LAWS OP THE TIDES FROM SHORT SERIES OF OBSERVATIONS. 239 



This question our discussion of the Bristol tides enables us to answer. For if we take 

 the parallax correction for 60', for the year 1834, and for the transit A, we find that 

 it has a maximum 16™ at 5^^ transit ; a minimum = 1°* at 71*" transit. Hence it may 

 be represented by 8 J™ — 7^^ . 5, 2 <p — 13^ where s, 2 (p represents a function of 2 (p, 

 which differs from sin 2 (p in having its maximum and minimum at a smaller distance 

 than six hours (2^ hours in this case), the distance depending on some other quan- 

 tity* ; but which, like sin 2 <p, is when (p is 0, + when <p is less than 6^, — when p is 

 greater than 6*"; and has for its maximum and minimum values + 1 and — 1, at 

 equal distances from the value 2 <p = 0. 



In the same manner we may reduce to formulae of the same kind the parallax cor- 

 rections for the other transits. And putting them together we have the following 

 results. 



mm h 



Year 1834. Transit A. 8j — 7i • ^, 2 (p — 13 



Transit B. lOf -- 12J .5, 2 ^ - 14 



Transit C. S^ — 7i . ^, 2 (p — 14 

 Year 1835. Transit A. 9^ - 7i . ^, 2 ^ — 13J 



Transit B. 8J — lOJ . *, 2 9 — 14 



Transit C. 2^ — 9§ . *, 2 9 - 14 



These results show, that by taking a later transit the quantity a is diminished, al- 

 though irregularly ; and therefore the epoch which would reduce the correction to 

 the symmetry of theory is later than C ; but we cannot pretend to say with precision 

 how much, without further calculation. We may observe that the circumstance of 

 the coefficients of the variable part being largest for the transit B, appears to indicate 

 that the discussion relative to that transit is the best-conditioned for bringing into 

 view the parallax inequality. 



The results of the Bristol observations for 1836 and 1837, discussed for transit B, 

 give, for the parallax correction of the times, 



for 1836, 6"" -f- 9°^.^, 2(p— 14^; . 

 for 1837, 1 1'" + 12°» . *, 2 <p — 13^ 



The Plymouth observations for 1834, 1835, 1836, 1837, referred to the transit B, 

 give a parallax correction, which follows nearly the same laws as those just stated for 

 Bristol. It has a maximum of 22°^ at 5^, and a minimum of — 3™ at 9^. Hence its 

 formula is (for 61' parallax) 



9i'» — 12§°^ .s,2(p - 14^ 



which agrees very nearly with the Bristol formula for transit B. 



IV. How does a change of the epoch affect the (lunar) declination correction of the 

 times P 



* The expression :; ^. ^ ox is an instance of such an expression, the maximum and miniTnum 



1 4- c cos 2 (^ — /3) ^ 



being equally distant from the value = /3, and each of these distances depending upon the value of c. 



