980 Vibrations of Strings eacited by Plucking. 
different thicknesses and the same length, tuned to the same 
pitch. In our experiments with pianoforte wires we obtained 
results in qualitative agreement with these conclusions. 
Working with gut strings the results were less regular. 
This we ascribe partly to the irregularity in the diameter and 
the want of homogeneity in structure of the strings, and partly 
to the varying effect of the moisture absorbed from the air. 
One string, which showed a pronounced rigidity effect when 
dry, gave equally pronounced end-motion shapes when slightly 
damped. The frequency with which, as compared with steel, 
the rigidity forms were obtained, seemed at first sight incon- 
sistent with the greater rigidity of the metal. But in the 
‘ 5 
expression found above for ai have the square of the 
density in the numerator and the first power of Young’s 
modulus in the denominator, so that the lightness of the gut 
may balance the effect of its smaller elasticity. We made 
some measurements of “gq” for gut strings, taking care that 
the string was not allowed to untwist when the load was 
: kilos me 
increased. The value came out 3°38 x 104 ap The density 
isabout 1:1. For steel the corresponding values are 2°2 x 10° 
and! 7-7. 
- Po —3-9x% 107 for out, 
7 
and 2:7 x 10-5 for steel ; 
values of the same order of magnitude. 
Gut strings show great internal viscosity and consequent 
rapid extinction of the high partials. 
Now it is known from the general theory that those partials 
which havea node either at the point which is plucked, or the 
poiut whose motion is observed, do not enter into the com- 
position of the vibration-curve. So with the higher partials 
disappearing, and certain of the lower ones evicted by a 
proper choice of the points of pluck and of observation, we 
can obtain curves built up of very few components. Photo- 
graph 4 is obtained from a gut string, plucked at 4 of its length 
from one end and observed at 3. The rapidly recurring cycle 
of forms shows that we have got practically the fundamental 
and third partial unaccompanied by higher harmonics ; and 
that the mistuning of the third partial is considerable. The 
cycle occupies 18 vibrations, whence it is easy to ge that 
ov 
a relative to 
the upper component is too sharp by the interval 
