232 Coast Survey of the United States. 
instances affect the mean force of gravity ; and it is owing to the 
gravitating force, not only of the base on which the pendulum 
stands, but also of the adjacent materials, that it is necessary to 
modify the rule, which would obtain, were the earth of an uni- 
form density, viz. that the reductions from one level to another 
are strictly proportioned to the squares of their 3, is distances 
from the earth’s centre. 
Instances appear of defect and excess in the vibrations of the 
pendulum, of the former at Maranham and Trinidad, and of the 
latter at Spitzbergen and Ascension, where the experiments were 
conducted with such extreme precision as to prove conclusively 
that the irregularities are not to be charged to the experiments 
themselves, but to the natural phenomena which it is their pur- 
pose to investigate. 
But to return to astronomical indications. Observations show 
that the attraction of masses comparatively small, is sensible. 
The discrepancies noted in comparing different parts of the same 
arc may be cited. At Arbury Hill there was found a difference 
of 5”, not to be accounted for upon any supposition of the earth’s 
figure. There is also an unexplained disturbance at Dodagoontah, 
on the great Indian arc, to nearly the same amount. In inferring 
the latitude of one place from the observed latitude of another 
not on the same meridian, through the medium of a geodetic 
measure, results are obtained differing from observation more 
than could happen in the use of the astronomical instruments, 
or of the geodetic measurements, without the most unreasonable 
neglect. ‘Thus the latitude of Turin deduced from that of Milan 
differs from the observed latitude by 8-9, that of Venice from 
the same origin 9-5, and that of Rimini 27-4. The same re- 
sults appear upon the journals of the coast survey. The latitudes 
of New York and Boston do not agree together. Boston, Cape 
Henlopen, and New York differ from Philadelphia, and the va- 
rious stations about the city of New York, when transferred to a 
central point, are all at variance with observation. 
Finally, the great disagreement, it may be observed, between 
various geometers as to the ratio of eccentricity, is attributed by 
some writers, in a measure to erroneous latitudes, occasioned by 
deviations of the level. 
These facts, and the theory which flows from them, prove the 
importance of the rule of observation adopted by the superin- 
