the muscles a more massive character. In
comparing the male and female forms thus geometrically constructed, it
will be found that that of the female is more harmoniously symmetrical,
because the right angle is the fundamental angle for the trunk and the
limbs as well as for the head and countenance; while in that of the male,
the right angle is the fundamental angle for the head only. It may also
be observed, that, from the greater proportional width of the pelvis
of the female, the centres of that motion which the heads of the thigh
bones perform in the cotyloid cavities, and the centres of that still
more extensive range of motion which the arm is capable of performing at
the shoulder joints, are nearly in the same line which determines the
central motion of the vertebral column, while those of the male are not;
consequently all the motions of the female are more graceful than those
of the male.
This difference between the fundamental angles, which impart to the
human figure, on the one hand, the beauty of feminine proportion and
contour, and on the other, the grandeur of masculine strength, being in
the ratio of 5:6, allows ample latitude for those intermediate classes of
proportions which the ancients imparted to their various other deities
in which these two qualities were blended. I therefore confine myself to
an illustration of the external contour of the form, and the relative
proportions of all the parts of a female figure, such as those of the
statues of the Venus of Melos and Venus of Medici.
The angles which govern the form and proportions of such a figure are,
with the right angle, a series of twelve, as follows:—
Tonic. Dominant. Mediant. Subtonic. Supertonic.
(¹⁄₂) (¹⁄₃) (¹⁄₅) (¹⁄₇) (¹⁄₉)
(¹⁄₄) (¹⁄₆) (¹⁄₁₀) (¹⁄₁₄)
(¹⁄₈) (¹⁄₁₂)
These angles are employed in the construction of a diagram, which
determines the proportions of the parts throughout the whole figure.
Thus:—
[Sidenote: Plate X.]
Let the line A B (fig. 1, plate X.) represent the height of the figure
to be constructed. At the point A, make the angles of C A D (¹⁄₃), F A G
(¹⁄₄), H A I (¹⁄₅), K A L (¹⁄₆), and M A N (¹⁄₇). At the point B, make
the angles K B L (¹⁄₈), U B A (¹⁄₁₂), and O B A (¹⁄₁₄).
Through the point K, in which the lines A K and B K intersect one
another, draw P K O parallel to A B, and through C F H and M, where
this line meets A C, A F, A H, and A M, draw C D, F G, H I, and M N,
perpendicular to A B; draw also K L perpendicular to A B; join B F and
B H, and through C draw C E, making with A B the angle (¹⁄₂), which
completes the arrangement of the eleven angles upon A B; for F B G is
very nearly (¹⁄₁₀), and H B I very nearly (¹⁄₉).
At the point _f_, where A C intersects O B, draw _f a_ perpendicular to
A B; and through the point _i_, where B O intersects M N, draw S _i_ T
parallel to A C.
Through _m_, where S _i_ T intersects F B, draw _m n_; through _β_, where
S _i_ T intersects K B, draw _β w_; through T draw T _g_, making an angle
of (¹⁄₃) with O P. Join N P, M B, and _g_ P, and where N P intersects K
B, draw Q R perpendicular to A B.
On A E as a diameter, describe a circle cutting A C in _r_, and draw _r
o_ perpendicular to A B.
With A _o_ and _o r_ as semi-axes, describe the ellipse A _r e_, cutting
A H in _t_; and draw _t u_ perpendicular to A B. With A _u_ and _t u_, as
semi-axes describe the ellipse A _t d_. On _a_ L, as major axis, describe
the ellipse of (¹⁄₃).
For the side aspect or profile of the figure the diagram is thus
constructed—
On one side of a line A B (fig. 2, Plate X.) construct the rectilinear
portion of a diagram the same as fig. 1. Through _i_ draw W Y parallel to
A B, and draw A _z_ perpendicular to A B. Make W _a_ equal to A _a_ (fig.
1), and on _a l_, as major axis, describe the ellipse of (¹⁄₄). Through
_a_ draw _a p_ parallel to A F, and through _p_ draw _p t_ perpendicular
to W Y. Through _a_ draw _f a u_ perpendicular to W Y.
Upon a diameter equal to A E describe a circle whose circumference shall
touch A B and A _z_. With semi-axes equal to A _o_ and _o r_ (fig.
