Researches on the Tides.--Fourteenth Series. On the Results of Continued Tide Observations at Several Places on the British Coasts

XI. Researches on the Tides.—Fourteenth Series. On the Results of continued Tide Observations at several places on the British Coasts. By the Rev. W. Whewell, D.D., F.R.S. Received October 24, 1849.—Read January 31, 1850. TIDE observations made at several different parts of the British and the neighbouring shores, and in some instances continued for a considerable period, have been discussed by Mr. D. Ross of the Hydrographer's Office, with great labour and perseverance; and as the results which his labours afford may be of use to mariners, I offer to the Royal Society a brief statement of these results. The discussions at present referred to relate to the height of high water, and the variations which this height undergoes in proceeding from springs to neaps and from neaps to springs. It is found, by examining the observations at 120 places and throwing the heights into curves, that the curve is very nearly of the same form at all these places. Hence the semimensual series of heights at any place affords a rule for the series of heights at all other places where the difference of spring height and neap height is the same. For instance, Portsmouth, where the difference of spring height and neap height is 2 feet 8 inches, is a rule for Cork, Waterford, Inverness, Bantry, Boucoul on the French coast, and other places. And the Tables of the height of high water at one of these places suffice for all the others, a constant being of course added or subtracted according to the position of the zero-point from which the heights at each place are measured. The series of heights of high water for a semi-lunation also agrees very exactly, as to the form of the curve, with the equilibrium theory. The following construction gives this curve. With centre C and radius CA (half the difference of the height at spring and neaps), describe a circle; and in AC produced take CD to CA as 12 to 5. Divide the circumference of the circle into twelve hours, representing the twelve hours of moon's transit; and join D with each of these divisions. The lines thus drawn to the hours will give the heights of high water for each hour of the moon's transit; a constant quantity being, as before stated, added or subtracted in order to refer the height to the proper zero. According to the theory, the $0^h$ or $12^h$ hour-points would be at A; the ratio of DC to AC would be that of the lunar to the solar tide; and the distances of the hour-points from D would be the heights of high water above mean water. But all these properties are, in the actual cases, modified in a manner which must be noticed. The tides in these discussions are not referred to the transit of the moon immediately preceding, but to some earlier transit, namely, the second, third, fourth or fifth preceding transit; it being found that in this way the accordance with the theory becomes more exact. Thus in the British Channel the tides are referred to the third preceding transit; and this extends also to Ireland and to the west coast of England and Scotland. On the east coast of England, in the northern parts, as at Shields, Sunderland, Scarborough and Hull, the fourth preceding transit is used; at Harwich, Sheerness and London, the fifth (see Table B). But this reference to an earlier transit does not make the highest tide correspond exactly with the hour of transit $0^h$ or $12^h$: and it is found, in the cases