32 



THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 



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

 for every Three Degrees of the Moon's Declination. 



It is clear that these sums decrease faster for the large declinations than for the 

 small ones, and the series is tolerably regular with the expression of the number cor- 

 responding to declination 3°, which appears to be affected by some anomaly. If we 

 reject this term, and subtract 629 from each of the terms, we find for 



Declination . . 0° 

 Correction . . 



3° 

 (-191) 



9° 

 -51 



12= 

 -185 



15° 

 -462 



18° 

 —590 



21^ 

 ■945 



24° 

 — 1240 



27° 

 1440 



It will appear that the law may be expressed nearly by — 7300 sin*^ ^, which gives 

 -0 -20 -79 -178 -315 -490 -697 -937 -1207 -1504. 



This agrees pretty well, except for the smaller numbers, which are obviously irre- 

 gular. Hence, if A be the mean declination, we shall have the correction to be applied 

 to the mean sums = 7300 (sin^ A — sin® I) ; and the correction to the single terms 

 will be 304 (sin' A - sin'^). 



If we suppose the mean declination to be 16° 45', as appeared in the correction for 

 the times, 7300 sin* A = 608, and the corrections are. 



