Prof. A. D. Bache on Tidal Observations. 345 



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crossing the eqnatorj and'are usually most regular and strongly 

 marked when in syzigies^ with declination nearly zero. Follow- 

 ing one set of high and low waters, it will be found that they 

 occur later and later as the lunar day gains on tlie solar, with 

 very remarkable differences, of which the explanation will be 

 given, towards the period of small declinations. The interval 

 from high to low water is generally less by some hours than that 

 from low to high. That as the moon approaches the equator, 

 there are a few days of singular double tides, or of sinele tides, 

 in wrncn the tmies from low to high water are very much in- 

 creased. That when the declination changes its name, a high 

 tide takes nearly the place of a low in time, and vice versa, with 

 an mterval of irregularity, or. in other wordsj the tides are dis- 

 placed by nearly twelve hours. 



2, There is, as Mr. Whewell has remarked, no proper estab- 

 lishment to be derived from such tides; yet we may obtain a de- 

 sirable datum by throwing the results into the form of tables, in 

 which the luni-tidal intervals are arranged according to the days 

 from the zero of declination and the corresponding superior and 

 inferior transits, and for north and south declinations. This will 

 De made more clear by subsequent explanation. These aflbrd a 

 test of the theory of these tides, by showing the displacement 

 of the ordinate of high and low water, and might be used for 

 the inverse purpose of forming prediction tables. Such tables of 

 luni-tidal intervals for three months I now submit. They show 

 considerable steadiness and similarity of intervals towards the 

 niaximum of declinations, and great variations near the zero, and 

 greater discrepancies than is usual in ordinary tides. These are 

 from a series of tables computed by Mr. R. M. Bache for the 

 year, and containing the tunes of high ^nd low water, deduced 

 ifom the daily curves, the readings of the gauge, the rise and fall 

 ^i the t'ldesj the times of the moon's superior and inferior transit, 

 ^"^the moon's declination. 



The intervals serve to show that the high water belongs alter- 

 nately to the superior and inferior transits of the moon, accord- 

 !''>§ as the moon's declination is north or south, with a few 

 cases only which admit of doubt. Two sets of luni-tidal inter- 

 vals were computed (see tables) for three months, to ascertain 

 the proper epoch of reduction (or age of the tide). In one case 

 the intervals were referred to the superior transit of one day be- 

 ^[e, and in the other to the superior transit of two days before. 

 ^ he square of the discrepancy of the mean in the latter case was 

 greater than in the former. An establishment deduced from 

 these numbers for high water without correction would have a 

 probable error, as tried by discrepancy from the mean, of nearly 

 ^'ghty-four minutes. I have little doubt of being able to reduce 

 this error, by computation, much within the limits of observa- 



