rise and fall of the tide; and record several successive tides on the same paper.*

47. The wind often produces a considerable effect upon the tides, especially upon the height, and should be noted, although it is difficult to give any general rule for the effect.

48. The surface of the sea rises and falls as the barometer falls and rises: namely, about 1 inch for every o inch of mercury. This may be applied as a correction when very exact observations are made.†

* Of tide-gauges, one of the most elaborate and successful is that invented by Mr. Bunt, and described in the 'Phil. Trans.' for 1838. It is also described by the Astronomer Royal in the article Tides and Waves' of the Encyclopædia Metropolitana.' Tide-gauges are constructed by Mr. Newman, of Regent-street, London, at an expense of about 301.

† Naval officers will be in a better condition to judge of the value of carefully made observations in bringing to perfection the theory of the tides, after reading the practical part of the invaluable article by the Astronomer Royal in the Ency. Metrop.' before referred to. References are there made to the researches of Dr. Whewell and Sir John Lubbock, printed in the Phil. Trans.' Sir John Lubbock's researches are contained chiefly in the Phil. Trans.' for 1831 and 1833, while those of Dr. Whewell, consisting of fourteen distinct memoirs, extend from the year 1833 to 1850. In the Phil. Trans.' for 1845 is a very valuable paper, by the Astronomer Royal, on the Laws of the Tides on the Coasts of Ireland;' and in the volumes for 1848 and 1851 are two papers by the late Admiral Beechey on the Tides in the Irish Sea and the North Sea and English Channel respectively. Some valuable observations on the Tides in the North Sea, by the late lamented Captain Hewett, will be found in the Report of the eleventh meeting of the British Association.-(R. M.)

APPENDIX.

NOTE (A.)

NOTE TO 12, 17, 36, and 37.

To find the Hour of High Water on any day, at any place, when the Establishment of the place is known.

THE rule is different (as to amount) according to the tidal force of the sun; for though the tidal force of the sun in theory is the same at all places, it is found by observation to be different at different places.

This difference appears in the different ratio of the rise of springtides to the rise of neap-tides (the semimensual inequality of heights). In general the rise of spring-tide above mean water is about double that of neap-tide, which gives the solar tide one-third of the lunar tide. But in some cases the spring-tide exceeds the neap-tide only by onethird, which gives the solar tide only one-seventh of the lunar tide.

Also the difference of the greatest and least lunitidal intervals (that is, the semimensual inequality of times: see 13 and 16) shows the difference of the solar tidal force at different places. The difference of the greatest and least intervals is 1 h. 28 m. at London and Liverpool, but at Plymouth it is 1 h. 36 m., and at Portsmouth 1 h. 21 m. On the coast of North America it is generally less than 1 h. 20 m., while at some places on the coasts of France and Ireland it is above 2 h. We may take 1 h. 28 m. as the mean value of this difference, which agrees with the supposition that the solar tide is about one-third the lunar tide.

In finding the hour of high water on any day when the vulgar establishment is known, the rule will also be different according to the age of the tide. We shall give the rule when the tide is a day and a quarter old, and also when the tide is two days and a half old. In general, the tides will be between these limits.

(1.) Tide a day and a quarter old. Minutes to be added to or sub

tracted from the establishments, according to the hour of the moon's transit on the half-day in question :

Hour of the Moon's
Transit after Sun.

Correction of the vulgar Establishment to find the Lunitidal Interval....

m. m. m. m. m. m. m. m. m. m. m. m. 0-16-32-47-57-60-47-16+15+28+25+15

For example-if the establishment be 2 h. 27 m., at what hour will the high water come after a moon's transit which takes place at 4 h. A.M.? The minutes to be added to 2 h. 27 m. for 4 h. transit are, by the table,- 57 m., that is, 57 m. to be subtracted; therefore the high water will be at 1 h. 30 m. after the moon's transit, that is, at 5 h. 30 m.

(2.) Tide two days and a half old :—

Correction of the Establishment

m. m. m. m.

m. m. m. m. m. m. m. m. 0-15-31-47-62-72-75-62-31 0 +13+10

This table is to be used in the same way as the other. Hence we see that the age of the tide most affects the lunitidal interval when the time of moon's transit is between 7 and 8 hours.*

The mean lunitidal interval, or mean establishment, is 16 minutes less than the former, and 31 minutes less than the latter (vulgar) establishment supposed in the above tables. (See 37.)

If the tides are observed for a semilunation, or any complete number of semilunations, the mean lunitidal interval, or mean establishment (see 37), will be found by taking the mean of all the lunitidal intervals observed.

The lunitidal interval corresponding to any given distance of the moon from the sun may be found by the following table. But the tide corresponding to the given distance may not really occur till one, two, or three days later, according to the age of the tide.

• Hence it is desirable to make tide observations in the first and fourth quarters of the moon, rather than in the second and third quarters.

G

(3.) Correction of mean establishment.

Hour of Moon's Transit)

(1, 2, 3 days preceding)

Corresponding Correc

tion of Mean Lunitidal Interval.

m.

3

5

m.

m.

m. m. m. m. m. m. m. m. m. 0-16-31-41-44-31 0+31 +44 +41 +31 +16

This table may be used when we know the age of the tide. Thus let the age of the tide be a day and a quarter, and the mean lunitidal interval 2 h. 11 m.; let the moon's transit take place at 4 h.; then at the birth of the tide, a day and a quarter earlier, the transit took place at 3h.; therefore the correction of the lunitidal interval is, by the table, 41 m., and the interval so corrected is 1 h. 30 m., which, added to 4 h., the time of moon's transit, gives 5 h. 30 m. as the time of high

water.

To find the Establishment at any place when the Hour of High Water on a given day is observed.

On the given day the time of moon's transit is known, and hence the lunitidal interval; and, by the above tables, the correction by which this differs from the establishment is known.

Thus, if high water occur at 5 o'clock when the time of moon's transit is 3h., the lunitidal interval is 2 h.; and the correction (if the first table be applicable) is 47 m.; hence the establishment is 2 h. 47 m.

NOTE (B).

NOTE TO 25 AND 28.

The Rule of the Diurnal Inequality.

THE Diurnal Inequality depends upon the moon's declination, as has been said already. It increases from 0 up to its maximum, and decreases to 0 again, as the declination does so; following these changes at an interval of one, two, or three days, according to the age of the tide. The rule is expressed in this way :

For north declination of moon,

Add to the tide following moon's south transit;

Subtract from the tide following moon's north transit.

For south declination of moon,

Subtract from the tide following moon's south transit;

Add to the tide following moon's north transit.

The south transit is the superior transit in the northern hemisphere, and the north transit the inferior. The contrary is the case in the southern hemisphere.

(Fixed scale in open water?
Tube with float?

Self-registering gauge?

Mode of deducing H.W. and L.W.(Mere looking?

Ordinates every 5 m. near max.?

The general progress of the tide-wave (35) along even the most frequented shores is still imperfectly known; and about the connexion of the tides over the general areas of large oceans we are as yet entirely in the dark; there is therefore an ample field of important and useful discovery in this subject, even by means of brief and scattered series of observations; still more is this the case if simultaneous or connected observations can be made, such as are described in 39 and 40.

The main general features of the progress of the tides, as hitherto ascertained, are the following:

The tide-wave which brings the tides to the coasts of Europe comes from the Atlantic, and brings high water to the western coast of Spain and Portugal about 2 hours after the moon's transit; to the western coast of France about 3 hours; to the western coast of Ireland and to