Bowdltch on the Ohlateness of the Earth. 31 



Calculation v.^e obtain for the oblateness of the earth, a result mucli 

 more couformable to those detluced from other methods ; and on 

 this account I have thought it would not be unacce^>table to the 

 Academy to have these mistakes corrected, and the sources of 

 them pointed out. This is done in the first section of the present 



^ 



paper. In the second section I have simplified one of La Place's 

 formulas relative to the figure of the earth. In the third section I 

 have corrected the expressions of the length of a degree, and also 

 the azimuths given by him in § 38, Book IIT, of hh '< MCcanique 

 Celeste/' (in the hypothesis that the earth is not a spheroid of 

 revolution) for the mistakes arising from the neglect of one of the 

 terms in the expression of the radius of the earth, which produces 

 a considerable effect in the value of one of the formulas. 



SECTION rmsT. 



There are/oztr methods generally used for the purpose of com- 

 puting the oblateness of the earth, supposing it to be au ellipsoid 

 of revolution. First, By comparing the observed lengths of two 

 consecutive degrees of the meridian. Second, By 



lengths of two degrees of the meridian measured in very different 

 latitudes. Third, By means of the observed variations in the 

 lengths of pendulums vibrating in a second of time in different lat- 

 itudes. Fourth. By means of two e<iaations in the moon's motion 

 (the one in longitude the other in latitude) depending on the ob- 



lateness of the earth. 



The first metiiod is liable to much uncertainty. For the 



es 



difference between the lengths 



glees, 



being only 9 or 10 fathoms, the least error in the lengths of the 

 lines, in the observed angles, or in the altitudes of the heavenly 

 bodies by which the length of the celestial one is determined 

 would produce a great error in the computed oblateness. This 



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