1), describe an ellipse with its major axis parallel to A B, and its
circumference touching O P and _z_ A.
[Sidenote: Plate XI.]
Thus simply are the diagrams of the general proportions of the human
figure, as viewed in front and in profile, constructed; and Plate XI.
gives the contour in both points of view, as composed entirely of the
curvilinear figures of (¹⁄₂), (¹⁄₃), (¹⁄₄), (¹⁄₅), and (¹⁄₆).
Further detail here would be out of place, and I shall therefore refer
those who require it to the Appendix, or the more elaborate works to
which I have already referred.
The beauty derived from proportion, imparted by the system here pointed
out, and from a contour of curves derived from the same harmonic angles,
is not confined to the human figure, but is found in various minor
degrees of perfection in all the organic forms of nature, whether animate
or inanimate, of which I have in other works given many examples.[21]
THE SCIENCE OF BEAUTY, AS DEVELOPED IN COLOURS.
There is not amongst the various phenomena of nature one that more
readily excites our admiration, or makes on the mind a more vivid
impression of the order, variety, and harmonious beauty of the creation,
than that of colour. On the general landscape this phenomenon is
displayed in the production of that species of harmony in which colours
are so variously blended, and in which they are by light, shade, and
distance modified in such an infinity of gradation and hue. Although
genius is continually struggling, with but partial success, to imitate
those effects, yet, through the Divine beneficence, all whose organs of
sight are in an ordinary degree of perfection can appreciate and enjoy
them. In winter this pleasure is often to a certain extent withdrawn,
when the colourless snow alone clothes the surface of the earth. But
this is only a pause in the general harmony, which, as the spring
returns, addresses itself the more pleasingly to our perception in its
vernal melody, which, gradually resolving itself into the full rich hues
of luxuriant beauty exhibited in the foliage and flowers of summer,
subsequently rises into the more vivid and powerful harmonies of autumn’s
colouring. Thus the eye is prepared again to enjoy that rest which such
exciting causes may be said to have rendered necessary.
When we pass from the general colouring of nature to that of particular
objects, we are again wrapt in wonder and admiration by the beauty and
harmony which so constantly, and in such infinite variety, present
themselves to our view, and which are so often found combined in the
most minute objects. And the systematic order and uniformity perceptible
amidst this endless variety in the colouring of animate and inanimate
nature is thus another characteristic of beauty equally prevalent
throughout creation.
By this uniformity in colour, various species of animals are often
distinguished; and in each individual of most of these species, how much
is this beauty enhanced when the uniformity prevails in the resemblance
of their lateral halves! The human countenance exemplifies this in a
striking manner; the slightest variety of colour between one and another
of the double parts is at once destructive of its symmetrical beauty.
Many of the lower animals, whether inhabitants of the earth, the air, or
the water, owe much of their beauty to this kind of uniformity in the
colour of the furs, feathers, scales, or shells, with which they are
clothed.
In the vegetable kingdom, we find a great degree of uniformity of colour
in the leaves, flowers, and fruit of the same plant, combined with all
the harmonious beauty of variety which a little careful examination
develops.
In the colours of minerals, too, the same may be observed. In short, in
the beauty of colouring, as in every other species of beauty, uniformity
and variety are found to combine.
An appreciation of colour depends, in the first place, as much upon the
physical powers of the eye in conveying a proper impression to the mind,
as that of music on those of the ear. But an ear for music, or an eye for
colour, are, in so far as beauty is concerned, erroneous expressions;
because they are merely applicable to the impression made upon the
senses, and do not refer to the æsthetical principles of harmony, by
which beauty can alone be understood.
A good eye, combined with experience, may enable us to form a correct
idea as to the purity of an individual colour, or of the relative
difference existing between two separate hues; but this sort of
discrimination does not constitute that kind of appreciation of the
harmony of colour by which we admire and enjoy its development in nature
and art. The power of perceiving and appreciating beauty of any kind,
is a principle inherent in the human mind, which may be improved by
cultivation in the degree of the perfection of the art senses. Great
pains have been bestowed on the education of the ear, in assisting it to
appreciate the melody and harmony of sound; but still much remains to be
done in regard to the cultivation of the eye, in appreciating colour as
well as form.