26 



hours let fall perpendieulars on the diameter joining ^KJl. and YI. i the in- 

 tercept hetween the feet of these perpendiculars, measured on the scale of the 

 diameter, is the Tidal Drift required. 



This construction, wbich is rapidly made in practice, will, I believe, 

 be found of great value to masters of vessels entering or clearing the 

 Irish Sea and English Channel. It may be thus proved : — 



Let V denote the velocity of the Tidal Stream. 

 ,, a ,, maximum velocity of the same. 

 „ t ,, time measured in Tidal Hours, from XII. o'clock, 

 on the tidal dial. 



2^ 



„ T= twelve tidal 



Then 

 therefore 



ds - 



and, finally, 



hours (12h 24™ = 744^"). 



= sin nt, 



a sin nt dt, 



8 - cos nt + const., 

 n 



a 



0 = — * + const. : 



n 



s = - (1 - cos nt). 



n ^ ' 



(1) 



(2) 



This is the Tidal Drift, measured from the commencement of the 

 Ebb. It is evidently proportional to the versed sine of the Tidal Hour ; 

 and therefore the construction is proved, provided we can show that 

 the radius of the Tidal Clock is double the maximum rate of the stream. 



Calling jETthe Tidal Hour, we have 



5 = - (1 - cos K), 



n^ ^ 



= l-973^?(l-cos^); 



and, taking this between any two Tidal Hours, we have 



s-s' = Tidal Drift = 1-973^? (cos E' - cos E). (3) 



Eor practical purposes, 1*973 is so nearly equal to 2, that the circle 

 whose radius is douhle the maximum velocity a, wiU answer for the 

 graphical calculation. 



