IOWA ACADEMY OP SCIENCE 
185 
A NEW APPARATUS FOR MEASURING SMALL INTERVALS OP TIME 
INDEPENDENT OP CLOCK OR CHRONOGRAPH. 
BY F. C. BROWN. 
In the Physical Review for June, 1912, the author discusses the theory of an 
electrical method for measuring small intervals of time. Time is measured in 
terms of the throw of a ballistic galvanometer, which is in the circuit of a 
Wheatstone’s bridge during the interval. 
The time to be measured is that which elapses between closing the key Ki 
and the opening of key K 2 , as diagramed in Pig. 1. This time is a direct func- 
tion of the resistance, the galvanometer constant and the electro-motive-force 
of the battery. It may be expressed as A t= ■ K-D-(K-X+K 2 )^ 
^ /\X.E(bK2+KiaR) 
where ki and k 2 are such functions of the resistance that 
ki=Gb+aG+bR+ah-f aR, and k 2 =aRG+bRG-f-abR, 
and where Ax is the amount by" which the resistance of x 
varies from that required for balance. 
The constant It is a function of the quantity of electricity 
that is necessary to give one division throw of the galvanometer 
as determined by discharging a condenser through it. 
The desired sensibility of the apparatus may be obtained by a suitable choice 
of galvanometer, resistance and battery. With these quantities fixed we may 
obviously write equation 1 in the form, 
' At=K.d, where K is the time interval corresponding to one 
division defiection. The value of this last constant may be satisfactorily found 
in either of two ways. The first may be called an absolute method. The con- 
stant K is determined by discharging a known capacity when charged to a 
potential E through the galvanometer. The other quantities are determined 
from the resistances used. The constant K is then calculated. 
The second method for obtaining the constant, is to measure the defiection 
obtained when the keys are operated by a body falling a short distance under 
the action of gravity. This time can be calculated very accurately, even where 
the value of gravity is not known accurately for the place of observation. Which 
method is to be used may well depend upon the aptitude of the observer. If he 
is at all familiar with the working of electrical apparatus the first method 
would probably be chosen. For very accurate work the two methods should be 
checked against each other. This insures the accurate working of the keys 
and the correctness of the electrical quantities. 
The following illustrates the reliability of the two methods of calibration. 
By letting an iron ball fall 6.2 cm. the defiections were 
28.5 
28.2 
28.4 
29.0 
28.9 
