THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



OCTOBER 1828. 



XL II. On the Method employed in the Trigonometrical Sur- 

 vey for Jinding the Length of a Degree perpendicular to the 

 Meridian. By J. Ivory, Esq. M.A. F.R.S.* 



TN the first volume of the Trigonometrical Survey, a method 

 ■* is given for finding the difference of longitude of two sta- 

 tions lying nearly in the same parallel of latitude, without as- 

 suming that the earth has any particular figure, and supposing 

 only that it is nearly a sphere f . An important part of the 

 Survey depends upon this method ; and, although its accuracy 

 has heretofore been called in question, yet we see from the 

 late volumes of the Phil. Trans, that it is now deemed suffi- 

 ciently exact and unexceptionable in its principle. It is how- 

 ever remarkable, that this method has never succeeded in prac- 

 tice, or rather, has in every case led to results evidently wide 

 of the truth. This failure it is usual to ascribe to errors in 

 the observed azimuths ; but we may reasonably doubt whether 

 this be the sole cause of deficiency, when we observe that the 

 difference of longitude of the two stations, computed by other 

 modes of solution unquestionable in point of accuracy, is al- 

 ways found to depend on the compression of the spheroid. 

 The method of which we are speaking, was first published in 

 the Phil. Trans, for 1 790 and 1 795 ; it is therefore time to sub- 

 ject to a strict examination a process which, although it has 

 never been of any utility, is still employed in practice ; and 

 as I have thrown out some doubts about the grounds of it in 

 this Journal for May last, I deem it incumbent on me to as- 

 certain fully its real character. 



Let A and m denote the latitude and azimuth at the first 

 station; V and m' the same things at the second station; 



* Communicated by the Author, 

 f Trigonometrical Survey, vol. i. pp. 154, 293. 

 New Series. Vol. 4. No. 22. Oct. 1828. 2 I y the 



