150 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



I May. 



the other orders; hut if it failed with the Doric, the proportions of which 

 were comparatively invnriahle, the Ionic and Corinthian must he still more 

 perplexing, the latter of which varied so much that the writer of the article 

 Architecture, in the " EncyclopiEclia liritannica." said it was scarcely possible 

 to give any general description of it. If it failed with any of these, there 

 «-ould remain for it hut a small chance of success with the Gothic or the 

 Elizabethan. 



Mr. Purdie said, it might aave the introduction of much irrelevant matter, 

 if it were kept distinctly in recollection that he was not attempting to refute 

 some imaginary theory which might he brought forward in the course of the 

 discussion, hut that advocated before the Society hy Mr. Hay, and contained 

 in his published works. That theory was founded on the harmonic ratios. 

 No doubt, order, proportion, and harmony were all necessary to the beauty 

 of architecture ; but it was not hy the harmonic ratios these were to be ob- 

 tained. The " Greek architects allowed themselves to be fettered in their 

 general proportions only." This theory did not establish general propor- 

 tions at all. In music, the application of harmonic ratios, while they allowed 

 all latitude as to general proportion, limited beauty to certain fixed points or 

 coincidences, from which when the slightest departure was made, discord 

 ensued. Thus a difference of a semitone would make as disagreeable a dis- 

 cord as a full tone, and one quite as easily recognised. It mattered not 

 whether too high or too low. The application of the harmonic ratios to 

 forms was intended to produce a similar eBect. Thus in the case of a well- 

 proportioned column, six inches added to its height would be as easily ob- 

 served as 18, and quite as destructive of its beauty ; and were the height 

 diminished by 18 inches instead of being increased, it ought to be no more 

 so, the departure from the harmonic ratio in either direction being equally 

 discordant. The instant the correct proportions were departed from, de- 

 formity would be the result ; hut let the alteration be continued a little 

 farther in the same direction, the deformity would be got rid of — a new 

 chord struck, and beauty and symmetrical proportion again obtained. 



Mr. Purdie stated shortly what he conceived to he the source of the beauty 

 of architecture and sculpture, and refeired.as the best sources of information 

 with which he was acquainted, to Lord Aberdeen's inquiry into the princi- 

 l)les of beauty in Grecian architecture — Gwilt's Preface to Chambers's Works 

 — the Essays of Alison and Lord Jeffrey, and the lives of Christopher Wren 

 and Michael Angelo Buonarotti, published by the Society for the Diffusion 

 of Useful Knowledge. It was not necessary to seek for any mysterious geo- 

 metrical law. The taste of a nation, and their power of producing and ap. 

 ])reciating beauty, depended on their progress in civilisation, on education, 

 and the refinement these naturally produce. " The beauty and perfi-ction of 

 the school of Phidias accompanied the great moral and intellectual improve- 

 ment of the times, and art was most perfect when yEschylus, Sophocles, and 

 Euripides, produced their tragic poems; and Socrates and Plato, and the 

 great Grecian statesmen, by their writin::s and example, improved the moral 

 and political state of mankind." — (Life of Michael Angelo.) That this 

 tended to prove the general correctness of Lord Jeffrey's definition of taste — 

 "That the power or faculty of taste is nothing more than the habit of trac- 

 ing those associations by which almost all objects may be connected with 

 interesting emotions." 



Mr. Purdie then took notice of some of the methods given for applying 

 the theory to practice, and contended it was equally potent to produce the 

 ugly or the beautiful. According to the method given by Mr. Hay for 

 drawing the human countenance, an oval was first described, and within it a 

 triangle, its apex undermost. At the apex the mouth was placed, and the 

 eyes at the two ujipir angles. But no rule was given for placing the apex 

 of the triangle undermost. One might, if he felt so disposed, reverse both 

 the triangle and oval ; it might be some bungling Grecian sculptor who thus 

 reversing his triangle, invented the Cyclopean type, with one large eye in the 

 centre of the forehead, and a mouth extending from car to ear at its base. 



A similar effect would take place with the profile, in drawing which an 

 oval is given for the face and a circle for the back of the liead. He said 

 the profile is not an oval, nor is the back of the head a circle. To render 

 the back of the head a circle, a large slice must be laken from "self-esteem ;" 

 and " philoprogeniliveness"would suffer an amount of reductiou which might 

 seriously interfere with the increase of the population. The back of ihe 

 bead was, strictly speaking, no more a circle than a square ; and if it 

 were a square, or a rectangle, provided always it were a harmonic one, its 

 consistency with the principles of the theory might have been quite as 

 easily manifested, 



Mr Purdie then proceeded to consider what are styled (p. 31, Sym- 

 metrical Beauty) a series of peculiarly symmetrical rectangles, which are 

 evolved by using Ihe diagonal of the square as the base of the first, the 

 diagonal of the first as the base of the second, and so on. Mr. Hay, 

 however, did not adopt these as they naturally arise. They did not accord 

 with the harmonic ratios, and were altered to suit. 



