172 SEC. 6. SOUND. 



well as to columns of air. Invented by James Baillie Hamilton, 

 April 1876. 



20, 21, 22. Apparatus for studying the laws of strings combined 

 with reeds. 



IX. EDUCATIONAL. 



787. Apparatus for illustrating lectures. Auguste Bel fy Co. 



788. Graphical Representations of Musical Scales, on 



paste-board. Gustav Schubring, Erfurt. 



The logarithms of the numbers of vibrations and their differences were 

 first recognised by Euler (Leonhard Euler, tentamen morae theoriae musicae, 

 1739). These logarithms were at a later period used by Opelt ( " Natur der 

 " Musik," 1834, "Theorie der Musik") for the graphical representation of 

 musical scales. Herbart, likewise, has employed them in his psychological 

 speculations, and, lastly, Prof. Drobisch (Leipsic) has extensively applied 

 them in his calculations of the musical intervals (Abhandlungen der furstlich 

 Jablouowskischen Gesellschaft, 1846). 



The exhibited plates are especially intended to illustrate the musical scale 

 calculations of Prof. Helmholtz ; they agree in their annotations with those 

 employed in the older edition of the " Lehre von der Tonempfindungen " 

 (Part III., sections 15 and 16).. A reconstruction of these plates, according 

 to the annotations used in the new edition, is in course of execution. 



789. Model for the Higher Tones. 



Gustav Schubring, Erfurt. 



Prof. Mach (Prague) has made use of the high-tone scales, drawn according 

 to logarithmical scales, in order to produce a model for the high-scale tones. 

 By means of the same not only can the higher tones of any sound be ascer- 

 tained directly, but the higher tones of several sounds can also be compared 

 the one with the other. Altogether the theory of the musical consonance 

 and dissonance advanced by Prof. Helmholtz can be demonstrated thereby in 

 the most excellent manner. 



Prof. Mach's model had a length of three octaves, and contained the high 

 tones according to the tempered free-balancing scale. 



The model exhibited is more than four octaves long, and contains the high 

 tones in the pure (natural) key. 



789a. Model, similar to the two preceding, but not on paste- 

 board. Gustav Schubring, Erfurt. 



790. Sir Charles Wheatstone's Mechanical Illustration 

 of the Vibration of Strings or Bods. W. Groves. 



