637 



attained vacua of 1 ji Hg and even higlier and were able to show, 

 that nrider such conditions the air danaping lias practically no more 

 infliienee on the irioveinent of the string. The vibrations do not die 

 away more slowly when the vacuum is made higher than 1 (i, since 

 the internal friction of the string itself, i.e. the fact that the material 

 of the string has no perfect elasticity is another cause of damping. 



It is not to be expected, that the vibrations of a coated quartz 

 fibi'e stretched like a string would die away as slowly as those of 

 a pure quartz roil which has been fixed at oidy one end. Experi- 

 ments of Habkr and Kerschbaum ') have shown that it took more 

 than 12 minutes, before the amplitude of a quartz rod vibrating in 

 vacuo was diminished to one half of the original size. Langmuir ') 

 succeeded in lowering the |)ressure in an incandescent bulb lamp so 

 much that the time of halving the amplitude was lengthened to nearly 

 two hours. 



But if we cannot make the vibrations of our string die away 

 equally slowly, neveitheless for the purpose aimed at the result is 

 satisfactory. We could for instance show, that a string performing 

 40.000 vibrations |)er sec, without the intentional application of a 

 damping factor needed a lime t = 0,65 sec. to diminish its ampli- 



1 



lude in the proportion ot 1;—, wheretrom it mav be interretl, that 



the logaiitlimic decrement of the mo\ement amounted to 4 10~*, 

 conf. fig. 2. 



Fig. 2. 



A string the vibrations of which are dying away freely. 



A = 7,5 1cm. r = 0,65 sec, J = 4 X 10-5. 



This decrement is of the gi-eatest value for our purpose, for the 

 smaller it is so much the belter is the selectivity of the instrument. 

 If the string has been put in tune with a definite wave, it will 

 react to atmospheric disturbances and to currents of different wave 

 lengths coming in from other stations so much the less, the smaller 

 the decrement is. Generally speaking we may say that the efficiency 

 of a receiving apparatus is determined by the amount of its decrement. 



For purposes of comparison it may be recalled, that the smallest 



') Zeilschr. f. Elektrochemie. Bd. 20, 1914, p. 296. 



^) Journal of the American Chem. Soc. 35, 107 (1913) cited from Habeb u. 

 Kerschbaum. 



