228 Professor Silvanus P. Tliomjpson [June 13, 



when the slit is least covered, or when the point of greatest 

 depression of the curve crosses the front of the slit. The negative 

 ordinates of the curves correspond therefore approximately to 

 condensations. Air is now being supplied to the slits ; and when I 

 open one or other of the valves which control the air-passages, you 

 hear one or other of the sounds. It must be audible to every one 

 present that the sound is louder and more forcible with a difference 

 of phase of \ than in any other case, that produced with £ difference 

 being gentle and soft in tones, whilst the curves of phase and ^ 

 yield tones of intermediate quality. Dr. Koenig found that, if he 

 merely combined together in various phases a note and its octave 

 (which was indeed the instance examined by me binaurally in 1876), 

 the loudest resultant sound is given when the phase difference of the 

 combination is \, and the mildest when it is £. 



Returning to Fig. 6, in the second line are shown the curves 

 which result from the superposition of the odd members only of a 

 harmonic series of decreasing amplitude. On comparing together 

 the curves of the four separate phases, it is seen that the form is 

 identical for phases and ^, which show rounded waves, whilst for 

 phases \ and '^ the forms are also identical, but with sharply angular 

 outline. These two varieties of curve are set out on the two edges 

 of the highest metallic circumference in the apparatus depicted in 

 Fig. 7. The angular waves are found to yield a louder and more 

 strident tone than the rounded waves, though according to von Helm- 

 holtz, their tones should be alike. 



A much more elaborate form of compound wave-siren (Fig. 8) 

 was constructed by Dr. Koenig for the synthetic study of these phase- 

 relations. Upon a single axis, one behind the other is mounted a 

 series of 16 brass disks, cut at their edges into sinusoidal wave- 

 forms. These represent a harmonic series of 16 members of de- 

 creasing amplitude, there being just sixteen times as many small 

 sinuosities on the edge of the largest disk as there are of large 

 sinuosities on that of the smallest disk. A photograph of the ap- 

 paratus* is now thrown upon the screen. Against the edge of each 

 of the 16 wave-disks wind can be separately blown through a slit. 

 This instrument, therefore, furnishes a fundamental sound with its 

 first fifteen pure harmonics. It is clear that any desired combina- 

 tion can be obtained by opening the appropriate stops on the 

 wind-chest ; and there are ingenious arrangements to vary the 

 phases of any of the separate tones by shifting the positions of 

 the slits. 



The brass tubes, which terminate in 15 mouth-piece slits, are 

 connected to the wind-chest by flexible rubber tubes. The mouth- 

 piece tubes are so mounted that they can be displaced laterally in 

 curved slots concentric with the disks. By the aid of templates 



* It is described fully by Dr. Koenig in his volume ' Quelques Expe'riences,* 

 and was figured and described in * Nature,' vol. xxvi. p, 277. 



