Height of the Tide at the High Waters of the Syzygies.

*This is the high water alluded to in the former note.

THE ANNUAL TIDE.

We have already said in explaining the monthly tides, that the annual movement of the tide in which its curve is seen is traced in Chart No. 2

shewing

1. Two tides, each of six months' duration in which the high waters correspond with the solstices, and the low waters with the equinoxes.

2. The difference in the height of the tides at the solstices and the equinoxes depends on the positions of the sun and moon in their respective orbits.

This can be easily proved by only taking from the foregoing table the data necessary to form the other equivalent, and noting in it the greatest high waters at the equinoxes and solstices.

Difference in height of the High Waters.

In the course of the observations made at the Island of Corregidor, the difference found between the heights of high waters have only

been as follows:

The Diurnal Tide.-From 5 to 8 inches between the tides of the syzygies and the quadratures at the equinoxes.

The Diurnal Tide.-From 2 feet 3 inches to 2ft. 7in., between the same at the solstices.

Mensual Tide. From 0 to 2 inches between the greatest tides at the syzygies of the same lunation at the equinox.

Mensual Tide.-From 8 to 11 inches between the highest tides of the lunation at the solstices.

That found between syzygies of the intermediate lunation is comprehended between these limits.

Annual Tide.-From 2 inches between the tides of both solstices. From 3 to 4 inches between the same at the equinoxes. The greatest difference of level between high and low water has been 9 inches at the equinoxes, and 5ft. 7in. at the solstices.

Mean level. This has fluctuated in the different semilunations of the year between 3ft. 10in. and 4ft. 74in., giving a mean of 4ft. 3.6in. in the scale of the tide guage.

The mean level is found with high and low water of the syzygy by the tide guage, that is, a' being the greatest height, and a the height at lowest tide.

Actual rise and fall.-This is found as in the case of the mean level, the highest tide corresponding to the proximity of the solstice, and the lesser to that of the equinox. The mean gives 2ft. 4.22in.

a + a' — 2 a" The actual rise (x) is determined by the formula x = 4f. in which a and a' represent the two highest consecutive tides, a" the intermediate low water, and f. the factor, which the Nautical Almanack gives for each syzygy.

Hour of the day when the greater High water occurs.

Hitherto we have only treated on the tides to shew the relation between them and the results which we have deduced: nevertheless their consideration not only has led to those results but also to deduce from them the utmost benefit to navigation, and therefore with that object before us we pursue our enquiry into those results. They shew that a second smaller, perhaps insignificant high water, which occurs near the syzygies, is not at first sight recognized, nor has it any application to navigation: therefore without reference to it we shall now only turn our attention to the great diurnal high water, or where there are two high waters in the day nearly equal to the greater of

these.

If we carefully examine the curve of the daily tide in reference to the moon's passage over the meridian of the observer, we shall readily perceive that during the S.W. monsoon, or in the summer, the highest tides happen during the course of the day; while in the N.E. monsoon, or in the winter, they occur during the night. If we would know how this change is produced, we have nothing to do but to refer to the Extract from the observations, and we shall immediately perceive, that, the first change from the evening to the morning* tide is shewn by our observations at 8 h. 45 m. a.m., while the second change is shewn at 8 h. 30 m., the third at 7 h. 45 m., etc. But to

* It is easily seen keeping this change in mind, how the hour of high water goes on delaying; one takes place when the hour of the morning tide comes to be greater than that of the afternoon of that day; and now we have only to attend to the greater tide of the day in which we observe the change of hour.

illustrate this change more clearly we have constructed the following table :

In the foregoing table we see, that, in the course of the year the changes go on progressively accelerating until they gain a day; and in this manner similar phenomena occur in the ensuing year.

In the same manner we can construct another table of the hours when the high waters of the greatest tides occur in the several months of the year.

