stand - indeed, the writer himself was not a match for them, for he says he "could not see the reason why the minor third from D to F should be a comma less than other minor thirds." He is evidently puzzled; but he gets out of the difficulty by saying that "music must always be a kind of metaphysical science!" The next book from the Rothesay Library, and a more important one, was Euler's Letters to a German Princess. Euler, while treating of music, shows that there are just three mathematical primes, namely 2, 3, and 5, employed in the production of the musical notes - the first, in ratio of 2 to 1, producing Octaves; the second, in the ratio of 3 to 1, producing Fifths; and the third, in the ratio of 5 to 1, producing Thirds. Moreover, he begins his calculations from F, the root of the Subdominant, instead of C, the root of the Tonic, which is the usual way. While Mr. Ramsay was meditating on these teachings of the great mathematician, Euler, and studying these notes and their vibrations, he was led to discover that the order of quantities above F, when taken below B, constitutes the Minor System. This was the discovery of the Law of Duality in Music. This Law of Duality in Mr. Ramsay's hands asserts an importance not second even to the Law of Mathematical Ratios which rules in the genesis of the notes.
     On December 24th, 1845, Mr. Ramsay announced to the people of Rothesay that he intended to open classes for the teaching of the science of music, commencing with the musical scale mathematically demonstrated as being the result of a System of vibrations which constitutes the basis of music, and accounts for every musical phenomenon of sound. Thus, by treating music in its origin, and viewing it not only in detached parts, but treating it as a whole, he would remove a multitude of unmeaning terms in common use, such as "imperfect" and "superfluous intervals," "discords," etc., etc., which tend to mystify and impede the learner's progress. From this date Mr. Ramsay continued, by one method and another, to communicate what he had discovered; to show