302 PROCEEDINGS OF THE AMERICAN ACADEMY. 



enough to disturb a person who is attempting to get an accurate value 

 of the so-called damping coefficient for use in the differential equation. 



Some of the constants of this galvanometer as determined by Mr. 

 Coulson are given in Table I. - 



Such slight departures from symmetry as these seem, however, not 

 to affect in the least the usefulness of a good d'Arsonval galvanometer 

 in measuring quantities of electricity sent through its coil ; the mean of 

 throws on opposite sides of the zero point due to a given impulsive 

 discharge remains practically constant, and a good calibration might 

 often be made to serve for a long time, though the instrument should 

 be tested, of course, every time it is used. 



In view of the fact that the motion of the coil of a d'Arsonval galva- 

 nometer usually deviates somewhat, as we have seen, from the course 

 laid down by the Gaussian theory, we may inquire whether such equa- 

 tions as (14), (33), (42), based on that theory, agree with the results 

 of observations on ordinary instruments. It may be well to say at the 

 outset that, according to my experience, the agreement is wonderfully 

 close. 



To support this assertion I may adduce first a simple test made a 

 long time ago upon the galvanometer X mentioned above. If we as- 

 sume for a the value 0.0611, the natural logarithm of 1.063, and for T 

 the value 149, it appears that a = 0.00082 and p = 0.0422. The time 

 required for the swing out from the zero to the turning point is then 



- tan _1 ( - j or 36.4 seconds : the return to the zero requires 38. 1 sec- 

 onds. If under these circumstances a given impulse be sent through 

 the coil, and after an interval t = 10 seconds, another equal impulse, 

 the resulting throw should bear to that which would be caused if both 

 impulses came together at the beginning, the ratio given by (42) when 

 git — 0.082, and pr = 0.422, which corresponds to 24.18°. In this 

 case R = 0.9597, 8 = 0.2064, VR 2 + S 2 = 0.982, log eT = 9.9980, 

 and A/A is about 0.977 -f. Now when a single impulse from an 

 induction apparatus without iron was sent through the coil, and after 

 a delay of ten seconds another equal to the first, the throw as given by 

 a number of readings was 1 144, but the reading when both came together 

 was 1170. The ratio of these numbers is 0.978. It is easy to show by 

 a little computation that if the delay were 5 seconds, the ratio of A to 

 A would be 0.994 ; but if it were 30 seconds, the ratio would be about 

 0.806. 



