PEIRCE. 



BALLISTIC GALVANOMETERS OF LONG PERIOD. 



305 



careful observations showed that the throw was 1471, 1470, 1468, 1464 

 1458, 1452, 1444, according as the interval between the impulses was 

 0, 1, 2, 4, 6, 7, or 8 seconds. At this circuit resistance, T = 139, 

 p = 0.0450, a = 0.0125, and if we assume the interval to be 8 seconds, 

 <*t = 0.1, and pr = 0.360, which corresponds to 20.63°. According to 

 (43) under these conditions, R = 1.017, £=0.195, VR 2 -+- S' 2 = 1.035, 

 tan" 1 (S/R) = 0.1891, and A/A = 0.982. That is, the throw when 

 the second impulse follows the first at the interval of eight seconds 

 should theoretically be only 982 thousandths of the throw due to the 



Figure H. 



two impulses coming together. The results of experiment give 

 1444/1417 or 0.982. This exact coincidence is, of course, a matter of 

 chance. 



When the interval is 4 seconds, <xt = 0.05, pr = 0.180, and 

 A/A = 0.995 ; here again the agreement with observation is exact for 

 1464/1471 = 0.995. For an interval of 6 seconds, theory gives for A/A 

 the value 0.992+ and experiment, 0.992—, so that the experimental 

 results, which were obtained long before any computations were made, 

 point to a complete agreement, within the limits of observation, with 

 theory. 



With this damping, corresponding to a value for R of about 25 ohms, 

 the time required for the coil to reach its elongation from the zero 

 point is about 28.9 seconds ; the return takes 40.6 seconds. When R 

 is 500, the time from the zero is 32.9 seconds, and the time back is 33. 1 

 seconds. 



VOL. XLIV. 



20 



