352 On a new and certain Method of ascertaining the Figure 



tudes, may be accurately distinguished. The importance of the 

 subject induces me to treat it more fully in detail. 



§4.1 shall not take up the time of the reader in demonstrat- 

 ing that no hj'pothesis is required to deduce the variation of cur- 

 vature from the observation of the parallax, For, since the va- 

 riation of curvature is nothing more than the inequality of the 

 terrestrial radii (and that is nothing else than the difference of the 

 parallax), it is evident that finding by observation the variation of 

 parallax at different latitudes is in fact finding the variation of 

 curvature by immediate observation. One involves the other with- 

 out any intermediate help. The only difficulty consists in freeing 

 from uncertainty those observations which show the unequal pa- 

 rallax : and this is precisely the special character of the particular 

 kind of occultations which I have in view. It is true that astro- 

 nomers, in calculating occultations, have niade the parallax vary 

 in conformity with that quantity of compression which they have 

 adopted as the true theory. Moreover, these variations do not 

 in general produce differences which are discernible in the rela- 

 tive duration of the occultations observed in different latitudes. 

 Those differences, which are discernible, arise only in certain cir- 

 cumstances, to which hitherto no particular attention has been 

 paid. It is on this account that occultations have not, as yet, 

 served at all to determine the amount or quantity of the compres- 

 sion of the polar axis. 



§ b. Before I proceed to describe what these favourable cir- 

 cumstances are, it will be proper, in order to appreciate their 

 utilitv, to define the precise degree of accuracy of which the com- 

 putation and ohservathn of occultations are capable. With re- 

 spect to the computatioii, it is evident that the apparent distance 

 between the star and the moon cannot be accurately determined 

 unless vv'e iuiow exactly not only the apparent place of the star, 

 but also that of the moon and its diameter. These elements are 

 obtained by calculating the piuenomena from observations made 

 in a place (the longitude of which is known) under circumstances 

 where the alteration of the parallax, on account of the variation 

 in the curvature of the earth, does not produce a perceptible dif- 

 ference irt the duration of the occultation: conditions not un- 

 common, nor difficult to be obtained. 



§ 6. Let us then suppose that the moon's diameter and the 

 place of the star are well determined (in which elements the least 

 uncertainty exists) ; and that any small errors, which may occur, 

 be thrown on the place of the moon. Let us, moreover, endea- 

 vour to discover (by comparing the calculation vvith the observa- 

 tion) the errors of the tables in the longitude and latitude of the 

 moon, mixed (as we have already stated) with the preceding 



errors. 



