116 
PRESTON. 
The time of vibration is subject to a number of correc¬ 
tions, of which the most important are: First, for the rate 
of the time-piece to which the period is referred; second, 
the reduction to an infinitely small arc; third, the correc¬ 
tion for temperature, and fourth, the atmospheric correction. 
This last is usually divided into two parts, one of which is 
statical and depends on buoyancy alone, and the other is 
dynamical and results from the influence of the air which 
is set in motion by the pendulum. The first part, being 
merely a question of the relative densities of the oscil¬ 
lating body and the fluid by which it is surrounded, can 
easily be found by calculation. The second part, depend¬ 
ing on the viscosity and humidity of the air and on the 
form of the pendulum, can only be computed for certain 
simple geometrical forms. It is now customary, however, 
to determine them together, by making observations under 
widely different atmospheric pressures. The temperature 
correction is susceptible of two independent determinations : 
either by measuring the coefficient of linear expansion of the 
metal composing the pendulum, and by computation, deduc¬ 
ing the correction for one oscillation, or by swinging at very 
different temperatures and noting the change in the period 
due to a given change in the temperature. Of the other 
corrections to the observed period of oscillation—that is, for 
the slip and wear of the knives, the flexure of the support, 
and the stretching of the pendulum by its own weight—we 
shall not speak in the present paper, merely remarking that 
in relative determinations of gravity they may in general be 
dismissed from consideration, except in so far as is necessary 
to assure ourselves that their amounts do not change from 
station to station enough to vitiate the results of the observa¬ 
tions, considered now purely as differential work. 
In the first place, let us see what has been the general 
experience by modern observers in the measurement of the 
time of oscillation of a seconds pendulum. Whether we 
examine the results of the invariable, reversible, or converti¬ 
ble instrument, the discrepancies in the separate observa- 
