370 PHILOSOPHICAL TRANSACTIONS. [anNO I768. 



as a floor by nature) the distance mp was measured twice, and found to be 5 



chains, 14 feet, and -^ of an inch. With this same chain the distance m a was 



measured=80 chains exactly. 



For the angle bam, by celestial measure. 



The AK of the meridian when « "j 22" J 6" 53'.8 by observ. made Oct. 12, 



Ursamajor passed an azimuth > 22 \6 55. 1 D° on the 13, 



in the direct, of the line A B.J 22 l6 54.7 D° on the l6. 



Mean = 22 \6 54. 5 = 334° 13' 3%" 



A R of a Ursa major 152 |6 54 



Angle at the pole = 17 1 56 44 



AR'sof the meridian when /8-| 1 58 7. 8 by observ. made Oct. 14, 



Ursa minor passed the direct. > 1 58 14. 2D" on the 15, 



of the line AB. J 1 58 7. ID" on the ". 16^ 



Mean of the first and last = ... . 1 58 7.5 = 29 31 52 



Att of /3 Ursa minor 222 53 30 



Angle of the Pole 166 33 22 



Now having the distance of the *s from the pole, the angles at the pole, and the latitude o( the 

 point A, per spherics, we find the star's azimuth from the north = the angle bam. 

 And for the said angle by terrestrial measurement. As am : Rad :: pm : 



Tangent angle pAm- = the angle bam. = 3° 43' 40" 



Angle per « Ursa minor 3 43 25 



D° per /3 Ursa minor 3 43 25 



Mean 3 43 30 = Angle bam. 



In the same manner as the point m, in the meridian from a was found, points 

 in the meridian, north of p and n, were also found; and having two points given, 



with them a right line was extended as follows: first np in a line with n e. 



At N the equal altitude instrument was set up, and the vertical wire in the 

 telescope was brought to bisect the mark at e ; and there the vertical axis made 

 fast. The spirit level showing the axis of the telescope to be horizontal. The 

 vertical axis being well secured, the telescope part is taken off the supporters, and 

 turned to point to the southward (carefully taking off, and putting it on the 

 supporters so as not to move the axis) ; then on the farthest rising ground that 

 could be seen, another mark was placed at 1, in a right line with the vertical wire. 

 A mark being left at n, the instrument is taken, and set up 3 or 4 feet south of 

 the mark 1, and having brought the vertical wire in the telescope in a right line 

 with the marks at 1 and n, the vertical axis is then made fast as before, the 

 telescope immediately turned, and a third mark placed to the southward ; and 

 so the operation was continued. 



In the same manner the lines ps, CD, ab, and ae were traced out; and to 

 prove that by this method a right line may be extended, we shall here give the 

 result of continuing the lines ab and ae. a and d being two points between 

 which a right line was to be drawn. , The point n was known to be nearly in 



