LAWS OF THE TIDES FROM SHORT SERIES OF OBSERVATIONS. 237 



II. How does a change of the epoch affect the semimenstrual inequalities P 



The moon's transit takes place every half-day about twenty-four minutes later by 

 solar time. The semimenstrual inequality, both of interval and of height, is referred to 

 the solar time of the moon's transit. The height is the same whether it be referred to 

 the transit E immediately preceding, or to the transit B, which is a day and a half 

 sooner. Also if the moon moved uniformly in her orbit, the inequality of the interval 

 of the tide and the transit would be the same, whether the tide were referred to 

 the transit E, or to any anterior one, as B ; for the interval is increased by a constant 

 quantity (twelve hours twenty-four minutes) for every transit that we go back. But 

 though the inequality of the interval for any given tide would be the same, it would 

 not occupy the same place in the table or curve, since it would be referred to a dif- 

 ferent hour of transit. For example, if the mean interval of transit and tide at Bristol, 

 referred to transit E, be 7^ and if when the moon's transit is 2^", the tide be at 8^, 

 the interval is 6^ and therefore in this case the inequality is minus one hour. If now^ 

 we refer this tide to the transit B, a day and a half sooner, the interval of the transit 

 and tide will be 6^ -f- 36^ + 72", and the mean interval will be 7^ + 36^ + 72°^ ; and 

 therefore, as before, the inequality is minus one hour. But the moon's transit E 

 taking place at 2^ solar time, the transits D, C, B will take place at 1^ 36"^, l'' 12'", 

 Qh 4gm respectively, and therefore the inequality of minus one hour, which was referred 

 to the transit happening at 2^ when transit E was used, is referred to the transit at 

 Qh 48"^, when we employ the anterior epoch B. 



We thus see, that by referring to an anterior epoch, the whole semimenstrual in- 

 equality is moved backwards through twenty-four minutes of lunar transit, for every 

 step of one transit backwards. This is the mean result ; supposing the moon's 

 motion to be uniform, and neglecting all other inequalities ; on which suppositions 

 nothing would be gained or lost in accuracy by the change of epoch. In the actual 

 case we shall find this mean result modified by the influence of the other inequali- 

 ties, which make one transit a better epoch than another. 



The transfer of the semimenstrual inequality curve which we are thus led to expect 

 on changing the epoch, shows itself in the results of the Bristol observations. For 

 example, the time of transit for which the semimenstrual inequality of the interval is 

 0, being taken for the three transits A, B, C, we find 



For A. For B. For C. 



In 1834, 6^' 4™ ; 6^ 28™ ; 6^^ 52"'. 

 In 1835, 5^^ SS'"; 6'' 22'" ; 7^ 4'". 



Again, for the semimenstrual inequality of heights we find that the mininmm height 

 corresponds to the following hours of moon's transit: 



For A. For B. For C. 



' In 1834, 5^ 30"; 5^' 54™ ; 6^24™. 

 In 1835, 5^29™; 5*^46™; G*" 18™. 



