Coast Survey of the United States. 231 
which demands these frequent determinations, is the necessity 
for reduction to a central point, arising from the irregularities of 
gravitation, occasioned by the variations in form and density of 
the materials composing the earth’s crust. The theory, though 
familiar to the student of physics, requires to be stated in this 
connection. If in consequence of the proximity of a mountain 
the plumb line be drawn from the position it would otherwise 
maintain, it is evident that the point of the heavens which cor- 
responds to the zenith of a station, as determined by astronomical 
observations, would not be the same as if the mountain did not 
exist. The apparent direction of gravity being different, the 
apparent horizontal line is also changed. The length of the 
radius of curvature of the meridian undergoes a corresponding 
alteration, and the angle which measures the elevation of the 
pole, has its vertex, not at the centre of the earth, but at a point 
at a distance from the centre, depending upon the apparent line of 
direction of gravity. 
The existence of such an attraction is a valuable part of 
knowledge, proved by accurate practical investigation. Obser- 
vations were made in the year 1774, by Dr. Maskelyne, for as- 
certaining the attraction of the mountain Schehallien. The 
points to be compared were connected by measurement, and de- 
termined astronomically. 'T'wo results differed 11/7! from each 
other, which great discrepancy is to be attributed to the sum of 
the deflections of the plumb line on the opposite sides of the 
mountain. 
Baron de Zach, also, in 1810 showed that the attraction of 
the Mimet mountains, near Marseilles, was appreciable. It ap- 
pears to have produced an error of 1.98 in the latitude. M. Arago 
condemns the repeating circle used by Zach, and Mr. Airy ob- 
serves that the stars were all on the same side of the zenith, a 
change therefore in the constant error of the instrument would 
produce an error in the result. Without attaching any impor- 
tance to the minute accuracy of the determination, however, it 
sufficiently illustrates the principle treated. ‘The same facts are 
attested by the observations of Boscowich and Beccaria in Italy. 
It might be expected that the pendulum, a more delicate means 
of experiment, would also indicate by its vibrations the existence 
of these irregularities. Such is indeed the case. It is now well 
known that the attraction peculiar to the locality, does in frequent 
