VOL. LXXXV.J PHILOSOPHICAL TRANSACTIONS. 655 



must be made to the degree on the meridian in 50° 41' in order to approximate 

 to a correct scale for the computation of the latitudes. But it is evident, that 

 any of the received hypotheses (supposing the length of the degree on the me- 

 ridian in 50° 41' to be 00851 fathoms) would give the degrees sufficiently correct, 

 since the principal stations, together with most of the objects fixed in this ope- 

 ration, are included between the parallels of 50° 37' and 51° 28'. 



In obtaining the latitudes of those places which are referred to the meridian 

 of Greenwich, it is easy to perceive that little error is introduced by spherical 

 computation, since the spheroidical correction for the latitude of Bagshot Heath 

 is only about -pJ-j- of a second. Had indeed the latitudes of the stations, which 

 are far to the westward, been computed with distances from the meridian, and 

 the perpendicular at Greenwich, some small errors might have been introduced, 

 from the uncertainty of the earth's figure, and the consequent inability of com- 

 puting the spheroidical correction with sufficient accuracy ; but as the distance 

 between the parallels of Beachy Head and Dunnose is obtained very nearly, the 

 latitude of the latter station may be considered as correct as that of the former 

 one, and consequently the places in the vicinity of Dunnose have their latitudes 

 determined with sufficient precision. After this follows a collection of the mea- 

 sures of the secondary triangles, in which two angles only have been ob- 

 served. 



In order to ascertain the situation of the Observatory at Portsmouth Academy, 

 Mr. Bayly, the master, measured 1 angles in the following triangle, viz. Ports- 

 mouth Academy 124° Q' 15", Observatory 53° & 15", Portsmouth Church. The 

 included angle at Dunnose between the ball on the cupola of the Academy, and 

 the spindle of the wind vane on Portsmouth Church, is 1° 9' 16", and the 

 distances of those objects from Dunnose are 66524 and 69787 feet; therefore 

 the distance between the Academy and the Church will be 3540 feet: this dis- 

 tance, used as a base in the above triangle, gives the distance between the Ob- 

 servatory and the Church 3663 feet: now the angle at the Church, comprehended 

 by the Academy and the Observatory, being 2° 44' 30", we find the angle at 

 Dunnose, between Portsmouth Church and the Observatory, to be 1° 3' 30", 

 and the distance of the Observatory from Dunnose 69962 feet. 



On the heights of the stations, and the terrestrial refractions, it is observed 

 that, with a view to obtain the heights of the stations nearly, from their eleva- 

 vations or depressions, we determined the height of that at Dunnose above low 

 water in May, 1793, by levelling down to the sea shore near Shanklin, a dis- 

 tance of about a mile. Instead of a levelling telescope, we made use of the 

 transit-instrument, which, on account of its very accurate spirit level, seems 

 extremely well adapted for the purpose. The whole perpendicular descent thus 



