REDUCTION OF PENDULUM OBSERVATIONS. 
117 
tions, reduced of course to the same conditions, are not 
widely different. This supposes the conditions to be not 
abnormal ones; because if the observations are made in an 
extremely rarefied atmosphere, or at a very high tempera¬ 
ture, or through a wide amplitude for the purpose of study¬ 
ing these conditions, manifestly discrepancies found here 
should not be taken as a criterion by which to judge this 
class of work in general, and at ordinary conditions. For 
swings that have a duration of four or five hours, and in a 
series having half a dozen sets, we get a range between ex¬ 
treme values of slightly more than a second per day. This 
is equivalent to differences between the independent meas¬ 
ures of the period of one hundred thousandth part. We 
may therefore assume this to be a standard of accuracy ? 
with reference to which the auxiliary quantities should be 
determined. 
The accuracy of any determination of time, as given by a 
chronometer or clock, varies with the mechanism of the 
time-piece and the conditions under which it is running. 
The modern custom of making pendulum observations ex¬ 
tend through the entire 24 hours, eliminates to a great 
extent the variations of rate; and when stars are obtained 
every night, the values given each swing are almost—and 
those given for each day are entirely—independent of the 
clock. But since, when the pendulum swings in the air, we 
are confronted with independent values extending over only 
a small fraction of the day, any variations of the clock rate 
are made apparent, and it becomes necessary to know to 
what extent the apparent discrepancies may be attributed to 
the imperfection of the time-piece; and the shorter, the 
swing, the more pronounced becomes these discrepancies. 
The unit chosen for discrepancies will be one in the sixth 
place of decimals—that is, one-millionth of a second. The 
Kater pendulums, beginning with an arc of vibration of 1°, 
will swing six hours before falling to an arc of 10'. Peirce’s 
pendulums will swing 4J hours with the heavy end down, 
and 1J hours with the heavy end up. The Repsold pendu- 
