644 PHILOSOPHICAL TRANSACTIONS. ("aNNO I/QD. 



and Beacliy Head, we find Ditchling Beacon from Botley Hill 1 39367.4, and 

 from Fairlight Down 1 67986.5 feet, and the included angle at Ditchling Beacon 

 82° 41' 6".8 ; hence the distance from Botley Hill to Fairlight Down will be 

 204276 feet nearly. So near an agreement in a length of almost 39 miles, can 

 only be attributed to chance. Hence it appears, that a difference of 5 or 6 feet 

 in about 27 miles (the distance of the stations Hollingbourn Hill and Fairlight 

 Down), maybe supposed in General Roy's deductions on account of the varia- 

 tions, or corrections in the bases on Hounslow Heath, and Romney Marsh, this 

 difference, however, is too trifling to be of consequence in any of his principal 

 conclusions. 



Next follows the 4th branch, consisting of the nearest triangles to the north- 

 ward of Beachy Head and Dunnose, for finding the distance between those sta- 

 tions. And afterwards the series containing the triangles belonging to the series 

 which have had only two of their three angles observed. 



The account next computes the directions of the meridians at Dunnose and 

 Beachy Head ; and the length of a degree of a great circle, perpendicular to the 

 meridian, in latitude 50° 4l'. 

 On April 2Slh in the afternoon, the angle between tlie pole star, when at its greatest 



apparent elongation from the meridian, and the staff', was observed i?4° 



And on April 2yth in the morning 18 



Therefore half their sum is the angle between the meridian and Brading staff", viz. 21 

 On May 12th, in the afternoon, the angle between the star and staff was observed 24 



And on May 13th, in the morning 18 



Therefore half their sum is the angle between the meridian and Brading staff", viz. 21 



Hence 21° 14' 11".5, may be taken for the angle between the meridian and 

 Brading staff', as determined by the double azimuths. 



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. 



April 21st 1° 47' 57".2 ( which, with the lat. of Dunnose, viz. 1 2° 50' 11".2 



April 22d 1 47 57 .4 < 50° 37' 8" nearly, give the azimuths > 2 50 11 .5 



May 5th 1 48 .7 L for Uiose days J 2 30 16' .8 



r 21° 14' 10".05 

 And these subtracted from the observed angles give . . J 21 14 10 .5 



L 21 14 10 .45 



The mean of which is 21° 14' 10''.3 for the angle between the meridian and the 

 staff, which is a little more than 1" different from that obtained by the double 

 azimuths; we shall however take 21° 14' 11".5 for the true angle. 



For the direction of the Meridian at Beachy Head ivith respect to Jevington Staff. 



On August 1st, in the morning, tlie angle between tlie pole star and the staff was 



observed 24" 38' 20".25 



And at night 30 ly 49 .5 



Therefore half their sum is the angle between the meridian aad Jevington staff", viz. 27 29 5 



