410 PHILOSOPHICAL TRANSACTIONS. PaNNO 1778. 



and central situation of this line, all or most of the other points in the survey 

 are visible from one or both of its extremities, by which it happens that the other 

 lines are mostly determinable from it alone, without so close a connection with 

 each other as in the other method of computation. By both of these methods 

 then, and by all the triangles furnished by each of them, he computed all the 

 principal lines in the plan, and either took a mean among the several values of 

 each, or else selected out of them such as from various circumstances he judged 

 it safest to rely on, as nearest the truth. The trigonometrical computations 

 were always accurately made by the common numbers, and generally repeated 

 by logarithms, and the result of every proportion determined to 2 or 3 places of 

 decimals. 



The mean among a great number of ways of computation from the south base, 

 gives the horizontal distance of the secondary base from k to n = 4032-2, and 

 the mean of all the results from the north base «y gives kn = 4058-9, and the 

 mean between these two gives 4055-5 for the mean distance of k and n. And 

 this value of kn was used in computing most of the other lines in the survey, 

 which were very numerous, and were then set down in a table. 



From the first 3 lines, or bases, and the horizontal angles observed at the 

 several stations, a very large and accurate plan of the whole survey was con- 

 structed, forming a map of 4 feet long by 4 feet broad, which was verified in 

 every part by the measures of the computed lines, both those above-mentioned 

 and others, and they were generally found to agree very exactly, according to 

 the scale by which the plan was constructed. The use of this large map was to 

 receive and admit of the distinct and accurate exhibition of the figures in their 

 true places, expressing the number of feet in elevation or depression with respect 

 to each observatory of every point and section of the ground whose elevation or 

 depression might be observed. But before proceeding to the computation and 

 construction of the points in the sections. Dr. H. here abstracts the numbers 

 which express the relative elevation of the principal original points in the survey, 

 being the extremes of the lines whose lengths are above abstracted. These few 

 numbers are the results of the calculation of several hundreds of triangles con- 

 ceived in a vertical position, their bases being either the horizontal lines above- 

 mentioned, or other lines drawn as diagonals between many distant points in the 

 survey, according to the number of vertical angles which had been observed ; and 

 of these bases, whether real or imaginary, each generally afforded 2 vertical tri- 

 angles, as the angles of elevation and depression were taken alternately at both 

 ends of the lines. It is scarcely necessary to remark, that all these triangles are 

 right-angled, the common base being one of the sides about the right angle, 

 and the other the difference in altitude between the two given points or extremes 

 of the base; and this difference in altitude is found from the application of this 



