RECORD AND REDUCTION OP THE TIDES. 



69 



5 h 30'" 6'' 3()"\ 7 1 ' 30'", where the curve is steepest; the value — is obtained from 



k 



the greatest range of the inequality determined, for a first approximation, by a 

 graphical process. I find from the observed high waters a = h 21 ra or 5° 15', and 

 from the low waters a = h 50 m or 12° 30'. Eange of inequality, from the high 

 waters, l h 51 m or 27° 48', the sin. of which is 0.4649, and for the low waters, range 

 l h 54 m or 28° 30', the sin. of which is 0.4771 ; hence the expression for the half- 

 monthly inequality in time becomes 



-r. , , t i • t. n/,v i«o^,m 0.4649 sin. 2 (d> — 5° 15') 



From the observed high waters tan. 2(0'— 175°49'.5)= — — — — — — £- -— ; ' 



v 1+0.4649 cos. 2 (<p — 5° lo') 



n,n, n ,«onnrt 0.4771 sin. 2 (rf> — 12° 30') 



» " " low witers tan 2 f fl — 267 00 1= — - 



low waters tan. * [V tot vv ) 1+04771 C05> 2 (<£— 12° 30') 

 These expressions furnish us with the following comparison : — 



HAXF-MONTIILY INEQUALITY IN TIME. 



Considering that the times of high and low water are only observed to the 

 nearest half hour and for some time to the nearest hour, the agreement as shown 

 above and by the diagrams, seems to be satisfactory. 



+1 1 ' oo» 



50 

 40 

 30 

 20 

 10 

 

 10 

 20 

 30 

 40 

 50 

 — 1» 00' 



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



gQm u u (( U « 11 t( (( (( (( it 3Qm 



0» 123456789 10 11 12" 

 30 m " " " " " " " " " " " 30™' 



