46 
PUTNAM. 
dividing the country into compartments. The formula for 
this case is 
dg = A£i y 
y 2 r A y/a 2 + h? 
which represents the difference between the vertical attrac¬ 
tion of an infinite plain of thickness h and a cone of height 
h and radius a. 
The effect of topographical irregularities has been inves¬ 
tigated in the manner described for all the stations of the 
past season, using where available the contour maps of the 
Geological Survey. Although applied in all cases where 
appreciable, at only one station (Pikes Peak) was this correc¬ 
tion found to be of real importance. This is partly due to 
the favorable location of the stations, but also to the fact 
that, except on the summit of rugged mountains or very 
close to their base or in deep narrow valleys, this correction 
must necessarily be small. The effect of placing an indefi¬ 
nitely extended horizontal plain 114 feet (35 meters) in 
thickness or a sphere 338 feet (103 meters) in diameter and 
of density equal to one half the mean density of the earth 
immediately above a station would be to diminish gravity 
by only .004 dyne, or about the 2 ToVoo^ 1 P ar h which may 
at present be taken as the utmost limit of probable accuracy 
of observation. 
The question of the proper reduction of pendulum obser¬ 
vations to the level of the sea, involving as it does the vari¬ 
ous theories of the condition of the earth’s crust and affecting 
very materially the use of such observations in deducing 
the figure of the earth, is a most important one and has led 
to the expression of many different opinions. Bouguer’s 
reduction, already described, has been frequently employed. 
Professor Helmert, in the discussion of pendulum observa¬ 
tions in his “ Hohere Geodasie ” (vol. II), develops and uses 
the condensation method, assuming that all the overlying 
material is condensed onto a surface twenty one kilometers 
below the sealevel. As approximately applied by him in 
the discussion of continental stations, this reduction amounts 
