August 28, 1896.] 



SCIENCE. 



253 



tion. It may be said that it has seemed 

 not impossible that the chemist should find 

 a vortex ring capable of exerting certain 

 chemical forces. But the fate of the hy- 

 pothesis rested, not with the chemist, but 

 with the mathematical physicist ; and it 

 has been found that the theory demands 

 that the weight of a body composed of vor- 

 tex atoms should increase with rise of 

 temperature. It is scarcely possible that 

 this can be the fact; if, then, the mathe- 

 matical and physical reasoning involved is 

 sound, it is scarcely possible that atoms 

 consist of vortex rings. The probability is, 

 therefore, but small that we are to learn of 

 the nature of atoms by means of this hy- 

 pothesis. 



Some spectroscopic and other optical 

 phenomena seem to promise more light as 

 to the structure of molecules and atoms, 

 though the dawn is not yet. Thanks to 

 the concave grating, we can determine the 

 frequency of vibration of the light from any 

 source with great accuracy. When the 

 light is complex we can determine, with 

 great accuracy, the relative frequency of 

 the component vibrations. In the cases 

 which have been best studied, the observed 

 frequencies have been reduced to rather 

 simple numerical relations. From the 

 study of these relations we may expect, in 

 time, to determine the structure of the 

 vibrating systems. But the way is long 

 and difl&cult. Let us illustrate the nature 

 of the method by means of a familiar ex- 

 ample, namely, by the study of the struc- 

 ture of a sonorous vibrating system by 

 means of the study of the sonorous vibra- 

 tions produced by it. 



Let us suppose a person deprived of the 

 sense of hearing, but master of the whole 

 mathematical theory of sound. Suppose, 

 further, that he has an instrument which 

 will do for sound what the spectroscope 

 will do for light. With this instrument, 

 let him observe the frequency and the rela- 



tive intensity of the vibrations produced 

 by certain musical instruments which we 

 cause to vibrate for him, but withhold from 

 his inspection. Let us, first, sound for him 

 a single note on a piano. The vibrations 

 produced are, as you know, somewhat com- 

 plicated. Our imagined experimenter, with 

 his instrument, observes vibrations whose 

 frequencies are 100, 200, 300, 400, 500 and 

 600 in one second ; and he also observes 

 that the vibrations of 100 and 500 are of 

 nearly equal intensity, that the vibrations 

 200, 300 and 400 have more than twice 

 as great an intensity, and that vibra- 

 tion 700 is very feeble. From these 

 facts, if his attainments are sufl&cient and 

 his imagination sufficiently fertile, he can 

 determine what system produced the sound. 

 He imagines every possible vibrating sys- 

 tem — drum, cymbals, trumpet, flute, organ- 

 pipe, harmonium- reed, violin- string, piano, 

 harp and more. Next, assuming each 

 imagined system of such size or tune as to 

 produce one hundred vibrations a second 

 for its gravest tone, he computes what other 

 vibrations will also be produced and what 

 the intensity of each. He finds, for in- 

 stance, that a closed organ-pipe will give 

 only the frequencies 100, 300, 500, but will 

 not produce the other observed frequencies 

 200, 400, 600. Therefore, he concludes, the 

 sound we produced for his study is not due 

 to a closed organ-pipe. He finds, after 

 many trials, that the observed frequencies 

 and intensities could be produced by strik- 

 ing a stretched cord with a soft hammer, 

 at a definite point near the end of the cord, 

 so quickly that the cord and hammer re- 

 main in contact about the six-hundredth 

 part of a second, and that the observed 

 phenomena could not be produced by any 

 other of the imagined vibrating systems. 

 Then he concludes that the observed sound 

 was probably produced by the stretched 

 cord of a piano. He will have detected the 

 true system, by first imagining every possible 