Mr. Purdie pointed out on a diagram the amount of the alteration. He 

 said Mr. Hay referred to ihe temperament used in music in its justifica- 

 tion. Mr. Purdie explained the nature of musical temperament, and 

 showed there was no analogy between it and the process adopted with 

 these rectangles. He stated the temperament in music was a modern in- 

 vention, and seemed somewhat out of place in a treatise which claimed 

 support as elucidating the principles of the ancient Greeks. Were such a 

 principle as this tempering admitted into science, it would be easy to ob- 

 tain any results. Such an arbitrary alteration of a series of figures in a 



science claiming mathematical accuracy, would have been conclusive 

 against it, had it been in other respects unassailable. 



Mr Purdie next referred to the egg oval, and Mr. Hay's method of 

 producing it, which might be new to many of the members, and was 

 (leaving out the harmonic ratios) the simplest and best meihiid. He said, 

 whatever merit its application to Ihe drawing of vases might possess, it 

 had not that of novelty to recommend it, but bad long been f.imiliar to 

 every one who had given any attention to the subject. He exhibited in 

 Nicholson's " Architectural Dictionary" several good examples of vases so 

 constructed, along with a variety of methods of producing the figures on 

 which they were based. 



Mr. Purdie explained the effect of engrafting the harmonic ratios on 

 them, and exhibited a variety of diagrams to test whellier any one could 

 point out the discordant from the harmonic. But the method adopted in 

 forming these ovals was, he contended, altogether subversive of the theory. 



tour pins are put in at certain fixed points, and a string tied round 

 them, for the purpose of obtaining the form of two harmonic triangles ; 

 but, before proceeding to produce the oval, one of the pins is pulled out. 

 For this no reason could be assigned but the will of Ihe operator. It did 

 away at once with all idea of harmonic relation. A figure so constructed 

 could bear no mathematical relation to the triangles on which it was based. 

 Extend the radii to infinity, and a circle would be obtained independent of 

 the shape of the triangles : reduce the string to a sufticient tension, and it 

 would become a triangle. A figure so constructed vibrates between the 

 circle and triangle. At no possible point between the two could it bear 

 any harmonic relation to the triangle on which it is based. 



In conclusion, Mr. Purdie said, that the origin of the fallacies contained 

 in this theory appeared to be an extravagant fondness for analogy, through 

 which the idea had been conceived of engrafting the principles of mnsic 

 on form : that, instead of analysing the phenomena of mind, and deducing 

 the principles of a science from the facts so ascertained, the mental phe- 

 noniena had been left out of view altogether, and the theory formed on a 

 mathematical basis depending on the harmonic ratios: and that the result 

 was a theory utterly at variance with those very phenomena on which it 

 ought to have been founded. The only method of iuvestigatiug the trulh 

 in metaphysical science was by inductive philosophy, the slightest atten- 

 tion to the principles of which would have saved the author of this theory 

 from the manifold blunders into which he had fallen. 



After the reading of the above paper, Mr. Hay made some remarks 

 " On the effects of Perspectire upon Proportion, being the first of a 

 series of shirt papers upon tlic Harmony of Form." 



Mr. Hay commenced by apologising to the members of the Society 

 generally, for calling their attention to a fact, with which he believed they 

 were familiar. But that fact had been denied at the previous meeting, in 

 an attempt to prove a fallacy in his system of applying the numerical har- 

 monic ratios to the proportioning of rectangular forms; and its denial 

 seemed to be well received by the younger members. Mr. H. therefore, 

 felt called upon to state the fact, and to demonstrate il. The fact, he 

 stated was " that whatever system of proportion may be applied in ar- 

 ranging the parts in the geometric elevation of a building, will also 

 operate upon the effect of that buililing, in whatever degree of obliquity it 

 may be viewed." He exhibited fi»e drawings, two of which fully ex- 

 plained his system of applying the numerical harmonic ratios, and the 

 other three demonstrated the fact which had been denied at the previous 

 meeting ; and therefore concluded that the attempt to prove the fallacy of 

 the system, by the denial of this fact, had failed. 



Mr. Hay observed, that an attempt had also been made, at the previous 

 meeting, to assimilate his system of the application of numbers to sym- 

 metrical beauty, with the mystical application of particular numbers by 

 the alchymists, and some of the philosophers of the middle ages ; and of- 

 fered to prove that this attempt was also a failure, iuasmuch as he em- 

 ployed numbers in an intelligible, not a mystical manner. 



PECULIARITIES IN THE CONSTRUCTION OF GREEK 

 ARCHITECTURE. 



Abstract of a paper " On the Geometrical Lines and Optical Corrections 

 of the Greek Architects." By F. C. Pisnrose, Esq. — (Read at the Eoyal 

 Institute of British Architects, February 21st.) 



I will observe, that although the scrupulous accuracy with which the 

 measurements which I shall produce have been recorded may seem almost 

 absurd to some, it will not appear so to those who have been so fortunate as 

 to see the originals, and observe the perfection of the workmanship with 

 which they are put together, and the exceedingly happy preservation of 

 many parts from the weather, which enables measurements to be taken with 

 precision in these, where in many buildings they could only be a matter of 

 approximation. 



I use as my standard of measurement the English foot, and divide it into 

 100 parts which I shall call cents. 



In the beginning of the year 1846 I was at Athens. I had an introduo- 

 tion to M. Riedel, a Bavarian architect, who accompanied me on my first 

 visit to the Acropolis, and pointed out to me the peculiarities of construc- 

 tion of which I am about to speak ; it was the first time I had any intima- 

 tion that there was any departure from ordinary line and rule work in these 



