﻿Hammer and String in a Piano. 



367 



amount of which the time of closing may be calculated. The 

 minimum resistance of the circuit when closed by holding up 

 the hammer was 2*7 to 3'0 ohms, to which a 10-ohm coil was 

 added to diminish the uncertainty arising from any variable 

 battery- or contact-resistance and to reduce the deflection. A 

 telescope and scale were used at a distance of 1*6 meters. 



The piano used was a Knabe Grand, put at my disposal by 

 my former colleague, Professor C. B. Cady, who believes that 

 such studies as these may throw light on the technically 

 important subject of " touch." The b (just below middle c) was 

 found on comparison with a Koeing's fork to make 2554 d. v. ; 

 therefore c' = 270-6 d. v. 



From the theory of the ballistic galvanometer we get the 

 equation 



_T R3 



'-^ X R/F 

 t = time in seconds of momentary closing of circuit. 

 T = time in seconds of single vibration of galvanometer needle. 

 R = resistance of circuit. 



R' = resistance of circuit when a constant deflection was observed. 

 S- =c throw of needle, in scale divisions. 



B'= constant deflection, in scale divisions, with R' ohms in circuit. 

 T .= 5-87 sec. R =13 ohms (12*7 for exps. 1 and 2). 



R'S-' = 440000. 

 .-. t = 0*000055 5 seconds. 



The correction for damping is so small that we may neglect it — 

 about 2 per cent. The results of the observations are shown 

 in the accompanying table. 



No. 



Tone. 



No. vibr. 

 n. 



No. 

 obs. 



Mean. 



t. 



Sec. 



txn. 



Stroke. 



1 



o, 



34 



11 



92-0 



•0051 



0-17 





2 







7 



113-0 



•0062 



0-21 



Soft. 



3 







3 



94-0 



•0052 



0-18 





4 







2 



82-5 



•0045 



0-15 



Hard. 



5 







1 



102-0 



•0056 



019 



Soft. 



7 







1 



830 



•0045 



015 





8 







1 



108-0 



•0060 



0-20 



Soft. 



16 







1 



94-5 



•0052 



0-18 





6 



c 



67-7 



3 



525 



•0029 



0-20 





12 



B 



127-0 



2 



34-0 



•0019 



0-24 





12 







2 



38-0 



•0021 



0-27 



Hard. 



11 



c 



1353 



6 



35-0 



•00193 



0-26 





10 



</ 



2706 



9 



160 



•00088 



0-24 







c" 





_- 











Broken. 



13 



c'" 



108-2 



3 



28-0 



•00154 



1-68 





14 







3 



20-5 



•00115 



1-23 





15 







2 



18-5 



•00102 



1-11 