The reason of high water happening in one monsoon during the day, while in the other it occurs during night, is, that the moon's declina

* The height of the tide in the N.E. monsoon, it will be seen, does not reach that of the equal syzygies in the S.W. monsoon. Besides other leading causes which there may be, it must be observed, that, the N.E. winds and the strong land winds of winter blow out of the bay with considerable strength, and consequently prevent the tide from attaining the height it would do were it not for them.

tion being nearly equal and of distinct kind with reference to the corresponding phases of the moon in both monsoons, it is natural that the effects should also be opposite.

With respect to the gradual change of the tide from one half lunation to the next former it is easily explained by the moon's declination, for it should always pass the equator, and as the change will correspond with the change of the time of passing the meridian on the same day it is easy to see that this passing goes on accelerating (for the orbit of the moon keeps the same position disregarding the change): for instance, if we take two successive lunations, that corresponding to the equinox and the following, we shall see that in the first the moon will be on the equator at the syzygies, and will therefore pass the meridian respectively at noon and midnight: but in the second as the sun has changed and increased his declination, the moon will be on the equator before the syzygies occur and the change will be effected previously. Thus each year should have two changes more than semilunations as really does take place.

It will also be observed that to these same changes the lesser heights correspond to the high waters of the semilunation; and allowing for some small alteration owing doubtless to special causes, it will be seen that an order follows in their absolute height and inverted in the same syzygies of the two distinct monsoons.

ESTABLISHMENT OF THE PORT.

There are two kinds of establishments of the port which we have to analyze in our tidal observations, one is mensual and the other annual. Variation of the mensual establishment. This which means the alteration which the establishment undergoes, in the different days of the lunation, is subject to the ordinary causes of locality; as for instance, the strength of the prevailing wind and that of the tidal current at springs, etc., etc., which never remains constant and equal for every day; although it is found that when the tide is powerful the establishment is then nearly always the same. Thus at the time of the syzygies we may always tell to nearly a minute, the time of high water; while at the quadratures the errors are much greater. In fact it is certain that the course of the tide at this period of the moon places precision out of the question as to the time of high water.

As the spring tide of the new moon, which is that next after the moon, passes the meridian it diminishes to nothing at full moon, and the contrary takes place with the minimum of the new moon; it follows, that, in order to determine the time of high water, two establishments of the port must be used, one of + 9 h. 56 m., and other of 2 h. 21 m. (the mean of those found by our observations ;) keeping before us, that, if one takes the negative sign, that is, the high water is accelerated as the moon passes the upper meridian, it is to avoid the assuming of an establishment equal to the difference of the negative to twenty-four hours, and which would be done to find the time of high water on any required days, it would be necessary to find

the time of the moon's passing the meridian two days before the day on which it is desired to find the height of high water.

The annual variation. This variation which signifies the alteration of the two establishments of the port in the course of the whole lunation is such that with the stations they completely change their sign. Thus, if we analyze the Extract from the observations we shall see that in the S. W. or summer monsoon, the establishment of the port is 9 h. 56 m. from the proximity of the last quarter of the moon until the first quarter of the next lunation; and — 2 h. 21 m. from that epoch to the proximity of the last quarter of the same lunation. In the N.E. monsoon or winter the reverse takes place; the establishment has the negative sign from the proximity of the last quarter to that of the first of the succeeding moon, and positive from this date to that of the last quarter.

However it is clear that if we wish to verify the times of high water of the same day we have only to apply the two establishments, and by this means we shall find the two hours of high water, the heights of which as we have already said will be in relation to the season and the age of the moon.

To show more completely the manner in which this change of establishment is effected, we have only to form the following table analogous to that of the hour of the change of the tides.

By this table we see that the change of signs of the establishment being accelerated each lunation, the time arrives when with the power of both monsoons, at the solstices they have distinct signs for similar syzygies of the moon.

Keeping this table before us we can always with sufficient accuracy find the exact time of the greatest high water, as it is only necessary to have the age of the moon when we require the time of the tide in the desired month, and apply the establishment of the port, positive or negative as noted in the column, not regarding the date of the month given in the table, as this only avails for the year of our observations. We have another means of knowing the class of the establishment