RECORD AND REDUCTION OF THE TIDES. 



71 



The values for h', h and a were found from the maxima and minima values of the 

 inequality, viz., for the high water: 



y = V \ lO.G- + 1.5' + 31.8 COS. 2 ( <?) — 15°)| ; 

 for the low waters : 



y = ^ 12.95- + 1.75^—5.16 cos. 2 (<?. — 15)| ; 

 These expressions may be changed to 



y = 10.6 + 1.5 COS. 2 (^—15°), andy = 2.7—1.7 cos. 2 ((|)— 15°); 

 they leave the following differences between the computed and observed values: — 



The differences may be considered within the uncertainty of the observations. 

 The annexed diagram shows the comparison given above : — 



Observed and computed half-monthly inequality in height from observations. 

 Of the high waters. Of the low waters. 



0" 1 2 3 4 5 6 7 8 9 10 11 12" 



OQlU (( (( t( (( (t (( i( (( t( (( t* 30™ 



C 1 2 3 4 5 6 7 8 9 10 11 12" 



30" 



tt (C (( 



(( (( t( u (( i( Qnm 



30" 



From the inequality in height— or -— ^ (notation of the wave theory) = 0.367 



7 C" 



whereas from the inequality in times — or — — 

 ^ ^ h' M" 



= 0.471 



