[ 364 ] 



LXII. A Letter from Professor Airy in reply to Mr. Gal- 

 braith's Remarks (p. 182.) on some late Computations of the 

 Earth's Ellipticity. 



To the Editors of the Philosophical Magazine and Annals. 

 Gentlemen, 



FN an article which appears in your Journal for September 

 ■*• last, Mr. Galbraith expresses himself much astonished at 

 the difference between the value of the earth's ellipticity which 

 he has obtained, and a result at which I had arrived. I think 

 that any person who reads my paper on this subject will see 

 the ground on which such a difference might have been looked 

 for ; but for those who do not, a single line may serve to point 

 out the state of the case. Mr. Galbraith's calculations pro- 

 ceed on the assumption that the earth is known to be an el- 

 lipsoid : mine, on the supposition that this is not known. It 

 is manifest that to satisfy the observed curvatures in different 

 places we shall have different proportions of the axes, accord- 

 ingly as the meridian is supposed to be an ellipse, or to be 

 some other figure. 



I am by no means disposed to consider his hypothesis to be 

 better founded than mine : but more pressing employments 

 compel me at present to abstain from the discussion of this 

 " much-vexed topic, to which he so obligingly invites me. 



I am, Gentlemen, yours, &c. 



Observatory, Cambridge. G. B. AlRY. 



Oct. 17, 1828. 



LXIII. On Mr. Dalby's Method of finding the Difference of 

 Longitude between two Points of a Geodetical Line on a 

 Spheroid^ from the Latitude of those Points and the Azimuths 

 of the geodetical Line at the same. ByDr. Tiarks, F.R.S. $c. 



f T' , HE ingenious method first suggested by Mr. Dalby, of 

 ■*■ deducing the difference of longitude between any two 

 points on a spheroid, from the latitude of these points and the 

 inclination of the geodetical line connecting them to their me- 

 ridians at these points, is founded on a remarkable property 

 of spheroidical triangles formed by geodetical lines, which may 

 generally be thus enunciated : The sum of the three angles of 

 any spheroidical triangle formed by geodetical lines is a func- 

 tion of the latitudes of the angular points and their differences 

 of longitude only, and is altogether independent of the excen- 

 tricity of the spheroid. This sum, accordingly, is the same as 



the 



