ELISHA MITCHELL SCIENTIFIC SOCIETY. 121 



We shall close by calling attention to one more interest- 

 ing result. The angle i that a chord from station Xj — i 

 to station X, makes with the Y axis, is found from (23J bv 

 changing X to Xj — i . '. / = 6 Xj - — 6 X^ — 2. Sub- 

 tracting this from the <? at X"i = 6 X^j - and we have a — / 

 = 6 X, — 2. If we regard X, as the point of connection 



20 Xj 



with the circular curve, we have D° = and the first 



c 

 deflection from the tangent on the circular curve for a 



c 

 chord of c feet is 3/ 60 D° = 6 X, minutes. This is 



TOO 



always greater b\- two minutes than the angle between the 

 tangent at station X, and the chord from station Xj — i to 

 station Xj, as we have just found the last angle to equal 

 (6X1 — 2) minutes. We should naturally expect such a 

 result from the definition of the curve. 



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