226 Professor Silvanus P. Thompson [June 13, 



between the component partial tones are continually changing, both 

 in relative intensity and in phase. The wavelets, as they follow one 

 another, are ever changing their forms ; in other words, the motions 

 are not truly periodic — their main form may recur, but with modifi- 

 cations ever changing. 



To estimate the part j)layed in such phenomena by mere differ- 

 ences of phase — to evaluate, in fact, the influence of phase of 

 the constituents upon the integral effect of a compound sound — Dr. 

 Koenig had recourse to the wave-siren^ an earlier invention of his 

 own, of which the wave-disks which have already been shown are 

 examples. 



In the first place, Dr. Koenig proceeded synthetically to construct 

 the wave-forms for tunes consisting of the resultant of a set of pure 

 harmonics of gradually decreasing intensity. The composition of 

 complex wave-form out of simple waves belonging to a Fourier- 

 series has long been a familiar subject to students of acoustics ; and 

 instruments have been devised by Wheatstone and others to produce 

 them mechanically. Of such devices one of the most elegant is the 

 curve-drawing machine of Mr. A. Stroh, here on the table, which he 

 has kindly lent me, together with a number of curves produced by its 

 means. "With this beautiful little machine it is possible to draw 

 curves compounded of any of the first eight waves of a harmonic 

 series, in various phases and of various amplitudes. 



In Dr. Kcenig's synthetic study he began by drawing to scale the 

 separate waves of the different orders. The curves of these, up to 

 the tenth member of the series, were carefully compounded graphi- 

 cally : first with zero difference of phase, then wdth all the upper 

 members shifted on one quarter, then with a difference of a half- wave, 

 then with with a difference of three-quarters. The results are shown 

 in the top line of curves in Fig. 6, wherein it will be noticed that 

 the curve for difference of phase = i is like that for zero differ- 

 ence, but reversed, left for right ; and that the curve for difference 

 of phase = J is like that for difference = J, but inverted. Now, 

 according to von Helmholtz, the sounds of all these four curves 

 should be precisely alike, in spite of their differences of form and 

 position. To test the matter, these carefully-plotted curves were set 

 out upon the circumference of a cylindrical baud of thin metal, the 

 edge being then cut away, leaving the unshaded portion, the curve being 

 re})eatcd half a dozen times, and meeting itself after passing round 

 the circumference. For convenience, the four curves to be comjjared 

 are set out upon the separate rims of two such metallic cylindrical 

 hoops, which are mounted upon one axis, to which a rapid motion of 

 rotation can be imparted, as shown in Fig. 7. Against the dentel- 

 lated edges of these rims, wind can be blown through narrow slits 

 connected to the wind-chamber of an organ-table. In the apparatus 

 (Fig. 7) the four curves in question are the four lowest of the set of 

 six. It will be obvious that, as these curves pass in front of the slits 

 from which wind issues, the maximum displacement of air will result 



