that the true root of the genetic scale is F, and not C. In a letter which he wrote about that time Mr. Ramsay says: "I saw that Euler was right in beginning with F instead of C, and I adopted his method."
     Years passed on, and Mr. Ramsay came to Glasgow, there to follow out the teaching of the new views, and to pursue his studies in musical science. He delivered a course of lectures in the city, in which he exhibited the whole System of musical vibrations; the True Genesis of the musical scale of notes, the true mathematical root of which had been shown by Euler to be F, the root of the Subdominant; and prominent in these lectures was set forth in the Law of Duality. He said - "The science of music has not yet been written; nor can it possibly be written until it is founded on the Law of Duality ... Such is the economy of Nature, that from one system of proportions employed in two ways - in the one case as periods of vibrations, in the other as quantities of a string - everything in music is derived; the numbers which are the periods in the one are the numbers which are the quantities in the other ... Through the Law of Duality the organic structure of music can now be shown to the eye and to the understanding, as its performance is to the ear, 'a thing of beauty.'" The opening lecture of this course was attended by some thirty of the musical artists and scientists of Glasgow. Among them was Mr. Colin Brown, who seemed much interested, and waited at the close to ask some questions of Mr. Ramsay. The lectures were illustrated by a system of pendulums and a number of beautiful and elaborate diagrams, and other means and appliances.
     Mr. Ramsay departed this life in the month of August, 1891, in his seventy-third year. His last great work has been to do for the Chromatic System of music what he had so many years before done for the Diatonic System. This will be found, when published, to be a work never before even attempted by any author; what was formerly in use of chromatic chords and resolutions being only a few fragments of a beautiful system of chords and resolutions which will become available for