of the Earth by means of OcciiUations of the fixed Stars. 413 



arises from the inequality of the terrestrial radii ; and that the 

 one is the measure or consequence of the other. Therefore, in 

 order to determine the parallax at any given point of the earth's 

 surface, it is necessary to know the distance of that poijit from 

 the centre of the earth. But, that the reader may see the ano- 

 malies which arise on this subject, (from the actual measurement 

 of the dei^rees of the meridian in different countries, and from 

 dififerent theories which have been assumed) I have calculated 

 the following table, which shows the radius of the earth in the 

 latitude of Greenwich (51°. 28'. 40"), according to the several 

 hypotheses of the compression of the earth's axis therein stated. 



No. 



Hypothesis. 



Radius in feet. Diiference. 



30 9 



I 



TTo 



20 S27 239 

 20 833 848 

 20 848 224 

 20 855 339 

 20 863 689 

 20 868 144 

 20 876 819 

 20 877 920 

 20 880 560 



6609 



14376 



7115 



8350 



4455 

 8675 

 liOl 

 2640 



The first value here given arises from the recent measure- 

 ment of the arc in France, by taking the middle arc at Evaux, 

 which makes the compression of the earth's axis = -^ 5 and the 

 length of the earth's radius in the latitude of Greenwich equal to 

 20 827 239 feet. By comparing this value with the last in the 

 table, which is one of the hypotheses assumed by the Bureau des 

 Longitudes in the recent tables of the Moon by M. Burg, it will 

 be found that there is a difference of no less than 53 321 feet, or 

 more than 10 miles ; a quantity sulihciently great to be detected 

 by the observation of the moon's parallax, and which would pro- 

 duce a very sensible effect on the duration of such occultations as 

 have been the subject of the ))rcceding Memoir : since we have 

 seen that, in some cases, a diflercnce of less than 200 feet will 

 produce a difference of one second in the duration. 



But, although such occultations may clearly show that the earth 

 is compressed at the poles, and althou^'h they may be effected by 

 quantities which differ so widely from each other as in the case 

 just mentioned; yet it may be douljted whether they are capable 

 of determining the precise qiiunlity of that compression ; and 



therefore 



