l899-'00 TRANSACTIONS 1 51 



longitude observations, the surveyors' and engineers' operations, 

 all have their zero of reckoning in the centre of the level bubble, 

 and any displacement of the latter, which is equivalent to the 

 displacement of the plumb line, affects the results, and will show 

 discordances when widely separated observations are geodetically 

 connected. 



It may be stated that a delicate level used for latitude work, 

 reading to a second of arc, has usually a radius of about 1,700 

 feet, or nearly a third of a mile, for the curve ground on its inner 

 upper surface. 



To digress for a moment. 



Boundary lines may be divided into three classes : — those 

 representing a social unity, those representing a physical unity, 

 and those representing a political unity. Those of the first find 

 the largest number of representatives in the older settled countries, 

 for the primal concept of boundary was to conserve the social 

 unity. It was not to define territorial extent as much as to 

 define or assert the domain of a like people ; like by language, 

 race, or religion or other afiiliation. Such boundaries are, as a 

 rule, very irregular and difiicult to describe. When the social 

 organism reached that development that written treaties became 

 necessary between adjoining peoples, the description of the 

 separating boundary was made from the boundary de facto, and 

 the boundary not laid down from the description, 



The second class we may consider an expansion of the first, 

 resulting from conquest, whereby a physical as well as a social 

 unity was to be preserved. Of the physical boundaries, — 

 mountains, rivers and lakes, — to serve the purpose of barriers, 

 by mountains, that end is undoubtedly best attained. Europe 

 furnishes a number of examples of this. 



The third class, which we may call the astronomic boundary, 

 is a development of recent times, and applies invariably to areas 

 practically unsettled, unsurveyed and little known. Such can be 

 laid down on paper, or described in treaties without scarcely any 

 knowledge of the country whatsoever. 



While Europe furnishes the most examples of the first, 

 America does so of the last. Many of the State boundaries of 

 the United States are astronomic lines, either meridians, parallels, 



