644 



wlieie / represents the wave-lengtli in kilometers, and t the time 

 in seconds necessary to raise tiie ainplitnde of the oscillations of 



he strii 



g from lo a value I 1 j of the end amplitude. The 



speed of transmission admissible is inversely proportional to t. 



The minute amount of energy sufficient to keep the string oscillat- 

 ing with its end-amplitude can easely be evaluated. For the sum 

 of the values neglected previously, can be determined by measuring 

 the decrement of the vibrations when dying away freely. 



Denote this decrement with (fi^s then the value to be found is 



or also 



B. = ^ X 10-^ X MU'N' 0,+s ..... (6) 



B.=B>.'^ (7) 



where tf/-|_s is again supposed to be small in comparison with <ƒ(,,„. 

 This is always the case with a good string, a moderate field and 

 an attainable vacuum. Under the conditions of the figures 2 and 3 

 we have (f/^s = 4X10^, whilst fig,,, with a magnetizing current of 

 4 amp. attains a value which is 75-tinies larger viz. 3 X 10~^ and 

 therefore B, =0,0133 A 



What value is to be computed for B when use is made of formula 

 (4)? The result depends on the dimensions, especially on the diameter 

 of the string inserted in the galvanometei'. 



If we take a fine siring') with a diameter of 0,2 fj, a vibration 

 amplitude of the same dimension will already be visible and suitable 

 to be recorded. We have then f7=2xlO '^ centim. The mass of 

 a string of the above mentioned diameter and of 1 centim. length 

 maybe taken as jiy^2x 10 " grams. Suppose, moreover, iV=20. 000, 

 and ff(,,„ == 0,001 , then we find, for the number of watts wanted, 

 that B = 3,2 X 10 "1^. From this we infer, that the sensitiveness of 

 the galvanometer is to be evaluated to an amount of the same order 

 of magnitude as that of the telephone. 



The use of such fine strings is attended with certain practical 

 difficulties, so that we prefer to work with strings 5 to 6 times 

 thicker and therefore considerably less sensitive. Moreover the sen- 

 sitiveness decreases, when the wave-length is shorter and the speed 

 of transmission higher, as may be seen from formula (5). 



1) Gonf. W. EiNTHoVEN, Ueber die Beobachtung und Abbildung dunner FSden. 

 Pflüoer's Archiv. f. d. ges. Physiol. Bd. 191, S. 60. 



