l899-'00 TRANSACTIONS 155 



varying from one to three miles. From the last mentioned offset 

 the relative station error (deflection of plumb line) was found 

 and distributed between the two stations in the ratio of the dis- 

 tances where offsets were taken. From this method it results 

 that the boundary line, as actually traced, is an irregular curve, 

 affected at each astronomical point by instrumental errors and by 

 the local deflection of the plumb line, making the closest probable 

 approximation, at every point, to a true astronomical parallel. 



Of the forty astronomical stations on the 49th parallel, four 

 were observed jointly, seventeen by the United States astronomer 

 and nineteen by the British. The mean of the probable errors of 

 the British stations was, ±".088 and of the United States ±".059. 

 The average of the probable errors is then a little over seven feet. 



The greatest difference of station errors is 13. "89 or i ,407 feet, 

 being in a distance of 97 7/10 miles, between the Cypress Hills 

 to the north of the boundary, and the Three Buttes or Sweet 

 Grass Hills near, and to the south of the 49th parallel. The 

 station error of the former is + 5. "94, of the latter - 7. "9 5, that is the 

 Three Buttes pulled the 49th parallel 805 feet south, and the 

 Cypress Hills 602 feet north of the mean parallel. The greatest 

 discrepancy between adjacent stations, about twenty miles apart, 

 is 7. "28 or 738 feet, near the Three Buttes. 



lyooking at the accompanying diagram, in which the upper 

 figure is a representation (much exaggerated) of the relative 

 position of the astronomic and mean parallels, while the lower 

 figure shows the main features of the topography for a distance 

 of about thirty-five, miles on each side of the boundary line, the 

 large deflections appear obvious from the topography. From the 

 lyake of the Woods, westward, into the valley of the Red River, 

 the station errors increase, and for a reason, which from our lack 

 of knowledge of the underlying strata, must be conjectural. The 

 escarpment of the Pembina Mountains, (elevation would be a more 

 appropriate term, height 1,695 feet), naturally draws the vertical 

 southward, continuing to do so until the Turtle Mountains (of 

 moderate elevation, 2, 5 50 feet) are reached, which too deflect to the 

 south. After entering the Coteau of the Missouri we pass along 

 the southern base of the high ridge, separating the waters flowing 

 into the Gulf of Mexico, from those flowing into Hudson's Bay, 

 and find, naturally, a deflection to the north, increasing to a 



