44 Mr. Buggers Latitudes and Longitudes 
circular instrument of 4 feet radius, which, at least at that 
time, was the only circular instrument of that size. 
By the trigonometrical operations, the meridian of Copen- 
hagen, and of several other places, and a perpendicular to the 
meridian of the observatory, are drawn. The special position 
of villages, farms, and cottages, the situation of the coast, 
woods, rivers, ponds, moors, roads, are laid down by the plain 
table, on a scale of 2000 Danish or Rhenish feet to one decimal 
inch. After a reduction to £th part, to a scale of 1 Danish 
mile to 2 inches, we have published 9 geographical maps, 
which, as well for the geometrical exactness, as for the beauty 
of engraving, seem not to be unworthy of the approbation of 
foreigners. 
I have described the instruments, and the methods of our 
geometrical surveying, and of the trigonometrical operations, 
in a treatise published in the Danish language at Copen- 
hagen 1779, and translated into the German by Major Aster 
at Dresden, 1787. In this paper I only shall lay before the 
Royal Society a new method of computing the longitude and 
the latitude of places, laid down by trigonometrical opera- 
tions. 
Let EAIH (Tab. VIII.) be an ellipsis; EH half the less axis; 
IH half the greater axis ; A the observatory at Copenhagen ; 
AV its vertical line ; the angle V the complement to the lati- 
tude of the observatory. Then by the nature of the ellipsis. 
AV _iHI -7-r AN is a great circle, perpen- 
AV — ^ Hi z sm .z y + HE* cos. 1 V) 5;. 
dicular to the meridian of Copenhagen. The tangent to the 
same meridian AF = AVx tang. V. A m n op . . . D is a 
series of triangles in the direction of the parallel of Copenha- 
gen. g t u r x . . . G is a series of triangles in the direction of 
