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 - •/ \ 10.G 2 + 1.5 2 + 31.8 cos. 2 ( $ — 15°) j ; 

 for the low waters : 



y = • J2.95 2 + 1.75 s — 5.16 cos. 2 (<p — 15) j ; 

 These expressions may be changed to 



y = 10.6 + 1.5 cos. 2 (cp— 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" 12345 6789 10 11 12'' 



30m << << " f( « If (( « tt U (t 30m 



1 ' 1 2 3 4 5 6 7 8 9 10 11 12>> 

 30iu << <t ti tt <( u if ff ff ff ft 301U 



h S'" 

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



1 Q// 



whereas from the inequality in times — or — — 

 1 J h' M" 



0.471 



