34 THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 



We may make a remark with respect to Mr. Lubbock's Tables for the heights, 

 similar to one we made with respect to those for the times. Table XVI., which gives 

 the differences of height for each hour of the moon's transit in the different calendar 

 months, is in reality composed mainly of the effects of the moon's declination. In 

 order to obtain these effects from the Table, we should have to eliminate the effects of 

 the sun (including the effects of the equation of time). By this means we should ob- 

 tain a result agreeing in part with that which we have obtained from Table XX. ; but 

 the accuracy of this result would necessarily be less than of that already obtained, and 

 I shall omit it. 



5. The Solar Correction of the Heights. — If we take the means of each month in 

 Table XVI., we have the sun's effect on the heights in that month. These are as fol- 

 low: 



This, like the solar correction for the time, passes from positive to negative, and from 

 negative to positive, four times in the course of the year, but has its maxima and 

 minima of unequal magnitude, and at unequal intervals. Hence we may, as in the 

 case of the times, express it by m sin 2 {0 — (ji>) -\- n sin (^ — v), where is the sun's lon- 

 gitude ; and we may account for this form by considering that the former term is the 

 eifect of declination, and the latter term the effect of parallax. To this is to be added 

 the effect of the equation of time, in order to obtain the whole of the solar correction. 



Recapitulation. — Hence it appears that the result of the London Dock observations, 

 which we have now examined, may be expressed in the following manner. 



If X' be the corrected establishment, S' the semimenstrual inequality of the time of 

 high water, P' the correction for lunar parallax, Q' the correction for lunar declination, 

 Q the solar correction, and if <p be the mean time of the moon's transit, we have for 

 the time of high water 



^ + ^' + S'H-P'+Q'-l-Q. 



In this expression it has appeared that 



« c»/ A sin 2 ((S — «) h' .^ ^, 



^^^^^= h' + kcoslif-uy T=^'^^^^'' « = 2hours. 



P' = (P ~ p) {B -f B sin2 (^ - (3)} ; B = S-" ; |3 = 1 hour. 

 Q' = (sin2 A - sin^) {C + Dsin2 (<p - y)} ; 



A = 16° 45', C = 132™, D = 84^", y = 4 hours. 

 Q = m sin 2 (ip — ^) + n sin (<p — */), 



w, n being small, and their determination here omitted. 



In like manner, if / be the height of the mean high water, s' the semimenstrual 

 change, /?' the correction due to lunar parallax, q' the correction due to lunar decli- 

 nation, q the solar correction, the height of high water is 



l+s'+p' + q' + q. 



