Prof. Bessel's Additions to the Theory of Eclipses, fyc. 417 



rectness of the views taken of this stratum in the foregoing 

 notice. That this patch of sandstone, which is now upwards 

 of six miles from the nearest point of the same rock, once 

 formed part of a continuous stratum, we cannot doubt, nor 

 that the intervening portion has been removed by the opera- 

 tion of water, that mighty agent which has been employed 

 universally in modifying the surface of the globe. It is diffi- 

 cult to obtain an idea of the extent of force necessary, but it 

 is, nevertheless, as probable, that such a removal of this bed 

 may have taken place, as that the strata on the high side of 

 the dyke have been removed, which, when the slip took place, 

 must have presented at this point, a face of rock, upwards of 

 one thousand feet high. 



LXIV. Additions to the Theory of Eclipses, and the Methods 

 ■ of calculating their Results. By Professor Bessel. 



[Concluded from page 347.] 



ET us now suppose that <$>', /x denote the latitude and 

 -*-^ longitude of the zenith ; D, A the longitude and latitude 

 of the star ; let (jw.) and (<p') express the right ascension and 

 declination of the zenith, and s the obliquity of the ecliptic. 

 We then obtain these equations : 



sin $' = sin (<p') cos s — cos ($') sin (jw.) sin s 

 cos <$>' sin ^ = sin ($') sin s + cos (<p') sin (jw.) cos s 



cos $'cos/x = cos (<p') cos (jx), from which we derive the 

 following expressions for u and v by (<p') and (/x) 



u ■= r sin (<p') sin s cos A + r cos <p' [cos A sin (jjt,) cos e — 



sin A cos (p.)] 

 v — r sin (4)') . [cos D . cos s — sin D sin s sin A] 



— r cos (<$>') [sin (fx.) (cos D sin s 4- sin D . cos s sin A) + 

 cos (ju,) sin D cos A] 



The differential quotients of r cos (<p') and r sin ($') give 

 therefore, if /3 retains the above signification, 



- — - = \ /3 2 . u — |3 . sin s cos A 



— v — = ^ /3 2 . v — /3 (cos D cos s — sin D . sin s . sin A) 



We have therefore, calculating with longitudes and lati- 

 tudes, and referring N + ^ to the same, for the term dependent 

 on A e 2 5 this expression : 



— w sin w . A e 1 1 \ /3 2 [x cos 4> + — {t — d —t) sin \J/ — k] + 

 N.S. Vol. 8. No. 48. Dec. 1830. 3 H /3 sin 



