1912-13.] Error caused by “Lag” in a Recording Instrument. 115 
exceptionally large discrepancy in the last case may be accounted for by 
the fact that here we are working at that end of the stopping curve at 
which greatest doubt exists as to its exact shape, since being a derived 
curve the slope of the integral curve is most difficult to determine at 
its ends. 
To find an empirical formula to represent the overrunning we may 
assume it to be of the form 
where Y 1 is the terminal velocity. It is useless to determine the constants 
K, a, b, c accurately, since their values will apply only to the set of experi- 
ments conducted above ; but we desire to know at least their sign and 
their order, so that the laws governing the overrunning in this case may 
roughly be determined. 
In the table quoted above, for the first eight sets, the values of N are 
constant, and these in pairs have constant also. Hence, if the formula 
we have assumed is at all justifiable we must have 
36 
( 5 V 
113“' 
^21*2/ 
54 
(7-2 V 
119 
\24'2/ 
56 | 
( 8*2 V 
122 1 
^ 27 - 2 ; 
96 
m-5v 
145 1 
V4i-5; 
a=' 78 
a — '65 
a = - 65 
a = ' 48. 
This gives us a rough average value a — '6. 
Again, using all the data, we obtain roughly a = ' 7, b= — 5, c= — 1. 
The values of the constants being thus determined approximately, the 
similarity between this formula and that already derived, viz. 
once seen. The overrunning in the experiments described varies from 36 
per cent, to 252 per cent. ; but as the apparatus used was specially designed 
to exaggerate this, no great stress can be laid on the magnitude of the result. 
It is doubtless significant, however, that the error is always found to be 
of the same sign. 
Summary. 
All instruments designed to give a record of some fluctuating quantity 
as a function of the time, both those employed to give “ instantaneous ” 
values of the quantity measured and also those which totalise or integrate 
it during a given time, are liable to suffer from error due to the inertia 
