422 PHILOSOPHICAL TRANSACTIONS. [aNNO 177B, 



been already done in the present case will render any future repetition more easy 

 and perfect. But improvements may be made, perhaps both in the mode of 

 computation and in the survey ; in the latter, especially, there certainly may. 

 Some improvements of this kind have been hinted at in some parts of this paper, 

 which with others are here collected together, that they may readily be seen in 

 one point of view. They are principally these. Procure one base, or more if 

 convenient, very accurately measured, in such situation, that as many more 

 points as possible in the survey may be seen from it. Assume as many principal 

 or eminent points and objects as may be proper and convenient ; and from each 

 one of them measure the angles formed by all the rest that can be seen, both 

 horizontal and vertical angles, and repeat these observations, if convenient, 

 with the instrument varied or reversed, taking the means among the several 

 quantities of each angle. Take then as many sections of the ground, and as 

 far extended in all directions, as the time and circumstances will possibly admit. 

 Of the sections, those that are horizontal or level are the best, as they require 

 no calculation ; procure therefore as many as possible of them. In vertical sec^ 

 tions observe the vertical angles, not in the plane of tlie section, but at some 

 other point of which the bearing is also taken from the beginning of the section 

 line, and where the horizontal angles of the poles are taken, for the reasons 

 beforementioned. And it will be a still further convenience if the section be 

 made in such direction as to form a right angle with the line drawn to the point 

 or station from which the vertical angles of the poles are observed, as may be 

 seen from what was before said. It might perhaps be proper to make some ex- 

 periments on a valley instead of a hill, taking two observatories at the two oppo- 

 site sides of it, both for the greater variety in this interesting problem, and be- 

 cause also the survey would be more easily made, on account of the ground 

 being more in view at each station than in the case of a hill, which generally 

 hides more than half the compass from the observer. In computing the relative 

 altitudes of all the principal stations, let the operations be performed mutually 

 both backwards and forwards, that is, from both of every two objects, having 

 for that purpose observed at each of them the vertical angle of the other, namely, 

 both the angle of elevation and the angle of depression, and take the mean be- 

 tween the two computed differences of altitude ; for this excludes the necessity 

 of making the proper allowances for refraction, and for the curvature of the 

 earth ; since the effect of each of these is balanced and corrected by that of the 

 counter observation. But as to those j^oints in the sections which are far distant 

 from the observer, and where great accuracy is required, it may be proper to 

 make the allowance for refraction and curvature, as there is generally no back 

 observation by which their effects may be balanced. These are the ciiief liints 

 which at present occur, besides the general information to be derived by the 



