Instruments as Resonators. 123 



sounded, but no other ; the other notes that can be produced 

 may be regarded as the notes 3 and 2 made flatter by their 

 nodes being drawn back, as it were, to the position of node 4, 

 where the cone is cut and the lips are placed; the original 

 notes 2, 3, 4, or c' ', </, c /x , becoming thus the 1st, 2nd, and 

 3rd notes of a new inharmonic series, with pitches approxi- 

 mately c#, e\} f , c" — thus approaching the notes of a cylindrical 

 stopped tube. I have here two other tubes tapering in differ- 

 ent degrees — the first two proper tones on the one being d and 

 eft", and on the other c f and e" (a major tenth). From these 

 experiments it may be seen that, by using portions of cones 

 of different proportions with their small ends closed, it is pos- 

 sible to get different series of intervals varying between those 

 of an open and those of a closed cylindrical tube — that is, the 

 first interval varying between an octave and a twelfth. 



One of the examples just shown (the tube with notes c' and 

 c#") appears to give intervals not very far removed from those 

 required : it may be made use of to illustrate the effect of the 

 combination of a cone with cylindrical tubing, such tubing 

 being of necessity used in practice in connexion with valves 

 or slides to complete the scale. Flattening this cone a fourth, 

 from e ! to g, by adding tube, it gives the intervals g, e' ', d" in 

 place of the g, g', d" required, or the ratios 1, If, 3 in place 

 of 1, 2, 3, the second interval being actually greater than the 

 first. 



These illustrations prove that neither a conic frustum, nor 

 a conic frustum combined with cylindrical tubing, can truly 

 be resonators to notes in the natural harmonic series; but 

 seeing that a bugle or other wind instrument, although it has 

 a considerable diameter at the mouthpiece, may nevertheless 

 be in tune, it appears that its nodal points cannot be in the 

 same positions as those in the cone. On the diagram is re- 

 presented a bugle of the same pitch as the open tube and cone, 

 with the positions of its nodes and semi- ventral segments as 

 determined by experiment with tuning-forks. Comparing on 

 the diagram the positions of the nodes of any given note in 

 both the bugle and the cone, it will be noticed that there are 

 great differences. The nodes of note 2 show this clearly. 

 Compare lengths from both ends : from mouthpiece to node 

 the length is more nearly equal to that between similar nodes 

 on cylindrical tubing than to that between similar nodes on 

 the cone ; but from node to open end it is greater than on the 

 cone, the bugle opening more rapidly. 



Thus, then, by altering the proportions of the different semi- 

 ventral segments of which such an instrument may be con- 

 ceived to be built up, the positions of the nodes may be so 



