118 CS. Peirce—On a Method of swinging Pendulums. 
both pendulums during any interval of time, then the mean of 
the average periods of the two during that interval, would give 
the mean period of either through a complete cycle of motion. 
A better method of observing, however, would be to set up a 
lens between the two pendulums, so as to bring the plane of 
oscillation of the one into focus on the plane of oscillation of the 
ot en, by means of a reading telescope set up at a little 
distance, the oscillation at which both crossed on the vertical — 
could be noted with some accuracy. It would then only be 
necessary to determine the mean period of oscillation of either 
from one such event to another. As the difference between 
the longest and shortest periods of oscillation would only 
amount to a few ten-thousandths of a second, it would not be 
necessary to be very exact in the time of beginning or ending 
the experiment. The number of oscillations between one coin- 
cidence at the vertical and another would afford a very accurate 
determination of y. For suppose n to be that number. Then 
whence 
- —1 
l4fae=(n—™ . 
i ( pay 
But as n is large (several thousand) we may take 2 = 4, 
and z as equal to y. 
This gives i aus 
Then z—y having been determined, we ascertain the value of 
x also. 
The greatest departure of the oscillations of the two pen- 
dulums from complete opposition of phase would occur when 
the phases of the harmonic components differed by a quadrant. 
In this case, the pendulums would cross at an angle equal to 
or from the vertical. The difference in the time of their 
passage over the vertical could only amount to a minute frac 
tion of a secon 
that d/ were greater than y, the-slower harmonic component 
would have a greater amplitude than the quicker one. this 
