INVESTIGATING ORGANIC FORMS. 217 



Having arrived at these conclusions in a legitimate manner, 

 he found the tonic repeated thrice, the dominant twice, and 

 the mediate once. Tlie ratios, which they would perceive the 

 angles of the triangles bore, as laid down, were ratios which 

 held in the musical chord. By simply prolonging the trans- 

 verse lines of the diagi-am, a perpendicular line would be 

 intersected in a series of fractional parLs, all of which were 

 indicated in the musical scale. If this perpendicular were a 

 musical string set a-vibrating, it would vibrate, for instance, 

 first as a whole string, then as two halves or octaves, then as 

 third parts or fifths ; another set of vibrations repeated the 

 octaves — viz. fourth parts or double octaves ; another series 

 of vibrations divided the chord into fifth parts or thirds, etc. 



This was certainly very remarkable. The artist who drew 

 as Mr. Hay dii'ected woidd produce a figure infinitely more 

 correct than by the mere eye or a prolonged study of figures. 

 It was remarkable that the angles which he had attained by 

 correcting liimself, by carefid measurement, and by preser\'ing 

 a certain ratio of one to another, shoidd repeat themselves at 

 intervals representing musical intervals. 



In the female figiu'e the conamon or primaiy chord of 

 music, where 2, 3, and 5 were the leading numbers, was indi- 

 cated. The male form differed essentially and materially 

 from the female. ^Ir. Hay had begun his researches with the 

 female form. It was necessary for him also to construct a 

 diagram of the male ; and he had made trials, but not at 

 random, from which he thought it probable that the male 

 dilfered from the female in harmonic ratio. By making the 

 figure on a dominant triangle, for which, instead of 30', 

 he took 33° 45' (and this related to the dominant angle 

 in the female, in the mathematical ratio of 9 to 8, or, to 

 express it musically, as a major tone to a minor tone), he was 

 enabled to constnict a diagram for the male into which you 

 can't draw a female figure ! It comes out a male ! It would 



