1850.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



359 



exists in the physical constitution of the organs of hearing and 

 seeina;, and the manner in which external nature affects tlie sen- 

 soriuni through these organs; showing the difference between 

 noises and musical sounds in the one case, and irregular and 

 regular forms in the other. He e.\]dained that each musical sound 

 was i)roduced by a number of e<|ual and regular impulses made 

 upon the air, the frequency of whicli determining the pitch of the 

 sound; tlieir violence its loudness; and the nature of the material 

 by which the impulses were made its <|uality or tone. In like 

 manner, he showed that the effect upon the optic nerve produced 

 by external objects is simply that of the action of light, and amen- 

 able to the same laws. Variety of form being analogous to variety 

 of pitch; variety of size to that of intensity or loudness; and 

 variety of colour to that of quality or tone. 



Mr. Hay next explained the nature of the h.armonics of sound, 

 which result from the spontaneous division of the string of a 

 monochord by the formation of nodes during its vibratory motion. 

 He then showed how the harmonics of form could be evolved from 

 the quadrant of a circle by tlie following process: — 



Fi2. 1. Pin. 2. 



From a horizontal line MR, fig. 1, he produced two parallel 

 vertical lines ML, and RS, indefinitely, and with a radius MR de- 

 scribed, from the centre M, the quadrant OR. From O, he di- 

 vided the arc of the quadrant into parts of i, i, i, A, ^, ^, and i. 

 From the centre M, and through these divisions, he produced the 

 lines MN, MP, MQ, MT, iMU, MV, and MS, until they met RS, 

 forming the right-angled triangles MPR, MQR, MTR, MUR, 

 MVR, and MSll. He then showed, that as the angles at the 

 vertex of each of these triangles, contained respectively 45°, 30°, 

 22°, 30', 18°, 15°, 12°, 51', 2(>", 11°, 15', they related to the right 

 angle, asj,he harmonics of sound, expressed by the signs c, g, c, e, 

 g, b, andc, relate to the fundamental note C, produced by the 

 string of the monochord. These triangles he combined in the 

 following manner upon a line A13, tig. 2, which he said might be 

 of any given length according to the size of the figure to be 

 formed. From B, at an angle of 11^ 15' with AB, he drew the 

 line B^, indefinitely, and from A at an angle of 15° with AB the line 

 Ar also indefinite!)', and cutting By, in K. Through K, he drew 

 KL at right angles with AB," forming the triangles ALK and 



KLB. Through K he drew the line ;)0 parallel to AB. From A 

 at an angle of 12° 51' 2«" with AB he drew AV, cutting yjO in M, 

 and drew MN at right angles with AB, forming the triangle AMN. 

 From A at an angle of l!S° with AB, he drew A»(, cutting pO in 

 H, and dreiv HI at right angles with AB, forming the triangle 

 AH I. From A at an angle of 22° 3(i' with AB, he drew At, cut- 

 ting yjO in F, and drew FG at right angles witli AB, forming the 

 triangle AI"G. From A at an angle of 30° with AB he drew A.s, 

 cutting ;j() in C, and drew CU at right angles with AB, forming 

 the triangle yVCU. From C at an angle of 45° with AB and CI) he 

 drew CE, forming the triangle CDE. Thus, he observed, were the 

 triangles arising from the harmonic angles constructed upon AB 

 in the same relative proportions to each other, that they were 

 when formed upon the line RS, fig. 1. Upon the other side of 

 AB he constructed similar triangles forming the equilateral tri- 

 angle ACC'; the right-angled isosceles triangle ECC, and the 

 acute-angled isosceles triangles AFF, AHH, AKK, AMM, and 

 BKK. Within this diagram he showed that the human skeleton 

 could be formed in the most perfect proportions, determining, at 

 the same time, the centres of all the various motions of the joints; 

 and also that the symmetrical beauty of the e.xternal form, whe- 

 ther in a front or profile view, was governed by these angles; thus 

 eiuleavouring to prove that an application of the laws of numerical 

 harmonic ratio in the jiractice of the sculptor and painter would 

 give these imitative arts a more scientific character than they at 

 present possess, and, so far from retarding the efforts of genius, 

 would rather tend to facilitate and assist them. 



Professor Kelland's Exposition of the Views of D. R. Hay, Esq., 

 on Symmetric Proportion. 



The fundamental hypothesis of the author was stated to be 

 this: — That the eye is capable of appreciating the exact subdivision 

 of spaces, just as the ear is capable of appreciating the exact sub- 

 divisions of intervals of time; so that the division of space into an 

 exact number of equal parts will affect the eye agreeably in the 

 same way that the division of the time of vibration in music, into 

 an exact number of equal parts, agreeably affects the ear. But 

 the question now arises — What spaces does the eye most readily 

 divide.'' It was stated that the author supposes those spaces to be 

 angles, not lines; believing that the eye is more affected by direc- 

 tion than by distance. The basis of his theory, accordingly, is, 

 that bodies are agreeable to the eye, so far as symmetry is con- 

 cerned, whenever the principal angles are exact submul'tiples of 

 some common fundamental angle. According to this theory we 

 should exjiect to find, that spaces in which the prominent lines 

 are horizontal and vertical lines, will he agreeable to the eye when 

 all the principal parallelograms fulfil the condition that the dia- 

 gonals make with the sides, angles which are exact submultiples of 

 one or of a few right angles. This application of the theory was 

 exemplified by a sketch of the new Corn E.xchange erected in the 

 Grassmarket, Edinburgh, by David Cousin, Esq., whose beautiful 

 design was slmwn to have been constructed with a special refer- 

 ence to the fulfilment of this condition. 



The author was stated to proceed to apply his theory to the con- 

 struction of the human figure, in which we should expect u priori 

 to find the most perfect de\elopment of symmetric beauty. Dia- 

 grams were exhibited which represent, with remarkable accuracy, 

 the human figure; and it was explained that not a single lineal 

 measure is employed in their construction. The line which shall 

 represent the height of the figure lieing once assimied, every other 

 line is determined by means of angles alone. F(jr the female" figure, 

 those angles are, one-half, one-third, one-fourth, one-fifth, one- 

 sixth, one-seventh, and one-eiglith of a right-angle, and no others. 

 It must be evident, therefore, that, admitting the suppositiiui that 

 the eye appreciates and approves of the equal division of tlie space 

 about a jioint, this figure is the most perfect which can be con- 

 ceived. Every line makes with every other line a good angle. 

 The male figure was stated to be constructed upon the female figure 

 by altering most of the angles in the proportion of 9 : 8; the pro- 

 portion which the ordinary untemjiered flat seventh bears to the 

 tonic. 



A drawing was e.xhibited, which had been designed with great 

 care from the life, by the distinguished academician, John A. 

 Houston, Esq. On tliis drawing tiie author had constructed his 

 diagrams; and the coiru-idence of theory with fact was seen to be 

 complete. Professor Kelland argued, that a principle so simple 

 and comprehensive in its character, and thus far apparently truth- 

 ful in the conclusions to which it leads, merits, and should receive, 

 the most complete and rigid examination. 



