108 Dr. R. Konig on Manometric Flames. 



eight spherical resonators are replaced by fourteen universal 

 resonators. These resonators consist each of a cylinder, its 

 length about equal to its diameter, which is formed by two pipes 

 placed one within the other. The outer of these pipes termi- 

 nates at one end in a hemisphere, from which the tube for the 

 ear is carried, as in the spherical resonators. The opposite end 

 of the inner pipe is closed by a plate, in the middle of which 

 there is an opening for the passage of the enclosed air to the ex- 

 terior atmosphere. This arrangement permits us by drawing 

 oat the pipe to increase the mass of air in the resonator, and to 

 lower its tone by a third. On the inner tube lines are drawn 

 which indicate how far the outer one must be drawn out for the 

 different notes. The deeper resonators of the series are so con- 

 structed that the highest note of the larger shall always reach 

 to the lowest of the next smaller one. In the higher-toned 

 resonators this would not be sufficient, because the sixth, seventh, 

 and eighth accessory notes approach each other so nearly that 

 the necessity might occur of forming two of thetn with the same 

 resonator. Since, therefore, the highest notes of the deeper are 

 a whole note above the lowest notes of the next upper resonator, 

 the whole series contains the following notes : — 1, G-B ; 2,B-dis ; 



3, dis-fis ; 4, jis-a ; 5, a-c ; 6, c-e ; 7, e-gis ; 8, gis-c ; 9, c-e ; 



10, d-f; 11, e-gis; 12, f-a ; 13, gis-e ; 14, c-d. 



The series of overtones for the notes of both octaves from C-c 

 are to be found in the resonators placed opposite to each in the 

 following Table : — 



c 



2, 4, 5, 6, 



7, 8, 9, 10. 



c : 2, 5, 



7, 8, 9, 



11, 13, 14. 



D 



2, 4, 6, 7, 



8, 9, 10, 11. 



tf:2, 6, 



8, 9, 10, 



12, 13, 14. 



E 



3, 5, 6, 7, 



8, 9, 10, 11. 



e:3, 6, 



8, 9, 11, 



13, 14. 



F 



3, 5, 7, 8, 



9, 10, 11, 13. 



/ 3, 7, 



8, U, 12, 



13. 



G 



1, 4, 6, 7, 8, 



9, 10, 11, 



9 : 4, 7, 



9, 11, 13. 





A 



. 1, 4, 6, 8, 9, 



10, 11, 12, 



a. 5, 8, 



9, 12, 14. 





B 



1, 5, 7, 8, 9, 



11, 12. 13, 



b . 5, 8, 

 c;5, 8, 



11, 12. 

 11, 13. 





For the fundamentals C-F the resonators are wanting, but 

 one can make observations up to the ninth note of the sound. 

 For the sounds G-d the resonators serve to the eighth note; 

 then they begin to fail; at e we can employ only six names, at 

 / five ; and at last at c but three for the overtones. 



Although, as before mentioned, it is indicated on each reso- 

 nator how far it must be drawn out for the different notes, yet it 

 is as well, in order to have exact results with the apparatus, par- 

 ticularly if the fundamental of the sound to be investigated does 

 not exactly coincide with one of the indicated notes, to employ 



