84 PHOTO-TELEGRAPHY 



displaced, and this light fall on a rapidly travelling 

 band of photographic film, and a tap be then given 

 with the Morse key as above described, a record of 

 the' movements of the string is obtained. If the 

 rate at which the film travels be known, it is easy to 

 calculate the period of the galvanometer. 



The string has a shorter period if its length be 

 shortened or its tension increased, and the damping 

 of its oscillations can be effectually increased if a 

 twist be given to one end of it in the manner 

 already indicated. The effect of damping can be 

 seen if we consider the equation of the move- 

 ment of the string, which is of the form 



d = ae~ kt cos (nt -f- a )> 



where d is the displacement ; ae ~ kt decreases as 

 t increases ; k is the damping constant, and e~ kt the 

 damping factor. K has got to be as large as pos- 

 sible, and can be made large if we increase the 

 friction at the ends of the string. Suppose the 

 string to be displaced still through the distance d, 

 where / is the elastic force, the work done is df ; 

 this is the measure of the potential energy of the 

 centre of the string, provided we subtract /, the 

 loss of energy through heating owing to the 

 friction ; I increases as / is increased, while d 

 is diminished for the same amount of current sent 

 through the string. 



The rapiditv of damping is readily seen from the 

 diagram shown in Fig. 39, which is drawn to scale 



