258 W. H. Finlay, 31. A. — Approximate Tide- Co?isfants, ^c. [Aug. 3 1 , 



If we desire to take account of the parallactic and declinational 

 corrections we may proceed as follows : — 



For SO (in above fig.) take the value 1'086 p, cos^ d^ Hg where p^ 

 is the cube of the ratio of the Sun's parallax at the time under 

 consideration to the mean parallax, and S^ is the Sun's declination. 

 Then from Tables III and IV take the small corrections depending on 

 the Moon's parallax and declination, remembering that these correc- 

 tions are to be taken out for the Moon's position at a time anterior to 

 the high water by the ^ age.' 



Table III. 



Argument — Minutes of 



Moon's Parallax in 



excess or defect of 



67' 2". 



Table IY. 

 Argument — Moon's Declination. 



/ 



1 



d, Rm = 



ft 



± 0-08 



2 





0-17 



3 





0-25 



4 





0-34 



5 





0-42 



a ' Dec. 



N. or S. 



^2 I^m. 



^ K^. 



^2*' 



o 

 



ft 



+ 0-12 



o 



+ 2-0 



+ 0-07 





0-11 



1-8 



•06 



10 



0-08 



1-3 



05 



15 



+ 0-02 



+ 0-4 



+ -01 



20 



-0-05 



-0-8 



- -03 



The height and time of high water can be found from the figure (as in 

 the general case) if we substitute 



Hm + ^1 Rm + ^2 Rm for OM 

 X -\- ^2 Km for the angle x 

 and add the time ^2* to the mean establishment. We can also easily 

 find an approximate value of the largest diurnal tide : — 



Let t be the time of H.W. and h the height of any afternoon tide 

 computed from the mean tide-table. Find?' (= K' — Sun's long. + 

 90^) and subtract it from t converted into angle at the rate of 15^ to 



H' Sin X 



the hour : call the remainder \ : then 

 iin decimals of an hour. 



h 



is the correction to t 



and H' cos \ is the correction to h. 

 The corrections to the morning tide may be taken as the same in 

 amount but of opposite sign. 



