tire is too biting, and the exhortations to uprightness || wretches feel, that they may shake their superflux and integrity too earnest altogether to suit the taste to them, and show the heavens more just." One of of this, fastidious and effeminate age. But that does the greatest blessings we could desire for the country not much signify. The book has vitality in it, and will is, that its entire literature should be pervaded by enforce admiration, not only from the present gene- Douglas Jerrold's spirit. In all possible and conration, but from all those, also, which are to come. ceivable reformations, the reformation of the heart It might smack, perhaps, a little of pedantry to in respect to money-worship is the most importenter into a systematic exposition of the philosophy ant. Delivered from this pestilential passion, we contained in such a work; because where it stands it should find leisure for thought, for the contemplais already popularised, and could hardly be rendered tion of works of art, of high poetry, of men, and more intelligible by any other mode of treatment. sculpture, and painting. We should go abroad into The author's object is to combat that idolatry of the world, and, looking quietly about us, discover gold which constitutes the besetting sin of this age. in what way we might be most beneficial to our We are not among the "laudatores temporis acti;" fellow-creatures, whether in large or small matters. we do not, upon the whole, think that there is less In some other countries there is already a greater virtue amongst us than amongst our ancestors; per- freedom from grasping avarice, or rather from a haps, if the question were peremptorily put to us, Catilinarian passion for money than exists here with we should be inclined to maintain the contrary They prefer the gratification of their better opinion. But in the worship of money we would feelings to the filling of their coffers, and consereally appear to have improved upon our predeces- quently think it well worth their while to make sors, insomuch that, without the slightest figure of|| sacrifices for freedom. speech, poverty has come to be regarded by us as a It is to diffuse this sentiment through English erime. We look fiercely at it, we chase it from our society that Douglas Jerrold writes. His intention presence, we hunt it down, we imprison, we trans- would be equally laudable, therefore, were he ever port it. God's image in a poor man is invisible to so inferior an author; but bringing, as he does, us. Like Pope's miser, Bond, we damn the poor,|| vivacity, wit, invention, and jocularity, and an inand hate them from our heart. And exactly in the || vincible power of amusing, to the task, we are consame proportion is the strength of the servile homage||fident we cannot be wrong in ranking him among we pay to riches. We besiege the rich man's door, we call him wise and beautiful, we fawn upon him, we lick the dust from his shoes-nay, we invite him, like Caliban, to put his foot upon our necks, and to treat us as his born slaves.

Against this all-pervading corruption, Jerrold has, throughout his whole life, lifted up his voice-in his "Chronicles of Clovernook," in "Punch's Letters to his Son," in his beautifully pathetic "Story of a Feather," in his "St. Giles and St. James," and, lastly, in his “Man made of Money." It is a mistake to suppose, as some do, that he decries wealth as wealth. He only inveighs against the abuse of|| it; against that hardness of the heart which it is too apt to superinduce; against its heartless selfishness and utter insensibility to the suffering of others. To come to a different conclusion is impossible, unloss we wilfully close our eyes to the purport of his entire writings. He has done good service for oppressed and persecuted poverty, but has not proved a whit less serviceable to the opulent themselves. He has endeavoured "to make them feel what

us.

the foremost and best writers of his age. That he has faults, we admit, though we do not care to point them out; there are plenty of others to do that, and pride themselves upon it. We, consequently, prefer devolving the agreeable labour upon them. It is enough for us to have acknowledged that he has his defects, which we do, in order to secure to ourselves the praise of impartiality that might otherwise be denied us. However, the thing is done, and there is an end of it. We infinitely prefer dwelling on his other qualities, which, in our opinion, so completely swallow up his defects, faults, and imperfections, that we should not have thought it worth our while to notice them, had we not been kindly reminded of this duty in several quarters. We pause here, not that we have no more to say, but that we must stop somewhere. It would be far more agreeable to us to go through the whole of his writings, as though they had been only published yesterday; and we look forward with confidence to a new and complete cdition, revised and corrected by the author.

HAY'S THEORY OF PROPORTIONS.*

AMIDST the efforts and researches now making in art, when Government commissions, presiding over public taste, are rearing monuments of our era, embellished with all the resources of native talent, and the opportunity is avowedly embraced to give a refining impulse to the age by direct tuition in the arts of design, a philosophy of the subject, especially a philosophy with a practical aim, must be well entitled to a hearing.

