398 



THE CIVIL ENGINEER AND AllCHITECTS JOURNAL. 



[OoTOBKft, 



natural objects as may be brought togetlier in forming a subject, inde- 

 pently of their individual nierils. The former class of works are 

 appreciated by the degree of deception jiroduced, while the latter 

 seem to be appreciated by an inherent feeling, res|)onsive to certain 

 niitheniatical principles of propriety and harmony existing in nature. 

 While these qualities constitute the excellence of works in painting 

 and sculpture, the beauty of all architectural composition depends 

 upon mathematical harmony alone, because in such there is no imita- 

 tion ; and it can scarcely be doubted that the five orders owe their 

 origin, and the perfections of their proportions to some systematic 

 mode of applying these principles practically in the art. In propor- 

 tion, therefore, as we acquire certain fixed principles of our own, we 

 shall be released from the servile necessity of continuing mere imita- 

 tors of those ancients, with the philosophy of whose practice we are 

 little acquainted, and who certainly did not work without principles 

 themselves. These general views the author seeks to illustrate and 

 explain: and in so doing, he has, in our opinion, been very successful. 

 He has reduced to fixed principles what was formerly but considered 

 dependant on some nndi'fined waywardness of taste or fancy, and he 

 has triumphantly established the fact that forms and figures are ren- 

 dered pleasing to the sight by tlieir geometrical quality of proportion. 

 Mr. Hay, as before remarked, assumes the square, the circle and 

 the equilateral triangle as homogeneous figures, tnd after giving a clear 

 and lucid description of the eye, with all its extraordinary parts and 

 functions, be proceeds to remark, that "the elFects of geometrical 

 configuration on that organ are, in the first instance, regulated by the 

 relation they bear to the conformation of tliat organ itself — hence the 

 soft influence of those figures of the curved kind, and the acute and 

 and more powerful effect of those whose outlines are composed of 

 angles." On the mode of proportioning these elements of form in the 

 combinations of various figures their effect upon the eye depends ; 

 when a proper mode is adopted geometric beauty is the result, while 

 the adoption of an improper mode results in deformity. In further 

 illustration of thr etfects of the three forms which Mr. Hay has assumed 

 as primaries, and by way of justifying himself for giving them such a 

 prominent position, he states that the circle is not only the most sim- 

 ple of the homogenous forms, but naturally so in reference to the 

 organ by which it is perceived. The square is the next most conso- 

 nant form to the eye, because its angles are less acute than the triangle, 

 while the triangle, from its being composed of acute angles and ob- 

 lique lines, exercises the most powerful influence on that organ. Now 

 as there can be no proportion without variety, and as in Mr. Hay's 

 primaries we have the source of endless variety, it is evident that the 

 most perfect beauty must be the result of a justly proportional admix- 

 ture of those forms. Nothing, amidst the many and most ingenious 

 analogical illustrations which the book contains, is, we think, finer 

 than the following observations on the similar eftect which the pri- 

 maries of sound and form have upon the eye. Analogy, therefore, 

 does obtain most certainly here, and analogy of the most perfect kind. 

 " It is well known in chromatics that the primary colour blue exer- 

 cises a softer influence upon the eye then either of the other two, red 

 and yellow, and this no doubt occurs from its being the most allied to 

 darkness, or black, of the three, and hence associating more intimately 

 with the colour of the retina itself. The colour that stands next to it 

 as a primary in the solar spectrum, is red, which consequently holds 

 the situation that the triangle docs in my series of forms, and this 

 colour is well known to affect the eye more forcibly than the yellow, 

 which in the natural series is furthest removed from the blue, so that 

 the more acute effect of the triangle upon the eye, although holding 

 a medial situation, is quite in accordance with the analogy of acoustics 

 and chromatics." p. 18. 



The author, for the purpose of rendering his analogy more com- 

 plete, assigns to the oblong, the rhombus, the hexagon, and the dodec- 

 agon, the same parts in form as the secondaries in sound and colour ; 

 after which, he gives a very full explanation, illustrated by a number 

 of diagrams, of the qualities of each of the geometrical figures referred 

 to in the work, and shows that the three primaries, with their attend- 

 ant secondaries, can be produced, within the range of ocular percep- 

 tion, in an endless variety of combination, and in various degrees of 

 modification in regard to their proportions. 



Mr. Hay then, for the purpose, as he says, of rendering more easily 

 comprehensive, and to systematize the harmony of geometry, has a 

 long chapter on the Geometry of Harmony. This portion of the work 

 is also illustrated by a variety of tables and diagrams, and altogether 

 contains a very simple and easily understood exposition of the laws of 

 acoustics, and although, as we have already stated, the analogy sought 

 to be established between sound and form is not satisfactorily proved, 

 yet this chapter is of itself, abstractedly considered, altogether a mas- 

 terly exposition of the geometry of harmony, while it forms a very 

 fittipg inttoductiou tg the study of >• the haimony of geometry." 



