Mr. Ivory on Measurements of perpendicular Degrees, 189 



The plummet P, and the screws at L, enable the operator 

 to detect and rectify any deviation from perpendicularity in 

 the instrument. 



XXXIII. On Measurements on the Earth's Surface perpendi- 

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



A FTER so many laborious researches undertaken to deter- 

 -^ mine the figure of the earth, the opinions of philosophers 

 upon that point are still very unsettled. In proof of this it 

 will be sufficient to cite what is advanced in the latest memoir 

 on this subject, in which it is said that the compression 7 £ n is 

 adopted, because it is the mean between 7 | n and ^g, the li- 

 mits between which the ellipticity is generally supposed to be 

 comprised f. There is at least great prudence in this pro- 

 cedure; for at the same time that the particular ellipticity is 

 pitched upon which is nearly the best fitted to reconcile all 

 the phaenomena with the measurements of the Survey, there is 

 no risk incurred that the truth, when it can no longer be dis- 

 puted, will fall beyond the boundaries mentioned. In the 

 Numbers of this Journal for May and June last, the elliptical 

 elements of the earth are deduced from the five most esteemed 

 measurements of meridional arcs in our possession ; and it is 

 fully proved that the elements found represent the five di- 

 stances on the meridian with great accuracy. As far as our 

 present knowledge extends, we are therefore entitled to infer 

 that the terrestrial meridians are equal ellipses of a known ex- 

 centricity, and the earth itself an elliptical spheroid having a 

 known compression at the poles. 



Till additional surveys shall enable us to establish the fore- 

 going conclusion, or to correct it, if it be erroneous, we may 

 inquire what light will be thrown on the question by measure- 

 ments perpendicular to the meridian. In this Journal for 

 July last, I have shown that, in the English Survey, the ope- 

 rations at Beachy Head and Dunnose, for finding the length 

 of a degree perpendicular to the meridian, lead to a result that 

 accords exactly with the same spheroid deduced from the me- 

 ridional arcs. My present intention is to examine some more 

 instances of the same kind ; and I shall begin with putting the 

 formula I used for computing the difference of longitude into 

 a form more convenient for calculation. 



* Communicated by the Author. f Phil. Trans. 1828, p. 132. 



Referring 



