238 THE REV. W. WHEWELL ON THE DETERMINATION OF THE 



The maximum height corresponds to the following hours of moon's transit 



We may observe, that if we could find an epoch which should make the results ex- 

 actly correspond with the theory, the semimenstrual inequality of the time would be 

 0'' for the time of transit 6'^; and the height would have its maximum and minimum 

 values for the times of transit 6^ and 12''. From the above results it follows, by an 

 easy calculation, that the epoch which makes the inequality in time agree with the 

 theory is about the transit A ; and the epoch which makes the inequality of heights 

 agree with the theory is about four hours after the transit B. We have therefore 

 here still clearer evidence, of that which the discussion of the Liverpool tides by 

 Mr. Lubbock sufficiently showed, that there is no one anterior epoch which will reduce 

 the observed tides to an agreement with the equilibrium theory. 



III. How does a change of the epoch affect the {lunar) parallax correction of the time P 



The parallax corrections of the times, calculated with different epochs, have a 

 general agreement with each other, and with the theory. Taking the correction for 

 parallax 60' as our example, it has a maximum and a minimum which correspond to 

 transits differing only about three hours from each other ; so that the inequality in- 

 creases from its minimum to its maximum through about nine hours of transit, and 

 then diminishes more rapidly from the maximum to the minimum through three 

 hours. In this all the empirical curves and the theoretical curve agree. But in 

 general the empirical curves differ in two respects from the theoretical one ; first, 

 according to theory, the transit which gives the maximum and that which gives the 

 minimum are equally distant from 6^ ; one being as much before as the other after 

 that period ; whereas in the observation, this mean point corresponds to 6^^ or 7^' 

 transit ; and secondly, the empirical correction contains, besides the variable part, a 

 constant part which depends on the parallax, but does not vary with the hour of transit. 

 This I had already noticed in the second series of these Researches*. 



It follows from what is there stated, that while theory gives the formula -f- 



(P — p) {h sin 2 (p), 

 observation gives such a formula as 



(P-^) (a + ^sin2(^-/3)). 



But the quantity a as well as |8, changes with the epochs as Mr. Lubbock has justly 

 observed ; and the question occurs, whether we can, by a proper assumption of the 

 epoch, cause the quantity a to disappear, and thus render the curve which represents 

 the observed law symmetrical with regard to the axis, as the theoretical curve is. 



* Philosophical Transactions, 1834, p. 40. 



t Here P is the parallax, p the mean parallax, the hour of moon's transit, |3 a time depending on the epoch. 



