Lateral Vibration of Bars. D87 
Obaracter | Distance of ‘Displecement of the middle of the bar. | 
ofthe force from i 
curve. free end. ir | B. / C. | 
a |__| — — — 
| Dynaniical... ~~ 2°63 i 2°63 2-63 | 
'Statical ...... Polnipar 2°45 [oo DAT 2-46 
ce... 4x |) 251 | 2:53 253 | 
of fies a / 2°59 2-60 2°60 | 
> ee 3XL 2-70 | 2-71 2°71 
Prime and Overtones—When we set a bar in vibration 
by drawing it aside and releasing, we must have present a 
series of vibrations in order to build up the initial state of 
things : these die away at different rates. If we had only 
the fundamental present, we should get a regular dying away 
of amplitude at all points on the bar; then the ratio of the 
amplitudes at the middle and the end would be constant 
throughout. The presence of the overtones makes this vary 
within certain small limits. This point is shown experi- 
mentally .in the following manner:—The stop A and the 
microscopes M, and M, are adjusted as previously described, 
but now we take readings at the extreme of the first swing. 
M, then remains fixed for the rest of the experiment, while 
A and M, are adjusted to take readings after three, five, seven, 
&c., swings (one swing being half a complete vibration). 
Thus after n swings we have made the amplitude of the top 
of the bar a constant amount a, and therefore the ratio of the 
amplitudes of the middle and the end will be simply pro- 
portional to the displacement as read by M,. Any change 
in the curve of the bar, other than simply dying away, will 
be shown by a change in this displacement. We have then 
a series of readings of M, as nis varied ; the variation in 
the former is shown very well by plotting. In this case 
series of readings were taken with the stop A (1) at the end 
of the bar (see curve C, fig. 7) ; (2) one-fifth of the way 
down (see curve C,); (3) two-fifths of the way down (see 
curve C3). The three diagrams are given below (p. 588). 
The total displacement at the middle was 26 mms., the 
greatest deviation from the mean 2 mms., while the experi- 
mental error in the most favourable cases was only about 
jo mm. 
The points determined le on a regular curve, something 
like a sine-graph of decreasing amplitude. C, and Cy; are 
very nearly the reverse of each other, C;, having a crest where 
C. has a hollow, and wee versa. This follows from the fact that 
we are a considerable distance from the point where the 