Mr. D. R. Hay, of Edinburgh, has laid before us, in the undernoted publications, at once a remembrance of his labours towards the foundation of such a philosophy, and a proof of his perseverance and improvement in the perception of its principles.

The former works of this author, seven in number, embrace the study and arrangement of colour in dress, furniture, flower-gardens, the manufacture of coloured fabrics, the study of natural history, as also the proportion and beauty of form in sculpture, architecture, painting, and ornamental design; and a descriptive catalogue has been called for by their growing utility. It facilitates reference, and points out, without the labour of research, the parts it is desirous for any one to consult.

To the eighth number of the catalogue, being a new volume, and the second of the works that are noted below, we propose devoting a little careful

examination.

Lord Kaimes, in his "Elements of Criticism," (p. 428), urges elaborate objections to the supposed analogy of proportion in "numbers" and proportion in "quantity," having previously complained that, by many writers, it is taken for granted that in buildings there are certain proportions that please the eye, as in sounds there are certain proportions that please the ear.

proximate calculations regarding the one branch
of the analogue, based upon the known circum-
stances of the other. It may be said with safety
of the great critical philosopher of the last century-
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
We remember Dr. Samuel Brown, when a stu-
dent, enunciating, as a positive perception of which
he was perfectly conscious, the correspondency of
vibrations amongst the various objects in a room;
every object, however dissimilar, having its vibra-
tion, and a definite harmony of vibrations subsisting
amongst them. We cannot pretend to say what
Lord Kaimes might have thought of this; but, as
regards, at all events, the relation betwixt number
and quantity, he is ludicrously wrong-number and
quantity being now literally synonymous terms of
science. Nothing has struck us more, however,
than that even Lord Kaimes, with all these blinding
prejudices to contest, should have all but stumbled
on the very idea wrought out by Mr. Hay. "An
arithmetical proportion," he observes, "is agreeable
in numbers; but have we any reason to infer that
it must also be agreeable in quantity? At that
rate," he continues, “a geometrical proportion, and
many others which are agreeable in numbers, ought
also to be agreeable in quantity." Mr. Hay has
justified the latent suspicion of Lord Kaimes re-
garding geometrical proportion; but not syntheti
cally, and embracing at random the whole propor-
tions of Euclid's sixth book, including the ex equale
in proportione perturbata! He has gone to work
analytically, and thus discovering the rules that
are specially applicable to proportion individual
objects in the symmetry of form, in architectural
and ornamental design, and, finally, in the human
head and countenance-has proved, indeed, that
forms and quantities are agreeable, because they
are proportionate; at the same time establishing a

this abstract but controverted proposition, namely, what are the proportions that realise aesthetic beauty.

In the latter instance, Lord Kaimes thinks it sufficient to oppugn that musical proportions and those of architecture are addressed to different senses, through the ear and the eye; and that ob-matter of far higher importance and utility than jects of different senses have no resemblance, nor indeed any relation to each other. In the former case he urges that number and quantity have no natural relation-quantity being a real quality of The power of analysis, more especially of geomatter, number merely an idea arising from the metrical analysis, has not been more remarkably sight of a plurality of objects. If not precisely the illustrated since the days of Lesslie. A special anaviews adopted by Sir David Brewster, in the Edin-lysis educes the rule particularly applicable to the burgh Review, of October, 1813, on the appearance || subject, or rather object, of investigation, and reof Mr. Hay's first three works, these arbitrary opi-lieves the wandering ingenuity of all the difficulties nions of Lord Kaimes are strangely allied to those of the reviewer. But Lord Kaimes at least would scem to have forgotten that analogy is not identity, nor even absolute, but only probable resemblance -sufficient, however, to admit of either strict or ap

of vague conjecture. It was on this that Sir John Lesslie triumphantly asserted a superiority over the earlier of the ancient geometricians, to whom the still incomprehensible enigma of the Porisms of Pappast were unknown :

1. A Catalogue Raisonne of the Works of D. R. Hay, F.R.S.E. Edinburgh: Blackwoods. 1849.-2. On the Science of Proportions by which the human head and countenance, as represented in the works of ancient Greek Art, are distinguished from those of ordinary nature. By D. R. Hay, F.R.S.E., author of "First Principles of Symmetrical Beauty, &c., &c., &c. Blackwoods. 1849.

