614 
for the deflection of the middle part of the totally relaxed ie” 
E being the elasticity modulus. 
Comparing the expressions 2) and 3) we see that variation of the 
diameter d — and as a matter of fact also of the length / — appears 
to have another influence with relation to the weight of the string 
than with relation to its elasticity. Halving the diameter should 
cause the sensitiveness to increase 4 times according to 2) and 16 
times according to 3). The significance of this is, that the two for- 
mulas should be combined in some way. Also we see that with 
thick strings the sensitiveness is principally limited by the elasticity 
of the material, whereas with very thin strings elasticity has little 
or no influence at all but it is the weight that counts. Finally there 
should be for any material a definite length and diameter with 
which the limiting influence of weight and elasticity are equal. This 
critical diameter can easily be calculated by equating 2) and 3). 
We find then: 
Be (2) 
With this formula table I can be calculated giving the critical 
value of the diameter (with a length of 10 and 5.6 centimeters) with 
which the influence of weight equals that of the elasticity. 
TABLE I. 
je | ‚_d with | d with 
98.1.106 | ” l= 10cm. | /=5.6 cm. 
Copper | 11000 | 8.9 8.2 u | 3.4 u 
Silver | 7500 10.5 10.8 » 4.5 » 
Gold | 7500 19.5 14.7 » 6.1 > 
Aluminium | 6750 | id 4.6 » 1.9 » 
Platinum 16500 lors 1032 en 
Silvered quartz | (6000) | (5.46) | 87» | 3.6% 
| | | 
The value for # used for silvered quartz does not take the 
silvering into account, which anyhow cannot possibly be of much 
importance. The figure given for the density is calculated from the 
weight divided by the volume in case of a silvering of a thickness 
which gives the highest possible normal sensitiveness (v. Theoretisches 
und Praktisches Zum Saitengalvanometer, Pfliigers’s Archiv. f. 
Physiologie V. 158 p, 107 1914). 
