Dr. Bowditch, President of the American Academy. — xlix. 
source-of the error committed by La Place in this instance ; as he 
also does, a few pages afterwards, another error “of considerable 
importance,” (to use his own words,) in a subsequent part of that 
author’s calculation. 
Now, in order to make this subject intelligible at least, if not 
interesting, I may be allowed to remind you, that there are four 
methods in general use for computing the oblateness of the earth, 
supposing it to be an ellipsoid of revolution; 1. By comparing 
the observed lengths of two consecutive degrees of the meridian. 
2. By comparing the lengths of two degrees of the meridian 
measured in different latitudes. 3d. By means of the observed 
variations in the lengths of pendulums vibrating in a second of time 
in different latitudes. 4. By means of two equations in the moon’s 
motion (the one in longitude, the other in latitude), depending on 
the oblateness of the earth. 
The two former of these methods, though they would at first 
view seem to be the most natural and accurate, as being the appli- 
cation of actual admeasurement, are from various causes the most 
uncertain; the fourth, which results from the moon’s motion, is 
almost wholly independent of any error arising from the inequalities 
of the earth’s surface, and is the most satisfactory ; and next to this 
is the third, founded on the observed length of the pendulum. 
On this last method, Dr. Bowditch gives, in his Notes to this 
volume, a most useful investigation of the Earth’s figure, from “the 
latest and best observations” of the pendulum in different parts of 
the globe. La Place, in his computation of the oblateness of the 
earth as deduced from the length of the pendulum, was obliged to 
use the ancient observations ; and his results were, many years ago, 
shown by Dr. Bowditch to be incorrect. Since that time, numerous 
observations have been made, and with more accuracy, from the 
equator to Spitzbergen, within eleven degrees of the north pole; 
ii 
