Boundary Between Nicaragua and Costa Rica 27 



the boundary was defined by long tan- 

 gents, including the proper area. 



On reaching the Sapoa River a monu- 

 ment was erected, and a broken line to 

 SaHnas Bay was run, the boundary of the 

 bay itself was surveyed, and the island 

 was located. 



The last important point decided by 

 General Alexander was perhaps the knot- 

 tiest of all. It was the definition of the 

 centre of Salinas Bay, and the decision 

 was both just and ingenious. The re- 

 marks of the Arbiter are as follows : 



" The Bay of Salinas was carefully sur- 

 veyed and mapped by officers of the 

 United States Navy in 1885, and a map 

 of the same is published in the United 

 States Naval Hydrographic office. No. 

 1025. I have adopted this map, with the 

 consent of both commissions, as correctly 

 representing the outline of the Bay. In 

 shape it is a curved pocket, starting east 

 and bending southward, about five miles 

 long, and about one-half of that in aver- 

 age width. Its outline a little resembles 

 the rounded handle or butt of a pistol, 

 with some irregular projections and in- 

 dentations. 



" It is desired to find the mathematical 

 centre of this figure, closed by the straight 

 line joining the headlands of the Bay. 



" The mathematical centre of an irregu- 

 lar figure is the mid-position of its area. 

 All mechanical centres, such as the centre 

 of gravity or of equilibrium, etc., in which 

 the action of any force is concerned, must 

 be excluded from consideration. 



" This will readily appear if we con- 

 sider for a moment the case of a bay in 

 the shape of a crescent. The centre of 

 gravity of its figure would not fall upon 

 the water of the bay at all, but upon the 

 promontory of land embraced by the wa- 

 ter. This, of course, could not be con- 

 sidered as the centre of the bay. 



" Neither is any general mathematical 

 process applicable, such as that of the 

 method of Least Squares. This method 

 will find the centres of any group of ran- 

 dom spots, but were they disposed in cres- 



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