174 Prof. Barton and Miss Browning on 



may be adjusted, at will, by simple pulling. The paper 

 cones mny each have a little soft wax inside and the cotton 

 suspension passed through by a needle and the end left free. 

 The cone may then be slid up and down the cotton at pleasure 

 to adjust in line with the others, and will stay where left. 



The white paper cones are much easier seen (or photo- 

 graphed) stroboscopically than the corks, and are on the 

 whole more satisfactory than the corks or the blown-glass 

 spheres. 



Since the phase of the forced vibration varies with the 

 natural period and therefore with the length of the re- 

 sponding pendulum, the full displacements are not attained 

 simultaneously. But on viewing the apparatus steadily 

 from one end, A say, the full displacements are seen to be 

 reached successively. Hence one may see a resonance curve 

 in which the squares of the various periods or lengths of the 

 pendulums are disposed vertically while the corresponding 

 amplitudes exhibit themselves horizontally. Thus the limits 

 to which the light bobs swing on each side form there a 

 resonance curve in which the squares of the periods are the 

 vertical abscissae and the amplitudes are the horizontal 

 ordinates. Thus a time exposure will give a photograph 

 exhibiting this resonance curve in duplicate to right and left 

 of the central line. The effect is shown for various types of 

 responding pendulums in figs. 1, 2, and 3 of Plate VIII. It 

 is seen that the blunt cones (fig. 1) give curves showing the 

 sharpest resonance, the small blown-glass spheres (fig. 3) 

 give the greatest range of resonance, and the sharp cones 

 (fig. 2) show an intermediate type of resonance. This is in 

 accordance with theory, since the values of k for these three 

 kinds of bob (as found from their logarithmic decrements 

 when vibrating alone) are 0*16, 0*265, and 0*2 respectively. 



In order to appreciate the various phases of the vibrating 

 systems of differing periods an instantaneous view of the 

 bobs is needed. The motion is so slow that it seemed quite un- 

 necessary to make any elaborate electric timing arrangement. 

 At first the camera was instantaneously exposed 40 times at 

 the desired instant as judged by sight, and this gave the 

 result reproduced in fig. 4 (PI. VIII.). Better results shown 

 in figs. 5 and 6 were obtained by the ordinary flash-light 

 process. One of these, fig. 5, corresponds to the central 

 position of the driver, and exhibits what may be called an 

 exaggerated resonance curve. This is because when the 

 driver is at the centre, the driven bob of about the same 

 length and having maximum response is then at one end of 

 its swing and therefore shows its full amplitude. But as we 



