fall do depend. This is the case in some parts of the Pacific, the rise and fall at those places being small.

9. If the tides are tolerably regular, it will not be necessary to observe, except for every five (or ten) minutes near the time of high water and low water-say, for an hour, so as to include the exact time near the middle of the hour. From these observations, by laying down the heights as ordinates, and drawing curves as directed in (6), the height and time of high water and of low water will be deduced.

10. It is desirable to compare the observations of the time of high water and low water with the time of the moon's transit (see 1) while the observations are going on; for if the tide follow this transit at very irregular intervals, the common modes of observation will probably be of no use, and the time and trouble employed in making them will be lost.

11. The time of high water at any place on the day of new or full moon is commonly called the establishment of the place; because, this being established, the time of high water on any other day may, in most cases, be known.

12. But if the tides are very irregular, this is not the case, and then the establishment of the place is of no use, or, rather, there is no proper establishment. And if the tides be regular, the establishment may be got from observations made on other days, just as well as from those made on the day of new or full moon. See Note A.

13. To compare the times of high water with the times of the moon's transit (see 10), we must take the moon's transit from the tables (see 1), and reckon how much the time of high water is after the time of the moon's transit, and put down these intervals, which are called the lunitidal intervals.*

* It is not necessary, for the purposes considered in these directions, to calculate the time of the moon's transit at the place of observation by differences of days. It is sufficient to take the time of the moon's transit at Greenwich, and to add two minutes for every hour of west longitude of the place. For the moon (on the average) moves away

Suppose, for example, that we have obtained (as in 4, 5, or 6) the observations of high water contained in the following table: we add to them the other columns, containing the moon's transit and the lunitidal interval calculated therefrom. The alternate transits are interpolated midway between the others, which are given by the table in the Nautical Almanac. The A.M. transit which happens at Oh. 32m. on the 14th is given in that table as 12h. 32m. P.M. on the 13th, the hour of the table being reckoned from noon in the Nautical Almanac.

In this table, by subtracting [10h. 33m.] the time of the [interpolated] moon's transit from 1h. 7m., or rather from 13h. 7m., the observed time of high water, we get 2h. 24m., the lunitidal interval; and so on for the rest.

14. To see whether the lunitidal intervals follow the regular law, the best way is to put them into a curve, setting off the lunitidal interval belonging to each tide as an ordinate, as in fig. 2.* If the curve drawn through the extremity of the ordinates be tolerably regular, the tides may be presumed to be so.

from the sun so that her distance from the sun is increased 48 minutes in time for every 24 hours, and therefore the transit of the moon is later at every other place by two minutes for every hour.

In actual practice it will be better to draw the figures on a larger scale than those here given.

Fig. 2 represents the lunitidal intervals given in (13).

15. In the observations given in (13) we may see how loose a term the "establishment" is. The 13th is the day of full moon, for in the course of that day the moon is 12 hours from the sun, as appears by the times of her transit. The time of high water on the 13th is— A.M., 2h. 11m.; P.M., 2h. 29m.; and either of these might, in the common use of the term, be called "the establishment."

16. If the lunitidal intervals be set off for a fortnight or more, the curve (14) will descend and ascend alternately every fortnight, as in fig. 3.

This curve is the curve of the semi-mensual inequality; and when this curve has been determined by observations at any place, the hour of high water at any time at that place may be predicted.

17. But the curve will be better determined if, instead of taking for the abscissa the day of the month, as in fig. 2,

we take for the abscissa the time of the moon's transit, as in fig. 3.*

In this case the establishment is the ordinate of this curve which corresponds to the time of moon's transit Oh. or 12h. In the figure it is 2h. 16m.

The mode of calculating the hour of high water on any day, when the establishment of the place is known, is given in Note A.

The establishment of the place may be known by observations made at any age of the moon, as well as by observations at new and full moon, by the same kind of calculation.

18. In order to determine the law of the heights of high water during the period from springs to neaps, we must set off the heights of high water as ordinates, and draw a curve through the extremities. This curve also will ascend and

Since the moon's transit is about 48 minutes later every day, there will be along the abscissa five days of the month for every four hours of moon's transit.

descend every fortnight (ascending at spring tides and descending at neap tides).

The heights may be set off as ordinates, taking for the abscissæ equal intervals to represent successive half-days, as in (16).

But the curve will be better determined if we take for the abscissæ the hour of the moon's transit, as in (17).

19. The maximum or greatest ordinate of this curve of heights (that is, the spring-tide height) follows the day of new and the day of full moon, by one, two, or three days; and as the new or full moon is supposed to produce the spring tide, this interval of one, two, or three days is called the age of the tide.

20. If the heights be set off from an abscissa which is the hour of the moon's transit (see 18), the distance of the maximum ordinate from the hour of transit, Oh. or 12h. (which are the same thing), will give the age of the tide more exactly than the process in (19).

21. The lunitidal intervals and heights of low water may be laid down in curves in the same manner as those of high water.

22. The curve of the semi-mensual inequality of times and heights should be determined, when opportunity allows, for several weeks or months in succession: for from such observations we can obtain other scientific results (the effect of the sun, the effect of the moon's parallax, and the like).

23. Besides the changes which are produced from day to day by the semi-mensual inequality of times and heights, there are at many places other considerable changes produced between the two tides of the same day by the diurnal inequality.

For example, there are many cases in which the height of high water is alternately lower and higher in successive tides.

24. In this case, if we set off the successive heights of high water as ordinates at equal intervals, and draw a