74 Transactions of the Royal Canadian Institute 



at exposed situations where tidal stations are erected for strategic 

 reasons; and if the break cannot be made good, the fine record obtained 

 during the previous summer season may be lost so far as the analysis is 

 concerned ; although this record is usually of service for other purposes, 

 such as comparisons between secondary stations and the principal station 

 during the season. 



After one or two complete years have been analysed and tidal con- 

 stants obtained from them, it is theoretically possible to fill a gap by 

 means of the prediction curves. But it can readily be explained why 

 this method is less desirable than an interpolation based on the actual 

 tide curves, as recorded by the registering instrument. 



Tidal variations and the Harmonic analysis. — There are three leading 

 variations in the tide which accord with the movements of the moon and 

 the sun; firstly, the variation from Springs to Neaps in accord with the 

 moon's phases in the Synodic month; secondly, a more or less marked 

 change in amplitude which accords with the moon's distance during the 

 Anomalistic month; and thirdly, an inequality between the two tides 

 of the day which follows the moon's Declination and only disappears 

 when the moon is on the equator. In regions where the tide is dom- 

 inated by declination, the annual motion of the sun north and south of 

 the equator, has also a great influence ; and the extreme tides of the year 

 consequently occur in the vicinity of the solstices. 



A difficulty which is probably the most serious one in tidal calculation, 

 results from the variation in the range of the moon's declination during 

 a cycle of 19 years. At one extreme of this cycle, the range in declination 

 is from 28° north to 28° south of the equator; while at the other extreme, 

 at the opposite phase of the cycle 9>^ years later, the range is only from 

 18° north to 18° south. Even in other operations, such as the deter- 

 mination of the low-water datum or the comparison of tidal ampli- 

 tudes, the position of the year in the 19-year cycle may have to be taken 

 into account, when the variations that occur are large. 



In the harmonic analysis, the effects of this change in declination 

 can only be allowed for by giving variable values to four of the leading 

 "tidal constants" during the course of the 19-year cycle. But the amount 

 of variation thus allowed at a new locality must be based to begin with 

 upon general theory, and it may be found later to differ considerably from 

 its observed amount; especially in a region where diurnal inequality, 

 due to declination, is the leading feature of the tide. It is evidently 

 undesirable therefore, to introduce prediction curves into the observed 

 series while the variation is under determination ; and it is better to accept 

 breaks or spaces between the complete years submitted to analysis; 

 as these years will fall at various points around the 19-year cycle and 