which have been included in the present examination, that a displacement of the $0^h$ point about fifteen minutes from A will best make the theoretical and the observed curves agree with each other. The ratio of DC to AC is, as has been said, 12 to 5; and this, according to the theory, would be the ratio of the lunar to the solar tide. If this were the case, the spring tide measured above mean water would be 17, and the total spring tide above spring tide low water would be 34. The neap tide in this case would be 7 above mean water, and therefore 24 above spring tide low water. Hence the difference of springs and neaps would be to the height of neaps above low water springs as 10 to 24, a ratio constant for all places. But in fact, this ratio of the excess of springs to the total height of neaps above low water springs is different at different places; and the observations now under consideration show in some measure the law of this difference. The ratio is smaller when the tide is smaller. This appears from the observations at different places, as arranged by Mr. Ross in the annexed Table A. We have there the following results, taking the means of groups of places according to the amount of tide. | Number of places | Mean neap tide above spring low water | Mean excess of spring high water above neap | Ratio | |------------------|--------------------------------------|------------------------------------------|-------| | 37 | ft. in. | ft. in. | | | | 9 3 | 2 5 | 38 : 10 | | 40 | 12 0 | 3 8 | 33 : 10 | | 39 | 17 10 | 5 9 | 31 : 10 | | 4 | 27 0 | 9 8 | 28 : 10 | Where it appears that the actual ratio approaches to the theoretical ratio in proportion as the amount of tide increases. If the ratio just spoken of were constant, we should be able to find the height of mean water by knowing the excess of springs above neaps: the excess being 10, the mean water would be 7 below the neap high water. But it appears that in general the mean water is lower than this: and the excess of springs being 10, the mean water is from 14 to 19 below neap high water at various points on the coast of Great Britain and France. In consequence of the law of the high waters, given alike by the theory and by the observations, the spring high waters are above the mean high water for a longer period than the neaps are below it. For it is evident that if DE and DF be each equal to DC, the heights are greater than the mean DC through the arc EAF, which is greater than a semicircle. And it is evident that the excess of AE above a quadrant will be an arc of which the sine is $\frac{1}{2} \frac{EC}{DC}$ or $\frac{5}{24}$; or $12^\circ$ nearly. Hence the two portions of the semicircle will be, in time, $3^h 24^m$ and $2^h 38^m$; and the tides will be above the mean during $6^h 48^m$ of lunar transit, and below the mean during $5^h 12^m$; and this is found to be very nearly the case at all the places examined; thus confirming the identity of the rule of different places one with another, and with the construction given above. Additional Note on the Tides of the Bristol Channel. Mr. Ross has traced the modification which the semimensual inequality of heights undergoes in ascending the Bristol Channel from Pembroke to Bristol. This modification is shown in the accompanying figure. It appears from the diagram which Mr. Ross has drawn from the observations, that the difference of springs and neaps increases gradually from Pembroke to Llanelly, Weston, Cardiff, and finally Bristol, the difference being 5 ft. 6 in. at the first place, and 10 ft. 6 in. at the last; and the curve which represents the change from day to day being at all the places of the same form, namely, of the form described in the preceding paper. W. W. Trinity College, Cambridge, Nov. 3, 1849. Table A.