Edinburgh:

"The doctrine of proportion, which is really but an application of arithmetic, the idea of number being transferred to quantity or magnitude by a process of subdivision."-Lesslie.

.

"The primary objects which geometry contemplates," he says, (Notes and Illustrations to Lesslie's Analysis, p. 395) are, from their nature, incapable of decomposition. No wonder that ingenuity has only wasted its efforts to define such elementary notions. It appears more philosophical to invert the usual procedure, and endeavour to trace the successive steps by which the mind arrives at the principles of the science, Though no words can paint a simple sound, this may yet be rendered intelligible by describing the mode of its articulation."

geometry.

"The founders of mathematical learning among the Greeks || This analogy, I may add, is in no way forced, but arises nawere, in general, tinctured with a portion of mysticism, transmitted turally and necessarily from these simple elements of plane from Pythagoras, and cherished in the school of Plato. Geometry became thus infected at its source. By the later Platonists who flourished in the Museum of Alexandria, it was regarded as a pure intellectual science, far sublimed above the grossness of material contact. Such visionary metaphysics could not impair the solidity of the superstructure; but did contribute to perpetuate some misconceptions, and to give a wrong turn to philosophical speculation."

66

"The two first of these triangles have been called the two symmetrical triangles of Plato, who refers to them in the following words Of the two triangles, the isosceles is allotted one nature, but the oblong or scalene is characterised by infinity; we ought, therefore, to choose the most beautiful amongst infinities, if we wish to commence our investigations in a becoming manner.' These three triangles are the primary elements of the five regular solids, or Platonic bodies, to which are the tetrahedron, bounded by four equilateral triangles; the octahedron, bounded by eight equilateral triangles; the icosahedron, bounded by twenty equilateral triangles; the hexahedron, or cube, bounded by six squares; and the dodecahedron, bounded by twelve pentaBesides these five, there can be no other solids bounded by like, equal, and regular plane figures, and the solid angles of "In describing these, Plato confines himself to the four first, and merely hints at the dodecahedron in these words:-' There also a certain fifth composition which Divinity employed in the fabrication of the universe.' The body may, therefore, have been discovered by some other geometer. Be that as it may, these triangles are not only the elements of the most beautiful rectilineal plane figures, but of the most beautiful rectilineal solid bodies.

which are all equal.

Yet it might not be extravagant to suppose that the Greek mathematicians had actually discovered in geometry the principles which guided their elegant arts in their unerring refinement, and that, having lost sight of the application of these princi-gons. ples, as, indeed, we know little or nothing of the constructive rules used in erecting and embellishing the monuments of antiquity, we blindly ascribe to visionary vanity, a pride and exultation really attri-is butable to that employment of geometrical principles which was either too familiar to be explained by their philosophical writers, or too recondite to be handed down to a darker age, and a more barbarous people. We cannot forget that there was an ancient "Every regular rectilineal plane figure has a curvelineal figure," geometric analysis, the origin, indeed, of all anawhich exclusively belongs to it. For instance, if we like, one of the equal sides of the primary isosceles triangle, which is half of lytical method, ascribed," in the language of the square, as a radius of a curvelineal figure, of which the right Playfair, "very generally to the Platonic school." angle of the triangle is the centre, a circle will be described whose Mr. Hay, it is true, has not gone into his geo-circumference will necessarily pass through both its other angles. metric analysis and composition altogether experi-The circle is, therefore, the curvelineal figure that exclusively mentally. He has endeavoured to assist or facilitate belongs to the primary isosceles triangle. "If, in like manner, we take the two unequal sides of the his researches, we may say, to limit or restrict them primary scalene triangle, which is half of the equilateral triangle, to the investigation of those harmonic ratios which as the semidiameter of a curvelineal figure, of which the right angle in nature appear to pervade with one common ana- of the triangle is the centre, an ellipse will be described, the logy the regions of sound, colour, and form. Far- circumference of which will necessarily pass through each of ther than we have entered into the question of the the other two angles. This ellipse, which has many peculiar reality of this analogy, by merely glancing at its properties, is, therefore, the curvelineal figure that exclusively belongs to the primary scalene triangle. As the revolution of possibility as we passed, we do not here mean to the circle upon its diameter will produce a sphere, so the revolu penetrate. But we must say, that in several of histion of the ellipse upon its transverse diameter will produce a works Mr. Hay seems to have adduced a series of very striking coincidences in proof that the same law of natural arrangement, and the same harmonic ratio of numbers known and practised in the diatonic scale of music, is applicable to the chromatic scale of colours, and may be traced in the analysis of beauty of conformation. His harmony of numbers, and method of applying it to form, is what we have at present to discuss.

