LOCAL DEFLECTION OF THE PLUMB 



LINE. 



Otto J. Klotz. 



In the present short paper it is only intended to lay before 

 the Society certain data of the deflection of the plumb line as 

 found by latitude observations and azimuth surveys along the 

 International Boundary, 49th parallel, from the Lake of the 

 Woods to the Pacific Ocean. Those westward, as far as the 

 Rocky Mountains, were published years ago in the United States 

 Report of the Northern Boundarj;- Survey, but those of British 

 Columbia have, to my knowledge, never been published. The 

 effect of deflection of the plumb line on longitude and azimuth 

 observations is not considered in the present paper. 



Deflection of the plumb line may be defined as the deviation 

 of the vertical at any point from the normal at that point to the 

 surface of an assumied figure of the earth. In dealing with the 

 earth,' we must assume its shape to be of some definite geometri- 

 cal form and of certain dimensions, for only then can observations, 

 at different points thereon, be correlated and adjusted. The best 

 assumed form (Clarke's 1880 spheroid at present), hovv^ever, dif- 

 fers at places widely from the actual form or geoid. To illustrate, 

 if the continents were traversed by narrow canals, communicating 

 with the ocean, their surface, although level, would be wavy or 

 undulating, and would be in some places above, in other places 

 below the surface of the spheroid or ellipsoid of revolution, the 

 divergence of the two surfaces being probably confined to a few 

 hundred feet. 



The position assumed by the plumb line, is due to the law of 

 gravitation, that is, it is the integrated result of the attraction of 

 the individual particles, composing the mass of the earth, and 

 hence the position is affected by the relative distribution of them. 

 We may, therefore, say that the unsymmetrical distribution of 

 the particles, whether on the surface, as mountains, etc., or in 

 the thin crust, is the cause of the deflection of the plumb line 