—Results of Tide Observations arranged according to the amount of excess of Springs above Neaps. Table B.—Places along the same coasts arranged in the order of their "Establishment." ## OBSERVATIONS AT SEVERAL PLACES ON THE BRITISH COASTS. ### Table A. | Number of observations from which curves were formed | "Establishment" of the port | Mean spring rise above mean low water spring | Mean neap rise above mean low water spring | Excess of spring over neap | |-----------------------------------------------------|-----------------------------|---------------------------------------------|------------------------------------------|---------------------------| | 128 | Ardrishaig | h m ft. in. ft. in. ft. in. ft. in. | | | | 704 | Lowestoft | 12 0 9 2 8 7 0 7 | | | | 673 | Belfast | 9 57 6 6 5 4 1 2 | | Third preceding transit. | | 375 | Greenock | 10 43 9 5 8 1 1 4 | | Third preceding transit. | | 107 | Ayr Harbour | 12 8 9 9 8 2 1 7 | | | | 418 | Harwich | 12 10 8 9 7 2 1 7 | | Fifth preceding transit. | | 595 | Donaghadee | 0 6 11 6 9 9 1 9 | | | | 218 | Crookhaven | 11 13 11 3 9 5 1 10 | | | | 190 | Baltimore | 4 9 9 10 8 0 1 10 | | | | 144 | Courtmaesherry | 4 23 10 2 8 3 1 11 | | | | 233 | Skull | 4 36 10 8 8 7 2 1 | | | | 1,059 | Kingstown | 4 2 9 8 7 7 2 1 | | | | 209 | Castletown | 11 10 11 0 8 10 2 2 | | Third preceding transit. | | 351 | Peterhead | 4 14 9 10 7 7 2 3 | | | | 130 | Bantry Harbour | 0 34 10 9 8 6 2 3 | | | | 90 | Arcachon, France | 3 47 10 2 7 8 2 6 | | | | 77 | Boucnot, France | 4 37 11 8 9 2 2 6 | | | | 123 | Dunmore | 3 39 8 8 6 1 2 7 | | | | 4,230 | Portsmouth | 5 27 12 3 9 8 2 7 | | | | 373 | Portsmouth | 11 41 12 8 10 0 2 8 | | Third preceding transit. | | 51 | Cork | 5 1 11 9 9 1 2 8 | | Third preceding transit. | | 299 | Castletownsend | 4 21 10 9 8 1 2 8 | | | | 193 | Waterford | 6 6 13 5 10 9 2 8 | | | | 171 | Inverness | 12 18 12 2 9 6 2 8 | | | | 522 | Kinsale | 4 43 11 7 8 9 2 10 | | | | 377 | Sligo | 6 0 8 8 5 9 2 11 | | | | 1,383 | Sheephaven | 5 25 11 11 9 0 2 11 | | | | 124 | Ramsgate | 11 41 15 6 12 7 2 11 | | | | 4,233 | Bordeaux, France | 6 50 14 1 11 2 2 11 | | Fifth preceding transit. | | 105 | Sheerness | 0 37 16 1 13 1 3 0 | | | | 69 | Loch Inver | 6 41 13 11 10 11 3 0 | | | | 446 | East Looe | 5 26 16 2 13 2 3 0 | | | | 76 | Inishbofin | 5 5 12 10 9 9 3 1 | | | | 692 | Omonville, France | 7 29 15 6 12 5 3 1 | | | | 92 | Westport | 4 57 12 8 9 6 3 2 | | | | 103 | Peel, Isle of Man | 11 8 16 3 13 1 3 2 | | | | 156 | Caernarvon | 9 33 13 9 10 7 3 2 | | | | 183 | Port Navallo, France | 3 42 12 11 9 9 3 2 | | | | 79 | Tobermorey | 5 36 12 10 9 7 3 3 | | | | 125 | Ramsay, Isle of Man | 11 12 19 3 16 0 3 3 | | | | 125 | Royan, France | 3 38 13 3 10 0 3 3 | | | | 86 | St. Surin, France | 4 11 14 3 11 0 3 3 | | | | 277 | Roundstone | 4 28 13 6 10 2 3 4 | | | | 117 | Goodick Pier | 6 56 11 7 8 3 3 4 | | | | 937 | Dundee | 2 32 14 7 11 3 3 4 | | | | 13,400 | Patiras, France | 5 10 15 6 12 2 3 4 | | | | 705 | London | 1 59 19 6 16 1 3 5 | | Fifth preceding transit. | | 541 | Sunderland | 3 22 14 5 11 0 3 5 | | Fourth preceding transit. | | 236 | Holyhead | 10 11 16 0 12 7 3 5 | | Third preceding transit. | | 356 | Foynes Island, Shannon | 5 35 15 5 12 0 3 5 | | | | 821 | Scarborough | 4 11 15 