N 



642 The Account of a 



P In the adjoining diagram, suppose B, Black Down ; D, 



/ \ Dunnose ; and, N, Nine Barrow Down : also, let PB, the me- 



/ \ ridian of Black Down, be prolonged to M, and DM be drawn, 



/ \ PM being — PD. Then we shall have three spherical tri- 



/ \ angles BPD, END, and BMD. Now, the angle NBD was 



/ \ found from observations to be 4 30' 28", and BND 172^ 



t/\ ]y^ 2 7' 33"'5 » these give the angle BDN — 3 r 59", 5, nearly, be- 



cause the excess of the three angles above i 8o° is 1". The 

 observed angle at D, Dunnose, between Nine Barrow Down 

 and the meridian DP, or PDN.was 87°56'53"; therefore, 87 56' 53" — 3 1' 59",$ — 

 84 54' 53",5, is the angle at D, between the meridian and the station on Black Down. 



Now, the difference of longitude between B and D, or the angle at P, has been 

 already found — i° 20' 46", 4; and, since BP is very nearly — PD, and BD is small, 

 we shall have rad. : tang. fP :: cosine DP : cosine BMD = 89 28' 47". But the 

 angle PDB has been found = 84 54' 53",$ ; therefore, 89 28' 47" — 84 S4'S3*,5 

 = 4° 33' 53>"S» tne an g le BDM ; hence, 180 o' 2" — 94 2' 4o",5 — 85 57' 21/5, 

 or MBD ; therefore, 94 2' 38/5, or DBP, is the angle at Black Down obtained in 

 this way, which differs nearly 16" from the observed one, viz. 94 2' 22",75. It is 

 probable, some portion of this arises from defects in the observation made at Dunnose, 

 on the lights fired at Nine Barrow Down : only two lights were seen; and, as the ob- 

 servations differed 5" from each other, some degree of doubt exists, as to the accuracy 

 of the angle. The angle at Nine Barrow Down, between Black Down and Dunnose, 

 is not absolutely to be depended on for purposes of this kind, although there can be 

 no doubt of its being sufficiently near the truth, for that to which it has been before 

 applied. In the correction of the angles at that station, in our former accounts, we 

 proceeded on the supposition of their being less satisfactory than the other angles of 

 the triangles to which Nine Barrow Down is a common station. For these reasons, I 

 am of opinion the computed angle cannot be applied as a test to the observed one ; 

 and it also appears to me, that greater objections lie against similar comparisons be- 

 tween the computed and observed angles at Butterton and St. Agnes; as those stations 

 could not be seen from each other, nor the latter from Black Down. Although the 

 computed directions of the meridians differ some seconds from the observed ones, I am 

 by no means doubtful of the truth of the latter ; as the double azimuths of the Pole 

 Star, found from computation, agree very satisfactorily with those which have been 



used in obtaining the directions of the several meridians. In finding the value of the 



oblique arc, or the line which joins Black Down and Dunnose, as used in the first 

 method of computation, I have had recourse to the following correct expression, viz. 



d ss . ■ r — ; where d is the length of the required degree, p that of the great 



p f m —p ■ s z 



circle perpendicular to the meridian, m that of a degree of the meridian itself, and s 



the sine of the angle constituted by the oblique arc and the meridian. 



