368 
Dr. Tiarks' account oj 
tude of Greenwich Observatory, which Captain Kater applies 
as the result of the latest observations, and the use of the 
French table of refraction 50* 37" Captain Kater finds 
this latitude by his observations with the repeating circle 
5°° 37' 5-" 2 7 > differing only 0^04 from the other. The lati- 
tude of Dunnose being therefore correctly deduced by geo- 
detical operations from the latitude of Greenwich, it is to 
be supposed that the latitude of Beachy Head, the more 
northern point, deduced by the same operations, has been 
equally well determined, and at least that there is no con- 
siderable error in the difference of latitude of the two places 
as laid down in the Survey. 
In order to understand the method which I have shortly de- 
scribed above, it is to be observed, that the spheroidical tri- 
angle PBD could not be resolved from the angles B and D and 
one of the sides PB and PD only, without assuming a certain 
ellipticity ; but from the two angles and the two sides, the 
ellipticity may be determined directly ; and from this, and the 
length of the arc of the meridian, the dimensions of the ter- 
restrial spheroid may be found. Introducing therefore the 
two angles and the two sides into the calculation, as is done 
in the Survey, is assuming that spheroid for the basis of the 
calculation, which has its compression determined by the 
relation between the two angles, the two sides, and the eccen- 
tricity of the meridians. For let the eccentrity of the meri- 
dian be e, the latititude of Beachy Head q> ] [ B =«' 1 
Dunnose , j the an S les [ D=«J 
and we have by the property of the geodetical line (the 
shortest line between two points on the terrestrial spheroid) 
sin. a. . cos. (p sin. a! cos. <p‘ 
or if J', | and be determined 
1/(1 — e^sin.p 2 ) ^/(i — e 2, sin . p' 1 ) ’ 