prolate spheroid; and these two bodies are consequently the curvelineal solids arising from the elementary figure, in which

the principles of geometric harmony have been found to exist. It will, therefore, be seen that the figures I have adopted as the elements of beauty, namely, the square, the equilateral triangle, the pentagon, the circle, and the ellipse, whose proportions are derived from the elementary figure of the equilateral triangle, have not been chosen empirically, but are what have been in

every age acknowledged to be the most beautiful of all forms."

From these known quantities of geometrical analysis, Mr. Hay has striven to define the unknown quantity of proportion in the human head and countenance in all the gradations it presents of accidental beauty and conformation. The union of the globular and spheroidal forms referred to present, at once, the most remarkable characteristics in the structure of the human head. Taken in connection with the approximation of the plane of the face to a vertical, in contradistinction to the grovel◄ ling facial horizontality of the lower animals

"Pronaque cum spectent animalia cætera terram,
Os homini sublimi dedit, cœlumque tueri
Jusset, et erectos ad sidera tollere vultus."
Ov. Met., I., 84.

-the union of the globular and spheroidal forms,
both in the external form of "the human head
divine" and its sections, comprises the whole secret
of the structure of that admirable piece of sym-
metry. Yet high as the conformation of the human
cranium ranks in nature, there is an artistical ideal

and capable of being applied to the production of artistic representations of the human head and countenance, with the results of beauty, form, and proportion, which distinguish the efforts of ancient Greek art, is, then, the aim and consummation of Mr. Hay's labours hitherto. He proves the practical value of his theory by the very means which, were it false, would most readily occur to disturb it-by entering into the deviations from this system by which ordinary nature is distinguished. In the Greek ideal heads and countenances themselves, a recent writer on art (Müller) has found a diversity which drives him to despair of definite rules ever being determined for regulating their proportions, Even from that difficulty Mr. Hay does not shrink; though, of course, he confines himself to such variety as belongs to the permanent form of the anatomy, conceding that it is for genius alone to embody those results of muscular action that give sentiment and expression to the countenance in obedience to mental impulse. Feminine delicacy and masculine power, the chief varieties in the types of ancient Greek art, are often blended and even exchanged in the ideal heads of their Minerva, Venus, Juno, Apollo, Hercules, Bacchus, &c. But these caprices of creative genius are beyond the province of systematic art; and it would indeed be unfair to task the definite laws of harmonic proportion with the higher themes of æsthetic criticism.

here demonstrated which nature has seldom, if ever, || ratio, forming a system of descriptive geometry, reached; the probability of which is, however, established by the fact, that the highly refined and most intellectual races of men approximate towards it, while the barbarous tribes exhibit the greatest departure from that exalted standard which, although superior in its developments to those of the most gifted races of men, can nevertheless be identified as the high ideal of Greek art. That interesting question then recurs with tenfold force-Could the Greeks, after all, have transcended reality in their ideal figure of the human head by mathematical deduction, since, after passing the natural boundary, and the modifiations of circumstance, race, climate, and civilization, the further developments are purely mathematical? Mr. Hay establishes, we think, conclusively that the nearer a head or countenance approaches to the combination of the most perfect geometrical figures, the higher will be its degree of beauty, unaffected by what Sir Charles Bell has termed "expression," and the greater its capacity for expression itself. Such beauty and capacity for expression the Greeks undoubtedly infused into the ideal heads of their deities. These rules of art are buried in oblivion, But, whilst it has been plausibly enough suggested that they reached the idea of perfect beauty by a collective process, embodying all the most perfect points of the most perfect models, and thus refining upon nature, there are not awanting those who hold (and Mr. Hay of the number) that the excellence of the Greeks resulted not from a study of nature, but from some creative and abstract principle. How else should it have happened that the same standard|| of ideal beauty which pervaded ancient Greek art is only to be reached by imitation.

