30 



THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 



It appears from the nature of the still residual differences, that we might bring our 

 formula still nearer to observation ; but as the differences do not exceed -rVth of a foot, 

 except in one instance, this exactness would be, in the present state of our knowledge, 

 superfluous. 



Hence the mean height in feet of the tide at London Dock is represented by 



21-1 + 17 cos (2<p— 51°) -f -23— -23 sin (4^ — 30°), 

 or 21-33 + 17 cos (2^-51°) — '23 sin (4 <p - 30°) 

 where <p is the hour-angle of the moon's transit, mean time. " 



3. Correction of the Heights for Lunar Parallax. — Table XVIII. of Mr. Lubbock 

 contains the effect of variations of the moon's distance. 



Table showing the Difference in the Height of High Water, and the Mean Height 

 for every Minute of the Moon's Horizontal Parallax. 



If we take the means of the vertical columns, they are, in hundredths of feet. 



Horizontal parallax 54' 

 Means —47 



55' 

 -33 



56' 

 — 18 



57' 

 + 7 



58' 

 + •20 



59' 

 + 37 



60' 



+47 



61' 

 + 67 



These are very nearly as the differences of the parallax. We shall find that the for- 

 mula \'7 {p- P) when;? is the parallax, and P is 57', will very nearly give this re- 

 sult. It gives, in fact, 



-51 -34 -17 +17 +34 +51 +68 



