line through their extremities (as directed in 18), this line will have a zigzag form, as in fig. 4. Heights H. W. Fig. 4. Height H. W. Jan. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. The width of the zigzag increases from nothing to a maximum, and then diminishes to nothing again, generally in the course of a fortnight; and so on perpetually. 25. In consequence of the diurnal inequality, it sometimes happens that the afternoon tides are higher than the forenoon tides, or the reverse, for many weeks together. And hence it has sometimes been stated as a Rule at such places that the afternoon tides are always the highest, or the reverse. But this is not the Rule. If the afternoon tides are the highest at one time of the year, they are the lowest at another. The Rule of the diurnal inequality depends on the moon's declination, and will be given in Note B. 26. There is often a diurnal inequality of the height of low water, and at some places it is greater than the diurnal inequality of high water (as at Sincapore, and at Port Essington in Australia). 27. Also there is often a diurnal inequality in the times. When this is the case, if we set off the lunitidal intervals as ordinates (see 14), the line drawn through their extremities will have a zigzag form, like that of the heights in fig. 4. 28. When this is the case, we cannot determine the esta blishment (see 17) without making allowance for the diurnal inequality. We make allowance for the diurnal inequality by drawing a curve, cutting off from the zigzags equal portions above and below. (See fig. 4). This mean line will be of a wavy form in consequence of the semi-mensual inequality; and the ordinate corresponding to the new or full moon, or to the hour 0 or 12 of moon's transit, will give the establishment. But if we apply this establishment to predict the time of tide on any day, we must also apply the diurnal inequality predicted according to its rule. (See 25, and Note B.) 29. The diurnal inequality sometimes becomes so large that there is only one tide in 24 hours (and then we have single day tides). But this does not generally happen through a whole lunation; it happens only for a few days in each semi-lunation; and at other times there are two tides as usual. Cases of one tide in 24 hours should be particularly observed, making the observations every half-hour, or, if possible, oftener-say every 5 minutes. 30. In some places the tide rises and falls four times in the 24 hours. The cases where this occurs are to be particularly observed. They may be observed, as in (29), by making observations every half-hour, 10 minutes, or 5 minutes. These may be called double half-day tides. 31. Where double half-day tides exist, they do not commonly extend over any considerable length of coast. If there be time and opportunity, it will be well to examine, by observation, how far they do extend. But if the object be to determine the laws of the tides in a larger area, it is better to make the observations out of the region of these anomalies. 32. It is well to observe the direction of the stream of flood and of ebb, and the time at which the stream turns. We must take care not to confound the time of the turn of the tide-stream with the time of high water. Mistakes and errors have often been produced in tide observations by supposing that the turn of the tide-stream is the time of high water. But this is not so. The turn of the stream generally takes place at a different time from high water, except at the head of a bay or creek. The stream of flood commonly runs for some time, often for hours, after the time of high water. In the same way, the stream of ebb runs for some time after low water. 33. The time at which the stream turns is often different at different distances from the shore; but the time of high water is not necessarily different at these points. The time of slack water is. not wanted for a theory of tides, though its knowledge is otherwise of considerable importance to the seaman. With regard to the streams of flow and ebb, they are often not merely two streams in opposite directions at different times of the tide; they generally turn successively into several directions, so as to go quite round the compass in one complete tide, either in the direction N., E., S., W. (with the sun), or N., W., S., E. (against the sun). It is desirable to note which of these ways the tidestream goes round, as this fact may help to determine which side the tide-wave comes from. 34. One important object to be answered by means of tide observations is to trace the progress of the tide from one place to another. This may be done in some measure by determining the establishments of a series of places in the region which we have to consider. For these establishments, reduced to Greenwich time by allowing for the longitude, give the time at which the tide is at each place, and hence its progress. 35. The progress of the tide may be conceived as the progress of a very wide wave which brings the high water to each place in succession. But the motion of this tide-wave is not that motion of the water which makes the stream of flood. Nor does the motion of the wave coincide with any motion of the parts of the water. The tide-wave may be going one way when the water is going another, as happens in some rivers when the tide is travelling upwards in them. 36. The establishment, which is wanted in order to determine one progress of the tide-wave (see 34 and 35), may be known from observations made at any age of the moon, as well as at new or full moon. (See 17 and Note A.) 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 (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 tidewave 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 (39), 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 (39). 43. The tide in its progress up inlets and rivers is often much magnified and modified by local circumstances. 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 Amazon). 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 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 halflunation 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 constructed so as to work with a tube and float, as described in (3). These machines give the whole course of |