Relating to the FIGURE of the EARTH. 29 



lion of the fuppofed feries of triangular planes relatively to one 

 another, involves in it the allowance to be made for the terre- 

 ftrial refraction, which it mull be confefTed is not accurately 

 known, and is the more difficult to determine, that it is una- 

 voidably combined with the irregularities in the direction of 

 gravity. It is poflible, indeed, to feparate thefe two fources of 

 error, but not without a fyftem of experiments inftituted directly 

 for that purpofe. 



36. The determination of the difference of longitude, which 

 enters neceffarily into this problem, except in the cafe when 

 both chords are -in the direction of the meridian, muft alfb be 

 performed with great accuracy. Among the different ways of 

 doing this, that which proceeds by obferving the convergency 

 of the meridians, though the beft accommodated to the nature 

 of a trigonometrical furvey, is not the leaft liable to objection. 

 For, not to mention that it is only practicable in high latitudes^ 

 we muft obferve, that it always implies a correction on account 

 of the ellipticity of the meridian, which is therefore neceffarily 

 hypothetical, and depends on the very thing that is to be found. 

 This inconvenience, however, may be obviated by repeated ap- 

 proximations, and by an accurate folution of fpberoidal triangles. 

 On this latter fubject it was my intention to offer to the Society 

 fome theorems, that contain more direct and fuller rules for this 

 kind of trigonometry than any that I have yet met with. I am 

 under the neceffity, however, of referving thefe, as well as the fo- 

 lution of the problem above mentioned, for the fubject s of fome 

 future communication. In the mean time, I think it is mate- 

 rial to obferve, that the principle laid down by Mr Dalby, viz. 

 that in a fpheroidal triangle, of which the angle at the pole and 

 the two fides are given, the fum of the angles at the bafe is the 

 fame as in a fpherical triangle, having the fame fides, and the 

 fame vertical angle, is not flrictly true, unlefs the excentricity of 



the 



