*3.10 AN ACCOUNT. GF THE. 
Appendix contaming Geodesic Calculations and Investigations of the For- 
mule, on which.they are founded.— With Tables... 
Y. Ir has been generally deemed sufficient to perform the calculations. 
required in a survey, according to the method called Mrrcator’s, rendered 
very expeditious by. means of the conformity, whicli:the scale of logarith-- 
mic tangents bears to Mercaror’s artificial table of cosecants of the- 
latitude.. In-navigation,. where the distance is measured on the Rhumb,. 
this method is strictly true,. but it cannot give the relation: between differ= 
ences of latitude, or longitude,.and the distances of places. Considering 
the earth:as.a sphere, it is evident that the shortest line between any two- 
points is the arc of a great circle;.and it is in this line that distances pro-- 
perly speaking should be taken.. In Geography, therefore, or Geodesie: 
this method is not allowable, where a certain degree of accuracy is aspired 
to; indeed. where-the distance is great,. the errors occasioned by it may be 
very considerable. 
2. 'To employ the common analogies of spherical trigonometry in 
these calculations, when they are numerous, as is the case of this survey,. 
would be a prodigious waste of time: it would involve too, meri petty. 
errors occasioned by the want of sufficient outoiss in: the tables, which: 
might by accumulation increase to something considerable, that would in 
all probability occasion mucli loss of time in fruitless endeavours to correct. | 
But supposing the contrary of all this were true, itis still to ke recollected, 
that the earth is not a sphere, but an irregular figure approaching 
so nearly to an ellipsoid, as to be safely considered as such in our finest 