“We find (says Mr. Hay) that the principle from which the ideal beauty arose in the head and countenance, as represented in the 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 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 bestowed upon the ancient Greek artists.

"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 of the periods of Pythagoras and Plato."

Strange if we would now, in the nineteenth century, begin to open our eyes to something couched in the rapt and inexplicable mysticism of these old heathens, Pythagoras and Plato, whom we have been rather apt now and then to judge a little "cracked," and should discover that the sublime old fellows were, after all, only glorying in the truth, as learning, genius, and enthusiasm had developed it to their lofty understanding!

To identify his principles of numerical harmonic

Having already explained the elementary principles, it will hardly be required of us to follow Mr. Hay into the ultimate details of the harmonic relations of the angles in the three triangles applied in his simple, ingenious, but effective diagrams. Suffice it that the resulting representations of the human head and countenance must always be understood as referred to a plane-from being so depicted on the retina of the eye. In one of these beautiful plates (VIII) the effects of this process of geometrical construction is illustrated in reference to the external appearance of the human head. In the first instance, where the predominating figure is the scalene triangle of 30 deg., 60 deg., and 90 deg., the head is decidedly feminine in charac ter. In the second, the medial combination, where the predominating figure is the scalene triangle of 30 deg. 52 min. 30 scc., 58 deg. 7 min. 30 sec., and 90 deg., the head is neither decidedly masculine nor decidedly feminine. But in the third, a decidedly masculine character of head and countenance results from that species of geometrical harmony governed by the triangle of 30 deg. 45 min., 56 deg. 15 min., and 90 deg.

Mr. Hay asserts the identity of this operation of the numerical harmonic ratios, with the well-estab- ̈ lished science of acoustics:

-

"If I have succeeded (says he) in proving that the science of these proportions is identical with the science of acoustics, the ideal head of ancient Greek art is not only the most beautiful, but also the most natural-its form and proportions being the full development of a law which is only partially developed in It will be shown in the sequel that, imperfect ordinary nature. as this development is in general, it is sufficiently decided in all cases to give to the human head that characteristic form which so distinctly makes the difference between it and those of the lower animals,

"His death took place on Good Friday, April 6, 1520. Great was the grief of all classes, unspeakable that of his scholars. The body was laid on a bed of state, and above it suspended the last work of that divine hand-the glorious Transfiguration.""-MRS, JAMESON

With the light of life fast fading, 'tis Raphael lies beneath
The scorching pang of fever, and the waiting hand of death;
And yet there is a holy calmness throned upon his brow.
Think ye not, while his spirit waits beside that canvas now,
The yet imperfect lives revealed-as first in mind it shone-
Ere the tears of Rome proclaimed that her Raphael was gone?-
Where the yellow waves of Tiber through mighty ruins pass,
They are coming-coming through the streets-a sad and silent

They gaze upon his hand-his brow-from whence the light hath
fled,

They marvel at the "Christ transfigured” raised above the dead;
Suspended, though unfinished, o'er the holy painter's bier
It hangs, a mind-wrought trophy of his soaring spirit here,
His hand hath, wrestling, won from death, when in the field of life,
With passionate soul-longings, and spirit-yearnings rife.
Oh! what to this the warrior's deeds, to which alone is given
The fame which from destruction springs-it has no light from
Heaven!

For gauntlet, helm, and standard rent, above the tomb hung high,
But speak of glory truth disowns, and time will soon deny;
But fame, thro' mental triumph, long the truthful world shall hold
By power of thought bequeathed, that gives to future time the
mould.

The progress of each age will prove of earthly rank this sense,
While spiritual beings seek ideal excellence :
Then think ye not exalted thought, diffused through future mind,
Will long perpetuate the fame of Raphael with mankind?
And trust ye not such earnest souls, when past the bond of breath,"
Wake from a gloriou death-in-life unto a life-in-death!