228 Length of a Degree of the Terrestrial Meridian. 



Boscovich, which is exceedingly well adapted to the solution of the 

 problem under consideration, and which is founded upon the condi- 

 tions : 1. That the sum of the errors committed in the measures of 

 the whole arcs ought to be zero. 2. That the sum of all these er- 

 rors taken positively, ought to be a minimum. Upon these condi- 

 tions the measure of the oblateness of the earth is found by Doctor 



1 



Bowditch, using the same degrees as before, to be equal to oTq •' it 



should be remarked, however, that in both cases Dr. Bowditch used 

 formula (4') instead of formula (4.) 



11. The second process employed by geometricians for deter- 

 mining the measure of the earth's oblateness, consists in observing 

 the length of a pendulum oscillating in a given time at different lati- 

 tudes, and then calculating the corresponding intensities of gravity. 

 Since the length of such a pendulum is directly proportional to the 

 intensity of gravity, it follows that the variations of the length of the 

 pendulum obey the same law as the variation in the intensity of 

 gravity ; and therefore if the earth were of a spheroidal form of a 

 sensible degree of oblateness, the variations in the intensity of its 

 gravity, arising from difference of distance from the different points 

 of its surface to its centre, would produce sensible variations, propor- 

 tionate to the degree of oblateness, in the length of a pendulum os- 

 cillating in a given time. The intensity of gravity, being calculated 

 with great precision from the observed length of the pendulum, is 

 found to increase in going from the equator towards the poles ; and 

 the excess of its intensity at any latitude above its intensity at the 

 equator, is thus found, as it were by observation, to obey exactly the 

 same law that results from calculation founded upon the hypotheses 

 of a spheroidal form for the earth, and of the intensity of its gravity 

 being inversely as the square of the distance from its centre ; and 

 when allowance is made in the calculation for the effect of the cen- 

 trifugal force arising from the earth's rotation, the absolute amount 

 of the calculated variations in the intensity of gravity, are found to 

 be verified in a remarkable degree, by the amount of variations as 

 deduced from the observed lengths of the pendulum. The results 

 of the researches founded upon the method now under consideration, 

 for determining a, show that the inequalities of the surface of the 

 terrestrial spheroid, have much less influence upon the variations of 

 the length of the pendulum, than upon the variations of the degrees 

 of the meridians ; and therefore it may be inferred, that the value 



