II. 



THOMAS KENNEDY. 



a pair of angles whose natural tangents differ from each 

 other by '01 when the base is *66 or 1. By using the *66 

 base the resultant heights are in feet and the distances in 

 links (should the heights and distances be required both in 

 feet, then the angles from the natural tangents correspond- 

 ing to '01, *02 and "03, etc., can be taken direct from a 

 table of natural tangents). The two tables of tangents 

 have been calculated to give distances in chains and links 

 or feet, from a level surface to a slope of sixty feet in 

 one chain. 



If any two angles be taken from the table and set alter- 

 natively on the vertical arc of a theodolite, and a levelling 

 staff divided to hundredths of a foot be read at each setting, 

 then the difference of the staff readings will give the hori- 

 zontal distance in chains and links or feet according to the 

 table used, and this distance multiplied by the natural 

 tangent ol* either angle will give the height in feet from 

 the instrumental axis to the intersection of the cross hairs 

 on the staff when that angle is set on the vertical arc cor- 

 responding to the tangent used for multiplication. 



The natural tangents are given on the table opposite to 

 their respective angles. As a practical example 





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