The author, in proceeding to develop this science in detail, divides 

 the circle into 3()0 degrees, and endeavours to prove that in the divi- 

 sion of these degrees by the harmonic ratios the jirinciple of geome- 

 tric beauty, or proportion, lies. In the first division, by two, the dia- 

 meter of the circle, or horizontal line, the base of all geometrical 

 figures, is produced. The second division by two, gives a radius per- 

 pendicular to the base, producing the right angles of 90°, and this, 

 again, divided by two gives the angle of 45", which is the first har- 

 monic ratio ; the next harmonic ratio is the angle of 60 , which is 

 produced by the division of the quadrant into three. 



Mr. Hay then goes on to show that rectangles only differ from one 

 another in their proportions, that is the ratio that their length bears to 

 their breadth, and this proportion is determined by one measurement, 

 which is the diagonal. The oblong is simply a modification of the 

 square, and this modification is regulated by the number of degrees in 

 the angle of the diagonal, which when the oblong is placed vertically 

 must exceed 45°, and when horizontally placed must be under that 

 number. If, therefore, a scries of these diagonals be produced by a 

 harmonic division of the degrees that occur in a quadrant, that is, by 

 2, by 3, and by 5, the rectangles formtnl upon these must bear an har- 

 monious relation to one another. Thus, the diagonal of 45° relates to 

 the right angle as 1 to 2 ; the diagonal 00° as 2 to 3 ; the diagonal 72° 

 as 4 to 5. 



These diagonals form the groundwork on which Mr. Hay's theory 

 of the harmony of form is based; and most admirable, so far as it can 

 be judged of in its present stage of progress, is the structure of har- 

 mony which will ultimately be reared therefrom. These diagonals 

 are the rules by which the building must be constructed, in every line 

 from its basement to the summit of its pediment. Already has Mr. 

 Hay laid the groundwork, in a series of beautifully proportioned rect- 

 angular figures, and whatever may be said about the analogy he has 

 laboured to establish between sound and form, there can be but one 

 understand as to his opinion of having been successful in discovering 

 the harmonic divisions of a circle, when a series of figures of such 

 perfect beauty, and in such perfect relative harmony is the result of 

 such divison. 



Mr. Hay after showing that the circle and the square seem to have 

 a reciprocal effect upon one another, in regard to the harmonious 

 mode of division, proceeds to illustrate, by a series of diagrams, that 

 if a quadrant be placed upon any diameter of a circle and lines drawn 

 through any of the harmonic divisions until they reach the circum- 

 ference of the circle, and another line drawn from this perpendicular 

 to the diameter or base, until it again meet the circumference, the 

 repetition of these two Hues from every similar division of the cir- 

 cumference will produce an harmonious arrangement. These diagrams 

 which are composed of a succession of harmonic angles and various 

 curves, and which display every variety of figure harmoniously ar- 

 ranged, are exceedingly ingenious and beautiful. In some the inter- 

 sections of the straight lines in the circular mode of combination form 

 various concentric polygons, which approach the figure of the circle 

 so nearly that they at first sight deceive the eye, while the curve as- 

 sumes the appearance of the straight line in those combinations that 

 are angular. Again, when viewed laterally, obliquely or otherwise, 

 these diagrams assume a variety of forms, all exquisitely beautiful, 

 harmonious, and suggestive of an endless diversity Jof ornamental 

 designs. 



A very clear and forcible illustration of the mode in which the har- 

 monic angles may be applied is afforded by the two last plates in the 

 work. They are harmonic combinations of rectangles, divided into 

 triangles agreeably to the Platonic system, and the strong lines show 

 how they may be formed into solids or vacuities in architectural com- 

 position. 



After a very able dissertation on the harmonic ratio of numbers, 

 which is also illustrated by a number of diagrams, Mr. Hay concludes 

 his treatise as follows: — "Thus have I endeavoured to analyse the 

 geometric principle of beauty — proportion — by showing that it is re- 

 gulated by the harmonic ratios of numbers. And by the application 

 of those ratiso to a quadrant of the tircle, I have shewn that an almost 

 infinite series of rectangles may be produced, bearing to one another 

 certain harmonious relations ; and that, within each of those a series 

 of six other distinctive characters of figures may be systematically 

 and harmoniously generated. In short, that the beauty arising from 

 the harmony of form may be on all occasions with certainty produced. 

 " But the application of this systt>m to the various arts in which it 

 will be useful, must form the subject of another treatise, as it would 

 be prematiirc to apply rules until their accuracy were acknowledged. 

 1 shall, however, in the mean time, add a few general rules which ob- 

 viously arise out of this theory : — 



" 1st. Rectangles, when arranged in succession, either horizontally 

 or vertically, should only differ from one another in one of their di- 



