37. In tracing the progress of the tide-wave, instead of using the vulgar establishment hitherto spoken of, it is better to use the mean establishment, namely, the mean of all the lunitidal intervals.

For the vulgar establishment is affected by the age of the tide (Art. 20), which the mean establishment is not.

The mean establishment is (say) 10m., 20m., 30m., or 40m. less than the vulgar establishment, according to the age of the tide. (See Note A.)

38. When the tides are regular, good observations, made for a few days or a week at each place, may give the establishment (either vulgar or mean) with sufficient exactness to determine the progress of the tide-wave.

39. But the progress of the tide-wave may be much better determined by means of simultaneous observations, namely, observations made at different places on the same days for a few days or a week.

For such a purpose persons must be posted at different points of the shore or shores where the motion of the tide-wave is to be traced; say 10, or 20, or 40, or 80 miles from each other, as may be convenient. They must observe the tides at these places on the same days, morning and evening, by the methods already described. The times of high water at the different places on each half-day, being compared, will give the progress of the tide-wave.

40. In order to trace the progress of the tide-wave still more widely, the observers described in the last Article, after having made the observations there spoken of, may be removed to new positions of the same kind, and thus trace the tide farther..

When this course is adopted, it will be well to have one (or more) fixed or standard station, at which tide observations are constantly made; and the observations made at any time at any other place may be compared with those made at the standard station.

41. The tides which take place far up deep bays, sounds, and rivers, are later than the tides at the entrance of such inlets, but they are not more irregular; on the contrary, the tides in such situations are often remarkably regular.

42. The progress of the tide-wave up inlets may be determined by the method described in Art. 39.

43. The tide in its progress up inlets and rivers is often much magnified and modified by local circum

stances.

Sometimes it is magnified so that the wave which brings the tide, at one period of its rise advances with an abrupt front of broken water. This is called a bore (as in the Severn, the Garonne, the Amazons River).

Sometimes the tide is divided into two half-day tides in its progress up a river (as in the Forth in Scotland).

In all cases, after a certain point, the tide dies away in ascending a river.

44. The tide observations made at any place, when the times and heights of high water (and of low water) have been deduced in the way directed in Articles 2, 3, 4, 5, 6, may be entered in a table of which the form will be given (Note C), and must then be sent to the Hydrographer's Office in the Admiralty.

45. It is to be remarked that, though there is generally an A.M. and a P.M. tide, there is one day in every half-lunation on which there is only one tide.

(Because the interval of the two tides is, on the average, about 12h. 24m.; so that if there be a tide at 11h. 50m. A.M., there will be no other tide till 12h. 14m. P.M., that is Oh. 14m. A.M. of the next day.)

46. Self-registering tide-machines are used in several places, and may be constructed at no great expense. (They are made by Mr. Newman, of Regent Street, for about 301.: they are constructed so as to work with a tube and float, as described in Art. 3.)

These machines give the whole course of 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 inch of mercury. This may be applied as a correction when very exact observations are made.

APPENDIX.

NOTE (A.)

NOTE TO ARTICLES 17, 19, 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: (this difference is 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 one-third, 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 Art. 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 subtracted from the establishments, according to the hour of the moon's transit on the half-day in question :

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 :—

Hour

h. h. h. h. h. h. h. h. h. h. h. h 2 3

of Moon's Transit..

0

5 6

8

9 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 Art. 37.)

If the tides are observed for a semilunation, or any complete number of semilunations, the mean lunitidal interval, or mean establishment (see Art. 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. (3.) Correction of mean establishment.

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