PENDULUM OBSERVATIONS. 17 
pressure the swings of the pendulum rapidly damp down, and a 
correction is required in consequence. 
If X be the logarithmic decrement, T the observed time, T, the 
true time of swing, then it can be shown that 
Tt oT: 
: Jn? +r 
To find \ we observe the amplitudes of a number of successive 
swings. If ©, be the amplitude of the first swing, ©, of the n”, then 
A is given by the equation 
A= =e log Cn 
gt = 1 PEC, 
If the pressure can be reduced to 50 or 60 mm. this correction 
will be very small indeed. 
The observations will normally be conducted on land. If oppor- 
tunity offered to take a set of observations on a fixed ice floe the 
experiment might be usefully made; in this case it would be desirable 
to know the thickness of the ice and the depth of the water. The 
object of the investigation is to determine the value of g, the accelera- 
tion due to gravity. For this purpose it is important to know, in 
addition to the time of swing, the latitude of the observing station 
and its height above sea level; the nature of the ground near the 
station should also be noted for the purpose of obtaining a value for 
the density of the material of the earth in the neighbourhood. 
A situation should if possible be selected for the pendulum house, 
not in the immediate neighbourhood of any high ground; with a view 
of eliminating local inequalities some subsidiary observations at points 
in the neighbourhood of the central station may, if opportunity offers, 
be made. 
If it is possible to transport the instrument to a point at a con- 
siderable distance to the south of the central station, so as to obtain a 
value for g at two positions differing appreciably in latitude, the 
information would be of value. In this case the geographical posi- 
tion and height above sea level of the second station should be 
determined. 
As a specimen, a series of observations at Washington, taken from 
Appendix I. of the ‘Report of the United States Coast and Geodetic 
Survey Department for 1894, is given. 
