OF THE TIDES IN THE PORT OF LONDON. 



27 



will therefore express, with considerable accuracy, the general course and average 

 values of the numbers in Mr. Lubbock's Table XIX. 



But if the correction, instead of being applied to the mean value of the interval (of 

 tide and transit), had been applied to the interval calculated for declination 0, it is 

 clear the correction would have been 



{132 + 84 sin 2 ((p — 4'') } sin' I. 



Mr. Lubbock has given other tables also, from which the mean correction for 

 lunar declination may be collected. His Table XV., which contains the differences 

 of the intervals of the time of moon's transit and high water from the mean interval, 

 arranged according to the calendar months and to times of the moon's transit, is in 

 fact principally a table of the correction for lunar declination. For by examination 

 of that table, it will be seen that the correction in each month goes through its cycle 

 of 0, 4-j 0, •— , in one semirevolution of the moon ; that is, while the declination passes 

 from its maximum north, to its maximum south, value : and since these results are the 

 mean of nineteen years, the moon will have been nearly as much on the north as on 

 the south of the ecliptic, and the result will be nearly the same as if she had moved 

 in the ecliptic. It may be observed, however, that it appears by what has been shown 

 above, that the corrections increase faster than the declinations ; and therefore the 

 corrections due to the high declinations will not be quite balanced by those due to 

 the declinations which correspond to an equal opposite celestial latitude. 



It is to be noticed, also, that this Table XV., being arranged for calendar months, 

 contains the effect of solar declination and parallax as well as of lunar declination. 

 It also contains the effect of the equation of time ; the times of the moon's transit 

 being given in mean solar time, whereas we suppose the tide to depend on the hour- 

 angle of the moon from the sun, that is, on the transit in true solar time. These 

 effects may be eliminated, and the effect of the changes of lunar declination upon the 

 tide-hour may be determined from this table in an approximate manner ; but the accu- 

 racy of such a determination is necessarily less than that of the one already obtained, 

 and I shall therefore not insert it here. 



5. The Solar Correction. — The sums of the positive and of the negative numbers in 

 each vertical column of Mr. Lubbock's Table XV. would be equal, if the inequality 

 depended on the moon alone, since each column contains the corrections which occur 

 in a half-revolution of the moon. Therefore the difference of these sums is due to a 

 solar inequality, and the mean excess or defect must be subtracted or added in order 

 to obtain the corrections due to the moon. These means are as follow : 



E 2 



