148 I'HILOSOPHICAL TRANSACTIONS. [aNNO 1/92. 



report to ine every 10th number. By these precautions, almost all possibility ot 

 a mis-reckoning was prevented; and we accordingly found no disagreement 

 throughout. The whole distance was afterwards re-measured, and gave correctly 

 the same number of rods. 



The sum of the 6 measured lines, or parts of the base, amounted, by the first 

 trial, to 700 double rods, 20 feet 64- inches; and by the second, to 700 double 

 rods, 11 feet li-|- inches; their difference being 2 feet 4.i. inches, by which the 

 2d measurement exceeded the first. The sliorter of these measures is made use 

 of, as operations of this nature have always a tendency to excess, rather than 

 deficiency. Besides this linear measurement, 7 essential angles were taken, with 

 an excellent theodolite by Ramsden. These were the angles formed, at each ex- 

 tremity of the base, by the nearest intermediate flag, and the remote signal; 

 and those formed at each intermediate flag, by the nearest flag to it, on each 

 hand. Mr. T. then gives the quantity of these angles, and the lengths of the 

 intermediate distances; from which he calculates the lengths of the several parts 

 of so many triangles parallel to the main straight base line extended between the 

 two farthest or extreme points of all; the sum of which sides, taken together, 

 will be the true measure of the base line. 



It is immaterial, Mr. T. observes, at which end of the base line we begin. In 

 the present case, in order to obtain as great precision as possible, the intei-mediate 

 angles have been deduced from both ends. Had however this precaution been 

 neglected, the error induced, by deriving the 4 required angles from either pri- 

 mitive, would not have affected the true length of the whole base line more than 

 0.27 of a foot, or not quite so much as 3^- inches. This method of obtaining 

 the measure of an inaccessible line, he says, where the measured lines every 

 where make small angles with it, :s a very accurate one; for though, in oblique 

 triangles, small angles, from the difficulty of taking angles accurately, are likely 

 to produce considerable errors, in right-angled triangles it is the very reverse; 

 as in them the smaller the angle taken, the more accurate will be the result. In 

 a table are then registered the several observed angles and the measured distances, 

 with the correspondent computed parallels of the base. After this, a table of 

 the observations taken, both with the theodolite and the Hadley's sextant, for 

 determining the position of the base line with respect to the meridian. The 

 result of which is as follows : 



The mean of 28 observations by the theodolite is 3° ig' \1" 



The mean of 7 observations with the Hadley is 3 28 6 



The medium of both is therefore (by which the south end of the 



base is westerly, and the north end easterly of the meridian) . . 3 28 39 

 A set of meridional observations of 13 stars for determining the latitude of 

 each end of the base is next given; by which it is found that the mean latitude 

 of the south end was 1 1° 33' 11", and of the north end 1 1" 39' A". 



