* 
Records of the Free Vibrations of a Tuning-fork. 449 
--(a—b). The possible error therefore in the counting of the 
number of siren revolutions in the interval between two coin- 
cidences amounts to 2(a—b), and is0 when a=0. If, however, 
the chemical record does not begin till a time ¢’ after the con- 
tact is closed and continues for a time ¢’” after it is broken, then 
making t=?’ ¢’’, what may be called the “ effective ” or “chem- 
ical” contact will have the duration 6-:t, and the error may 
amount to 2(a—b-t). The quantity ¢ may be due to either 
the delay in the starting or the stopping of the chemical action 
after the circuit has been made or broken, or to the dragging 
of the color under the point of the pen when the paper is too 
wet. The former appears from experiments to be inappreci- 
able, the latter becomes large arid uncertain if the paper is too 
wet, but is apparently insignificant when care is taken to have 
the paper only just wet enough to let the current pass. If 
a<, the siren-record will never be completely elided, but it may 
be shortened at either end or cut into two. It may be thus so 
set-screw. After adjusting the magnet and the spring of the 
relay W, so as to give the shortest possible excursion of the 
armature A, the duration of the siren contact was made equal 
to that of the excursion by moving the spring to the proper 
position. In effecting this equalization, the duration of the 
siren-cotnact was measured by drawing the 
paper very rapidly under the pen, while the 
siren was rotating, and measuring the length 
of the dashes and the distance between the 
middle points of two consecutive dashes. The 
ratio of the first to the second, gives the dura- 
tion of the contact in terms of the duration of 
a revolution, which latter is known. The 
duration of the armature excursion is found oe 
by stopping the siren, setting it in such position that its circuit 
18 closed, drawing a paper rapid!y under the pen, and measuring 
the ratio of the short gaps in the now nearly continuous record, 
to the interval between the centers of two gaps, which latter is 
