414 On a new and certain Method of ascertaining the Figure 



therefore whether they are more eligible for that purpose than 

 the methods at present in use. In reply to which, it may be re- 

 peated that this plan is at present proposed only in aid of the 

 modes hitherto adopted for determining the true figure of the 

 earth ; and by no means as supplying the place of other methods 

 for deciding that difficult problem. 



In order, however, that the reader may have a more compre- 

 hensive view of this subject, and be enabled to see the differences 

 which would arise in various latitudes and under various circum- 

 stances, according to two nearly similar hypotheses of the earth's 

 compression compared with the hypothesis of its being a perfect 

 sphere, I have inserted the three following tables ; which show 

 the alteration in the position of the star within the moon's disc, 

 and its consequent effect on the duration of the occultation, ac- 

 cording to the three several hypotheses of the earth being consi- 

 dered as a perfect sphere, and of its being compressed at the poles 

 T^, and -^ ; at the several heights of 10°, 20*^ and 30" of the 

 moon above the horizon ; and at the several latitudes of 50°, 60°, 

 and 70°. The chord of the star's apparent path behind the moon 

 being, in all these cases, assumed to be perpendicular to the ver- 

 tical circle of the place. 



Thus, by an inspection of Table II, it will be seen that in lati- 

 tude 60^, when the moon is 10° high, and the star 60" within the 

 moon's disc, the duration of the occultation v/ould be 20'. 7", if 

 the earth were a perfect sphere. But, if the polar axis were com- 

 pressed -j-ro> *^'i® star would then be only Sl^'jS within the moon's 

 disc, and the duration of the occultation only 18'. 41": which is 

 the case alluded to by M. Cagnoli § 10. Or, if the polar axis 

 were compressed only ^-i-o, the star would then be 52",3 within 

 the moon's disc, and the duration of the occultation would be 

 1 8'. 50" ; being a difference of 9" between the results of the two 

 hvpotheses. This difference would be the same, if the moon were 

 20° high ; as may readily be seen by an inspection of the same 

 table: it vvould also be the same under corresponding circum- 

 stances, if the observation were made in latitude 70°: as maybe 

 seen by an inspection of Table III. 



This difference however may probably be considered as too 

 small to enable us to derive any satisfactory result as to the pre- 

 cise qjiantily of the compression of the earth's axis. But, if we 

 take the position of the star within the moon's disc equal to 10" 

 only, and the moon at the height of 10° as before, we shall have 

 the duration of the occultation 8', 19" on the supposition that 

 the earth is a perfect sphere. Then, supposing the axis to be 

 compressed ^-I-jr, the star would be only 2",3 within the moon's 

 disc, and the duration of the occultation only 4'. 0" : or, sup- 

 posing the axis to be compressed -j-^o-^ the star would be only 



r',5 



