5G2 HYDROGRAPHICAL SURVEYING [app. w. 



Appendix W 



^ ,,..,. , number of feet subtended x 34 



To prove that Angle m seconds = ,.— - . ., - — . 



^ distance in sea miles 



In cases involving small angles : 



^. , , , arc it subtends 



Circular measure of an angle = — ^. rii • 



° radius oi the arc 



Angular unit = Angle, whose circular measure is unity, 



= ^ = 206267". 



Zir 



And since angles are to one another as the arcs they subtend 

 (Euc. VI.), and therefore as their circular measures 



6 _ circular measure of 

 20207" ^ i "' 



arc 



= 206267 X 



radius* 

 being small, chord may be substituted for arc. 



... e = 206267 X feet subtending ^- ^ 

 distance in feet 



_ 206267 X feet subtending g" 

 ~ distance Ln miles x 6080 



, - , , number of feet subtended x 34 , 



.'. Angle in seconds = ^r— -. -, very nearly. 



distance in sea miles 



