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SCIENCE. 



[N. iS. Vol. IV. No. 87. 



system, by computing the frequencies and 

 corresponding intensities due to eacli hypo- 

 thetical system, and by then comparing 

 computation and observation. 



For a second example, suppose we ring, 

 for our imagined observer, a bell of a certain 

 form, and that he notes the frequencies 

 200, 475, 845 and 1295 in one second ; in 

 which, also, he finds that the vibration 845 

 so predominates as to give its pitch to the 

 compound tone. Our observer will not be 

 able to refer this sound to any stretched 

 cord, or to any organ-pipe or other wind 

 instrument; for all these are limited to 

 frequencies contained in the series 200, 400, 

 600, 800. A uniform metallic bar, sus- 

 pended and struck like the triangle of an or- 

 chestra, will give frequencies not contained 

 in this Ust, but they will be 200, 550, 1080, 

 and 2670, instead of 200, 475, 845 and 1295. 

 But if our observer has adequate powers 

 he will imagine a hemispherical bowl of 

 suitable dimensions, and will, in imagina- 

 tion, add mass and rigidity in suitable 

 places, until, in time, he will have devised 

 a system whose computed vibrations agree 

 in frequency, and in distribution of energy, 

 with those of the invisible sounding body. 

 Then he would conclude that the observed 

 sound was due to a bell of the form assumed 

 in the successful computation. 



This illustration sketches, imperfectly, I 

 fear, the laborious method by which we 

 may learn the structure of a vibrating sys- 

 tem from a study of the vibrations pro- 

 duced by it. When we attempt to use this 

 method in order to learn something about 

 the structure of molecules and atoms, our 

 powers of imagination and our mathemat- 

 ical skill are none too much. "We know 

 but little which can suggest plausible 

 hypotheses. The facts which are to be 

 explained have been but recently reduced 

 to order. Accordingly, little has been act- 

 ually accomplished. But there are some 

 few examples of the use of this method 



of studying the structure of molecules and 

 atoms. 



In one such example the structure im- 

 agined consisted of a system of concentric 

 spherical shells, each connected with the 

 adjacent shells by springs. This compli- 

 cated structure admits of relatively simple 

 computation, and was taken because it 

 fairly well represents a rather simple im- 

 agined structure, for which, however, com- 

 putation is difficult. But it was found that 

 the results computed on this hypothesis 

 gave little promise of agreement with facts. 



This was a dynamical hypothesis ; it sug- 

 gested, not only vibrations, but the forces 

 which were to produce them. A second 

 example suggests certain possible motions, 

 but not the forces which might produce the 

 hypothetical motions ; it is not dynamic, 

 but kinetic. 



As we know, many of the lines in the 

 spectra of the elements are double. For 

 instance, when a volatile compound of so- 

 dium is brought into a colorless gas flame, 

 this is colored yellow. When we examine 

 this yellow flame with a spectroscope of suf- 

 ficient power, we see that there are two 

 frequencies, difiering from each other by 

 only one part in a thousand. Now it is 

 probable that these two frequencies are due 9| 

 to the vibrations of one and the same body. 

 There are many illustrations of the fact 

 that a given body may perform two diifer- 

 ■ ent vibrations whose frequencies differ but 

 slightly. For instance, if we suspend a ball 

 by means of a cord and let it oscillate as a 

 pendulum it is well known that a swing 

 of six feet takes a little more time than a 

 swing of three feet. Suppose, then, that we 

 let our ball swing six feet north and south, 

 and also three feet east and west at the same 

 time ; the two motions may be combined so 

 that the ball moves in an ellipse —an ellipse 

 whose longer axis is north and south. If 

 the longer and the shorter swing had pre- 

 cisely the same frequency, the axis of the 



