VOL. LXXXV.] PHILOSOPHICAL TRANSACTIONS. 6-15 



On August 2d, at night, the angle between the star and staff was observed 30° 19' 50". 25 



And on August 3d, in the morning 24 38 23 .5 



Therefore half their sum is the angle between the meridian and Jevington staff, viz. 27 29 7 



Hence 27° 29' 6', the mean by the double azimuths, may be taken as the 

 angle between the meridian and the staff. 



The apparent polar distances of the star, on those days which do not refer to 

 corresponding observations on the opposite side of the meridian, are as follow : 



Azim. 



which, with the latitude of Beachy Head, viz. \ 2 

 50° 44' 25" nearly, give the azimuths for < 2 

 those days 12 



r 27° 29 5".I 



\ 27 29 8 .4 



And these applied to the observed angles, give N *^ ^^ ^ -7 



j 27 29 5 .2 



{, 27 29 6 .25 



The mean of which is 27° 29' 6". 1, for the angle between the meridian and 

 Jevington staft, being the same as that obtained from a mean of the double 

 azimuths. 



Next follows a determination of the length of a degree of a great circle, per- 

 pendicular to the meridian, in latitude 50° 41'. — In pi. 7, fig. It), let d and b be 

 Dunnose and Beachy Head, and p the pole, forming the spheroidical triangle 

 DPB ; and let c and A be the staffs at Jevington and Brading Down, respectively. 



Now the angle at Dunnose, between the meridian and the staff, or pda, was found 



by the double azimuths to be 21° 14' 1 1".5 



And the angle between the staff and the station on Beachy Head, or adb 60 42 41 .5 



Therefore their sum is the angle between the meridian and the station on Beachy 



Head, or pdb ; which is 81 56" 53 



Again} at Beachy Head the angle between the meridian and the staff, or pbc, 



was found by the double azimuths to be 27 29 6 



And the angle between the staff and the station on Dunnose, or cbd 69 26 52 



Therefore their sum is the angle between the meridian and the station on Dunnose, 



namely 96 55 58 



Hence, in the spheroidical triangle dpb, we have the angles pdb and pbd 

 given. 



Again, in fig. I7, let pgm be the meridian of Greenwich ; then, if mb be the 

 parallel to the perpendicular at o, Greenwich, we shall get mb = 58848 feet, 

 and GM = 269328 feet ; therefore, taking 60851 fathoms for the length of the 

 degree on the meridian, as derived from the difference of latitude between 

 Greenwich and Paris, applied to the measured arc, we get gm = 44' J5".26; 

 consequently the latitude of the point m, (that of Greenwich being 51° 28' 40"), 

 is 50° 44' 24".74 ; and the co-lat. pm = 39° 15' 35".26. 



With respect to the value of the arc mb, for the present purpose, it is not of 



