150 TRANSACTIONS iSgg-'oo 



from its theoretical position. The ablest mathematicians have 

 been engaged, ever since the era of precise measurement, upon 

 this difl&cult question of the form and dimensions of the sea level 

 surface. 



In some instances we are quite prepared to find local de- 

 flections of the plumb line, for example, when observations are 

 taken on the plains at a point near a more or less isolated up- 

 heaval, as the Three Buttes or Sweet Grass Hills in Montana, 

 just south of the International Boundary. These hills, as we 

 shall see later, pulled the 49th parallel out of its theoretical posi- 

 tion about 800 feet. On the other hand, large deflections show 

 themselves without any visible reason or cause as evolves from 

 numerous observations and their geodetic connection. A remark- 

 able instance is that of the comparativel}^ plain area surrounding 

 Moscow, which I visited recently, where, on the margins of an 

 18 mile east and west zone, large deflections of opposite signs 

 were found. From this it must be concluded that there exists 

 beneath the surface & cavity or at least matter of small density. 



It is evident, therefore, that the' observations alone, at any 

 particular point, are not conclusive for fixing its geographical 

 position upon the surface of the earth, but that numerous 

 astronomically determined points must be connected linearly by 

 triangulation, and. from their inter- accordance, or discordance, 

 the most probable values determined, based upon an assumed 

 figure of the earth. 



In our own city here, there appears, due to the topographical 

 configuration, to be a deflection of the plumb line ; for, the 

 latitude determinations made by me at the observatory on the 

 summit of the escarpment, compared with those made some years 

 ago by Mr. Lindsa^^ Russell on the opposite side of the river, 

 show a discrepancy of about a second of arc, equal to about a 

 hundred feet, a quantity greater than the error of observation. 

 However, a more or less extended hypsometric survey would be 

 necessary for a plausible a priori conclusion with reference to the 

 probable discordance in latitude to be expected between two 

 stations. 



All observations for the determinations of positions upon the 

 earth depend upon the direction of the vertical. I^atitude and 



