Model to illustrate Helmholtz's Theory of Dispersion. 563 



We have seen that waves of high frequency are propagated 

 along the upper system of particles in the model with a 

 velocity independent of the wave-length, and that for such 

 waves the lower system remains undisturbed during their 

 passage. Similarly, when pulses of short duration are sent 

 along the upper system, the hanging weights remain at rest, 

 the velocity of propagation being independent of the inertia 

 of the hangers, and only influenced by the latter inasmuch as 

 their weight increases the tension of the threads. 



Thus the way in which the model propagates such short 

 pulses illustrates the passage of #-rays through media which 

 are dispersive for light. 



Conclusion, 



If another model similar to that described above had to be 

 constructed, the changes most desirable would be to increase 

 the length of the whole apparatus, and to set it up in a lofty 

 room so that the influence of the supporting threads would 

 be lessened. The object of these threads is simply to counter- 

 act gravity, and so enable small velocities to be used. 



Although more troublesome to construct, either of the 

 following arrangements might be used. Still employing 

 transverse waves, the bullets might be fastened to the lower 

 ends of a series of light rods. These rods could be vertical 

 and free to move about a horizontal axle through their centre 

 and parallel to the spring. The free end of each rod would 

 carrry a bullet like those in the spring. 



If compressional waves were used, a similar arrangement 

 could be employed, the rods being in this case horizontal, and 

 their free ends loaded with a mass equal to the sum of the 

 masses of a bullet and hanger. The rods would be supported 

 at their centres on pivots. 



It need scarcely be pointed out that the values of a and b 

 would have to be computed before the construction of the 

 model, and the masses chosen so as to have the interesting 

 portions of the curve in a region of accessible frequency. 



I am indebted to Prof. J. J. Thomson for having recom- 

 mended this work to me, and also for many valuable sug- 

 gestions. 



Cavendish. Laboratory, 

 Cambridge. 



