Distance traced on the Surfuce of an oblate Spheroid. 249 
polar semi-axis in the same parts with s, and if we take the 
é l 
mean latitude +. for u, we shall have 
ME, SU OTE: eS) 
u—l (1+ e2cos2 i+u yi 
and by expanding the radical and retaining only the first 
power of e*, we get, 
“~~ =P} ri “ = 2= cos (1 + u)}. 
Two such equations are required for determining P and the 
> ey e2 
ellipticity ae 
But in determining the figure of the earth by means of ter- 
restrial observations, instead of the difference of latitude, we 
may employ the difference of longitude of the two extremities 
of the line measured, or the change in azimuth at the same 
Stations. And in the case of a perpendicular to the meridian, 
one or other of the two quantities mentioned must be used, 
since it has been shown that the difference of latitude is in- 
adequate to the purpose. It therefore becomes necessary to 
form the expressions of a geodetical line in terms of the dif- 
ference of longitude, and in terms of the azimuth at its further 
extremity; but, as this would make too great an addition to 
what I have already written, I shall reserve it for a future 
communication. 
April 5, 1826. J. Ivory. 
XXXIX. On the Phenomena connected with some Trap 
Dykes in Yorkshire and Durham. By the Rev. ADAM 
Sepewicx, M.A. F.R.S. M.G.S. Fellow of Trinity College, 
and Woodwardian Professor in the University of Cambridge. 
[Concluded from p. 219.} 
Extent and Position. 
N O other dyke has, I believe, been yet described, which in- 
tersects so many secondary formations, and preserves such 
an extraordinary uniformity of direction and inclination. The 
whole length, reckoning from the quarry at Gaundlass Mill, 
is more than fifty miles: and if any one should object to this, 
as including a considerable space in which the continuity is 
not apparent, there will still remain from Coatham Stob a di- 
stance of about thirty-five miles, through which it is almost 
certain that the trap ranges without any break or interruption. 
Perhaps it might with more justice be objected, that the first 
Vol. 67. No. 336, April 1826. eI com- 
