RELATING TO THE FIGURE OF THK EARTH. 175 



plete folution of the probkm, and the full detail of the invefti- To determine 

 gation, I am, under the neceffity of delaying to fome future figure, by a 

 communication. general method 



There feems to be but one difficulty of any confequence that^''^ twang cs. 

 -ilands in the way of this method of determining the figure of 

 the eartlj. It arifes from this, that the afcertaining the pofition 

 of the fuppofed feries of triangular planes relatively to one 

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

 reftrial refradion, which it muft fcje confefTcd is not accurately- 

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

 voidably combined with the irregularities in the dire6lion of 

 gravity. It is poffible, indeed, to feparate thefe two fources 

 of error, bufnot without a fyftem of experiments inllituted 

 directly for that purpofe, 



36. The determination of the difference of longitude, which 

 enters neceflarily into this problem, except in the cafe when 

 both chords are in the dire6lion of the meridian, muft alfo 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 obje<5lion. 

 For, not to mention that it is only pra6licable in high latitudes, 

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

 of the ellipticity of the meridian, which is therefore necetfarily 

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

 This inconvenience, however, may be obviated by repeated 

 approximations, and by an accurate folution of fpheroidal 

 triangles. On this latter fubjed it was my intention to offsr to 

 the Society fome theorems, that contain more direct and fuller 

 rules for this kind of trigonometry than any that I have y^i met 

 with. I am under the neceffity, however, of referving thefe, 

 as well as the folution of the problem above-mentioned, for the 

 fubjeds of fome future communication. In the mean time, I 

 think it is material 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 iides 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 ftridfy true, unlefs 

 the eccentricity of the fpheroid be infinitely fmall, or the 

 triangle be very nearly ifofceles. The application of the prin- 

 ciple may therefore lead into error, unlefs it be made with due 

 5 attention 



