. [ n 1 



To render the application of the above table and fubfequent 

 procefs more intelligible, I have annexed a flcetch of the pro- 

 jetftion and outline of the map of Germany. 



Havnig drawn the contour of the country with all pofTible 

 accuracy, and exprefled it by a very fine, line, obferve what qua- 

 drilateral fpaces lie entirely within it ; enclofe thefe by a flrong 

 black line, and the area of all within it we may call the inte- 

 gral area, as it confifts of entire quadrilaterals ; and that withr 

 out it, the fra&ional area, as it is compofed of parts of quadrir 

 laterals. 



The integrah area may be found with the greatefl accuracy 

 thvis : I find, in the table, that a quadrilateral between the 53d 

 and 54th parallel contains 2138.2 fquai-e miles,, and that there 

 are fix fuch in the integral area ; therefore 2138.2 x 6 = 12829.2 

 will give the true contents of that portion of it which lies be- 

 tween thefe parallels, and a fimilar operation for the zones 

 between the other parallels will give 144023.6 as the entire 

 integral area of Germany. 



Thus far (fuppofing the map corre^fl) there is no poflibility of 

 error. The contents of the fradlional area can be found only 

 by approximation : The method I propofe is this : 



Let it be required to find the area of the fpace A in the qua- Fig. i 

 drilateral abed: having conftruded a fcale, from the extent of 

 a degree of latitude, reduce the irregular waving contour tf^*: 



K into 



