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of harmonic ratio, between Sir John Harrington and Sir Isaac New- 

 ton, in which the latter expresses his belief in such laws in the fol- 

 lowing words : " I am inclined to believe some general laws of the 

 Creator prevailed with respect to the agreeable or unpleasing affec- 

 tions of all our senses ; at least the supposition does not derogate 

 from the power or wisdom of God, and seems highly consonant to 

 the simplicity of the macrocosm in general." The belief of this 

 great philosopher, the author trusted, would form some apology to 

 men of science for the repeated attempts he has made to establish 

 the fact. These attempts he had hitherto made with reference to 

 architecture, to ornamental design, and latterly to the human head 

 and countenance ; but on the present occasion he intended to shew 

 the operation of these laws in constituting the symmetrical beauty of 

 the entire human figure. 



He next proceeded to point out the remarkable similarity that 

 exists in the physical constitution of the organs of hearing and see- 

 ing, and the manner in which external nature affects the sensorium 

 through these organs ; shewing the difference between noises and 

 musical sounds in the one case, and irregular and regular forms in the 

 other. He explained that each musical sound was produced by a 

 number of equal and regular impulses made upon the air, the fre- 

 quency of which determining the pitch of the sound, their violence 

 its loudness ; and the nature of the material by which the impulses 

 were made its quality or tone. In like manner, he shewed that the 

 effect upon the optic nerve produced by external objects is simply 

 that of the action of light, and amenable 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 harmonics of sound, 

 which result from the spontaneous division of the string of a mono- 

 chord by the formation of nodes during its vibratory motion. He 

 then shewed how the harmonics of form could be evolved from the 

 quadrant of a circle by the following process : — 



From a horizontal line MR (figure 1, of the annexed Plate), he 

 produced two parallel vertical lines ML and RS indefinitely, and 

 with a radius MR described, from the centre M, the quadrant OR. 

 From he divided the arc of the quadi-ant into parts of f , 4, J, J, 

 J, J, and ^. From the centre M, and through these divisions, he 

 produced the lines MN, MP, MQ, MT, MU, MV, and MS, until 



