TRANSACTIONS OF THE SECTIONS. 37 



Dr. Williams first endeavoured to diminish these disturbing sounds 

 by lateral apertures, which would give exit to the transverse vibra- 

 tions ; but although this plan succeeded to a certain degree, it caused 

 a great loss in the concentrating power of the instrument, the sides of 

 which were no longer uniformly reflective. After many other trials. 

 Dr. W. succeeded in avoiding the above-named defects to a great 

 extent, by combining in an instrument great concentrating power with 

 the greatest simplicity of construction. A conical tube 12 or 15 inches 

 long, its sides forming an angle of 25°, its apex terminating in a short, 

 slightly curved tube adapted to the ear, and its base or open end 

 forming an elliptic aperture, the plane of wliich forms an angle of about 

 45° with the axis of the cone, was found to answer best. Such an 

 instrument receives the direct waves of sound in so large a liody at its 

 open end, and concentrates them to its narrow end by so few reflec- 

 tions, that the original sound is conveyed, simple and distinct, unmo- 

 dified by aberrant vibrations, and greatly increased in intensity. It is 

 found to be nearly free from the roar ; and it inci-eases the intensity of 

 articulate sounds to such a degree, that words spoken only just above 

 a whisper, could by its aid be distinctly heard at a distance of 50 yards 

 during the daytime, and at a much greater distance at night. It 

 rendered the tickings of a watch audible at more than three times the 

 distance at which they could be heard with the unassisted ear. 



This instrument may be made of tin plate or other light metal, or, 

 what is better, fine card-board. For the sake of portability, it may 

 be constructed of oiled or gummed silk, folding and unfolding in the 

 manner of an umbrella. 



On the higher Orders of Grecian Music. By Samuel Rootsey, M.D. 



That the ancients admitted many primes into their expressions of 

 musical intervals is known to the learned, but (the author believes), 

 exclusively from the writings of Ptolemy as edited by Dr. Wallis. 



The only three simple and prime ratios admitted by the moderns, are 

 the octave 1 : 2, the fifth 2 : 3, and the major third 4:5. Those systems 

 of music of which these form the three bases, the author calls the three 

 lowest orders of music, using this term order in the general sense of 

 mathematicians ; the first being that in which the only perfect interval 

 is the octave, the second having the fifths perfect, and the third being 

 our ordinary music as improved by the labours of Smith, Liston, Farey, 

 Chladni, and others. 



The number of small intervals, called semitones, brought into use by 

 the adoption of these bases, is seven. 



Besides the above semitones, the ancients used many others which 

 Dr. Burney believes are, to modern ears, perfectly intolerable. Some 

 of those notes by which these Greek intervals are formed are frequently 

 heard upon certain instruments, such as the trumpet; but having a most 

 peculiar character, and differing so widely from the notes of the piano 



