REDUCTION OF PENDULUM OBSERVATIONS. 
129 
Two pendulums have recently been measured, using a 
method of illumination due to Mr. 0. H. Tittmann, in 
charge of the Bureau of Weights and Measures at the Coast 
Survey Office. Without going into the details of the arrange¬ 
ment, it may be said that the image of the edge was reflected 
from a surface of polished steel, and the mean of the measures 
on the direct and reflected image was taken as the reading 
on the surface of the plane. The space between the two 
images appeared as a dark band, the width of which depended 
on the closeness of the contact between the edge and surface. 
Leaving to one side for the present the question as to what 
should be considered the defining line of the length of the 
pendulum, the fact is to be noted that after having made 
measures on the direct and reflected images the reflecting 
plane was removed and the illumination introduced behind 
the knife edge. Readings were then made on the dark edge 
of the pendulum, and these agree quite satisfactorily with 
those on the direct and reflected images, corrected for the 
width of the band; so that it would .seem to be sufficiently 
accurate to measure on the edge directly, having the field 
bright enough to make the threads visible when projected 
against the body of the knife. 
As to the value to be accepted for the length of the pen¬ 
dulum, it is to be remarked that although the true edge at 
the point measured is not in perfect contact with the plane, 
as is made evident by the perceptible thickness of the dark 
band, yet the middle of this band should be considered as 
making the line about which the pendulum oscillates. If 
the steel surface is a perfect plane and the pendulum is rest¬ 
ing upon it, certainly the existing conditions are precisely 
similar to those that obtain when the gravity observations 
are made, and the best value for the position of the line 
about which the oscillations take place is that given by the 
surface of the plane or the mean of the direct and reflected 
images. The thickness of this band was in one case as 
much as thirty microns; so that, admitting the plane to be 
perfect, the edge at the point measured departs from a 
straight line as much as fifteen microns. The two knife 
