360 Captain A. R. Clarke on the Course of 



the curve of intersection formed by the plane containing the 

 normal at Cadiz, we shall compute the meridional distances of 

 points P on the geodesic from corresponding points Q on the 

 plane curve. We take approximate latitudes and longitudes for 

 the terminal points. 



Cadiz. St. Petersburg. 



Latitude . 36° 32 . . 59 56 

 Longitude . 6 18 W. .30 17 E. 



From these we obtain, neglecting e 2 in the calculation, 



«, = 33 13 

 a' = 61 29 

 </=33 1 



Taking for a the equatorial radius of the earth 20,926,060 feet, 

 and for the ratio of the axes 294 : 295, we have 



log a •% =4-85013. 



It is convenient to divide the distance a r into eight equal parts, 

 and so determine seven points on the geodesic. Since a' is about 

 33° 1' 28", we take for the eighth part 4° 7' 40". The result of 

 the calculation is contained in the following Table : — 







Q. 



P 



_ 







north of 





Latitude. 



Longitude. 



Q- 



t II 



/ 



o / 



ft. 







36 32 



6 18 W. 



00 



4 7 40 



39 57 



3 21 „ 



255 



8 15 20 



43 17 



6 „ 



4580 



12 23 



46 31 



3 32 E. 



589-2 



16 30 40 



49 37 



7 37 „ 



6370 



20 38 '20 



52 34 



12 13 „ 



597-3 



24 46 



55 18 



17 28 „ 



473-2 



28 53 40 



57 47 



23 28 „ 



271-4 



33 1 20 



59 56 



30 17 „ 



00 



It appears from this that, at the middle point of the geodesic, 

 the length of meridian intercepted between it and the plane 

 curve is upwards of 600 feet. With respect to the azimuths of 

 the geodesic at its extremities, they differ, as we find by equation 

 (13), from the azimuths of the vertical planes by 20"*37 at Cadiz 

 and 12"'71 at St. Petersburg. How such quantities should be 

 dealt with in practical geodesy is a question foreign to the object 

 of this investigation, which is merely to ascertain what sort of 

 magnitudes we have to deal with in the divergence of the geodesic 

 from plane curves. 



