3840 :4096 15:16 128 Ut_{2} 3904 : " 61:64 96 Sol_{1} 3936 : " 123:128 80 Mi_{1} 3968 : " 31:32 64 Ut_{1} 3976 : " 497:512 60 Si_{-1} 3989.3 : " 187:192 53.3 La_{-1} 4000 : " 125:128 48 Sol_{1} 4010.7 : " 47:48 42.7 Fa_{-1} 4016 : " 251:256 40 Mi_{-1} 4024 : " 503:512 36 Re_{-1} 7936 : 8192 31:32 128 Ut_{2} 8064 : " 63:64 64 Ut_{1} 8096 : " 253:256 48 Sol_{-1} 8106.7 : " 95:96 42.7 Fa_{-1} 8112 : " 507:512 40 Mi_{-1} 8120 : " 1015:1024 36 Re_{-4} 8128 : " 127:128 32 Ut_{-4} On sounding two forks nearly in unison, the sound heard corresponds to a number of vibrations equal to the difference of the numbers of vibrations of the forks. On sounding two forks, one of which is nearly the octave of the other, the ear perceives a sound, which is that given by vibrations whose number equals the difference in the number of vibrations of the higher fork and the upper octave of the lower fork. Koenig has also found out the laws of the resultant sounds produced by other intervals than the octave, and has extended his researces to intervals differing by any number of vibrations, as may be seen from the above table. His conclusion is that beats and resultant sounds are one and the same phenomenon. Thus, for example, the lowest number of vibrations capable of producing a musical sound is 32 per second; in like manner, a clear musical sound is produced by two simple notes of sufficient intensity which produce 32 beats per second. Koenig also made a very ingenious modification of the siren for the purpose of enabling Seebeck to sound simultaneously notes whose vibrations had any given ratio. It is furnished for this purpose with eight disks, each of which contains a given number of circles of holes arranged at different angular distances. A description of this instrument, which is also the property of the Stevens Institute, and of Seebeck's experiments is thus given in a letter by Koenig himself. I. _Effects produced when the isochronism of the shocks is not perfect_. A. In order to produce a note, the succession of shocks must not deviate much from isochronism. If the isochronism is but little impaired, we obtain a note corresponding to the mean interval of the shocks.