10 12 5 3 5 | | Fourth preceding transit. | | 688 | Hartlepool | 3 28 15 0 11 7 3 5 | | Fourth preceding transit. | | 148 | Granton Pier | 2 20 16 0 12 7 3 5 | | Fourth preceding transit. | | 159 | North Shields | 3 30 13 8 10 3 3 5 | | Fourth preceding transit. | | 2,820 | Socoa, France | 3 19 12 3 8 10 3 5 | | Fourth preceding transit. | | 2,823 | Dunkirk, France | 12 8 16 10 13 5 3 5 | | Fourth preceding transit. | | 2,820 | Devonport | 5 43 15 5 11 11 3 6 | | Fourth preceding transit. | | 2,823 | Leith | 2 17 16 4 12 9 3 7 | | Fourth preceding transit. | | 299 | Barfleur, France | 8 51 17 0 13 5 3 7 | | Fourth preceding transit. | | 155 | Concarneau, France | 3 12 13 1 9 6 3 7 | | Fourth preceding transit. | | 154 | Port Louis, France | 3 11 13 1 9 5 3 8 | | Fourth preceding transit. | | Number of observations from which curves were formed | "Establishment" of the port | Mean spring rise above mean low water spring | Mean neap rise above mean low water spring | Excess of spring over neap | |-----------------------------------------------------|-----------------------------|--------------------------------------------|------------------------------------------|---------------------------| | 104 | Cordouan Lighthouse, France | h m ft. in. ft. in. ft. in. ft. in. | | | | 3 37 | 13 10 | 10 2 | 3 8 | | | 437 | Thurso | 8 27 | 13 3 | 9 6 | 3 9 | | 134 | Melville, France | 9 36 | 21 1 | 17 4 | 3 9 | | 107 | La Hougue, France | 8 42 | 18 5 | 14 7 | 3 10 | | 66 | Aberystwyth | 7 31 | 13 5 | 9 7 | 3 10 | | 684 | Galway | 4 35 | 14 10 | 10 11 | 3 11 | | 164 | Belleisle, France | 3 18 | 14 3 | 10 4 | 3 11 | | 147 | Calais, France | 11 49 | 19 6 | 15 7 | 3 11 | | 121 | Ile d'Yeu | 3 6 | 14 2 | 10 2 | 4 0 | | 125 | Pwllheli | 7 46 | 13 8 | 9 8 | 4 0 | | 1,207 | Great Grimsby | 5 36 | 19 2 | 15 1 | 4 1 | | 153 | Limerick, Shannon | 6 20 | 16 10 | 12 8 | 4 2 | | 194 | Tarbert Island, Shannon | 4 57 | 14 6 | 10 4 | 4 2 | | 259 | Cherbourg, France | 7 49 | 16 11 | 12 9 | 4 2 | | 134 | Havre, France | 9 51 | 22 1 | 17 11 | 4 2 | | 2,116 | Dover | 11 12 | 18 8 | 14 5 | 4 3 | | 170 | Aix Island, France | 3 20 | 16 11 | 12 8 | 4 3 | | 174 | St. Nazaire, France | 3 40 | 15 2 | 10 11 | 4 3 | | 154 | Beagh Castle, Shannon | 5 49 | 17 6 | 13 2 | 4 4 | | 157 | Mellon, Shannon | 6 1 | 18 3 | 13 10 | 4 5 | | 115 | Port en Bessin, France | 8 57 | 19 11 | 15 6 | 4 5 | | 703 | Hull | 6 29 | 20 10 | 16 4 | 4 6 | | 118 | Alderney | 6 46 | 17 4 | 12 10 | 4 6 | | 258 | Douglas, Isle of Man | 11 12 | 20 8 | 16 1 | 4 7 | | 156 | Noirmoutier Island, France | 3 2 | 15 11 | 11 4 | 4 7 | | 129 | Goury, France | 7 6 | 21 11 | 17 3 | 4 8 | | 153 | Cape Grisnez, France | 11 27 | 21 6 | 16 9 | 4 9 | | 223 | Tarn Point | 11 22 | 23 1 | 18 1 | 5 0 | | 213 | Whitehaven | 11 14 | 23 3 | 18 2 | 5 1 | | 138 | Beaumaris | 10 32 | 21 5 | 16 4 | 5 1 | | 132 | Fécamp, France | 10 44 | 23 3 | 18 1 | 5 2 | | 513 | Brest, France | 3 47 | 19 1 | 13 10 | 5 3 | | 62 | Honfleur, France | 9 29 | 23 4 | 18 1 | 5 3 | | 13,400 | Liverpool | 11 16 | 25 7 | 20 3 | 5 4 | | 135 | Boulogne, France | 11 25 | 24 10 | 19 5 | 5 5 | | 74 | Sein Island, France | 3 21 | 17 6 | 12 1 | 5 5 | | 4,236 | Pembroke | 6 12 | 21 0 | 15 6 | 5 6 | | 74 | Ushant | 3 32 | 19 4 | 13 9 | 5 7 | | 143 | Pontasval, France | 4 26 | 22 4 | 16 8 | 5 8 | | 305 | Roscoff, France | 4 46 | 23 1 | 17 4 | 5 9 | | 175 | Poulton-le-Sands | 11 26 | 27 3 | 21 6 | 5 9 | | 149 | Ploumarach, France | 5 15 | 24 3 | 18 5 | 5 10 | | 176 | Abervrach, France | 4 14 | 21 9 | 15 10 | 5 11 | | 184 | Morlaix Roads, France | 4 53 | 23 9 | 17 10 | 5 11 | | 122 | St. Ives | 4 44 | 21 0 | 15 1 | 5 11 | | 72 | Ifracombe | 5 42 | 27 4 | 21 4 | 6 0 | | 221 | Dieppe | 11 6 | 27 0 | 20 8 | 6 4 | | 303 | Fleetwood | 11 12 | 26 3 | 19 8 | 6 7 | | 292 | Port des Enfans, France | 5 17 | 25 5 | 18 10 | 6 7 | | 117 | Cayeux, France | 11 5 | 27 6 | 20 11 | 6 7 | | 391 | Brelat, France | 5 51 | 31 2 | 23 7 | 7 7 | | 81 | Lezardrieux, France | 5 54 | 30 3 | 22 2 | 8 1 | | 119 | Jersey | 6 15 | 29 9 | 21 5 | 8 4 | | 370 | Weston-super-Mare | 6 54 | 37 3 | 28 9 | 8 6 | | 129 | Erecuh | 6 32 | 30 11 | 22 5 | 8 6 | | 139 | Erqui | 5 59 | 33 3 | 24 5 | 8 10 | | 153 | St. Malo, France | 6 5 | 35 0 | 25 10 | 9 2 | | 277 | Chausey, France | 6 9 | 35 2 | 25 10 | 9 4 | | 294 | Granville, France | 6 13 | 37 1 | 27 2 | 9 11 | | 138 | Portishead | 7 11 | 41 4 | 31 1 | 10 3 | Third preceding transit. ### Table B. | From the Land's End to Ramsgate | Establishment | From Bantry Bay up St. George's Channel round the North of Ireland to the Shannon | Establishment | |---------------------------------|---------------|--------------------------------------------------------------------------------|---------------| | **East Looe** | 5 26 | **Bantry Harbour** | 3 47 | | Devonport (4th transit?) | 5 43 | **Castletown (Berehaven)** | 4 14 | | Portsmouth (3rd transit) | 11 41 | **Skull** | 4 2 | | Dover (3) | 11 12 | **Crookhaven** | 4 9 | | Ramsgate | 11 41 | **Baltimore** | 4 23 | | **From the Land's End up St. George's Channel round the North of Scotland to London** | | **Castletownsend** | 4 21 | | St. Ives | 4 44 | **Courtmaesherry** | 4 36 | | Ilfracombe | 5 42 | **Kinsale** | 4 43 | | Weston-super-Mare (3) | 6 54 | **Cork (3)** | 5 1 | | Portishead | 7 11 | **Dunmore** | 5 27 | | Pembroke (3) | 6 12 | **Waterford** | 6 6 | | Goodick Pier | 6 56 | **Kingstown (3)** | 11 10 | | Aberystwyth | 7 31 | **Donaghadee** | 11 13 | | Pwllheli | 7 46 | **Belfast (3)** | 10 43 | | Caernarvon | 9 33 | **Sheephaven** | 5 25 | | Holyhead | 10 11 | **Sligo (3)** | 6 0 | | Beaumaris | 10 32 | **Westport** | 4 57 | | Liverpool (3) | 11 16 | **Inishbofin** | 5 5 | | Fleetwood | 11 12 | **Roundstone** | 4 28 | | Tarn Point | 11 22 | **Galway (3)** | 4 35 | | Poulton-le-Sands | 11 26 | **Tarbert, Shannon** | 4 57 | | Peel, Isle of Man | 11 8 | **Foynes Island, Shannon** | 5 35 | | Douglas, Isle of Man | 11 12 | **Beagh Castle, Shannon** | 5 49 | | Ramsay, Isle of Man | 11 12 | **Mallon, Shannon** | 6 1 | | Whitehaven | 11 14 | **Limerick, Shannon** | 6 20 | | Ayr | 12 10 | **Inverness** | | | Greenock (3) | 12 8 | **Peterhead** | | | Thurso (3) | 8 27 | **Dundee** | | | Inverness | 12 18 | **Granton (4)** | | | Peterhead | 0 34 | **Leith** | | | Dundee | 2 32 | **North Shields (4)** | | | From Arcachon in the Bay of Biscay to Dunkirk | Establishment | |---------------------------------------------|---------------| | **Arcachon** | 4 37 | | Bordeaux | 6 50 | | St. Surin | 4 11 | | Royan | 3 38 | | Cordouan | 3 27 | | Ile d'Aix | 3 20 | | Ile d'Yeu | 3 6 | | Noirmoutier Island | 3 2 | | St. Nazaire | 3 40 | | Belleisle | 3 18 | | Port Louis | 3 11 | | Concarneau | 3 12 | | Brest (3) | 3 47 | | Ushant | 3 32 | | Morlaix Roads | 4 53 | | Brehat | 5 51 | | Erqui | 5 59 | | St. Malo | 6 5 | | Granville | 6 13 | | Chausey | 6 9 | | Jersey | 6 15 | | Ecrehou | 6 32 | | Alderney | 6 46 | | Cherbourg | 7 49 | | Barfleur | 8 51 | | La Hougue | 8 42 | | Honfleur | 9 29 | | Havre | 9 51 | | Fécamp | 10 44 | | Dieppe | 11 6 | | Cayeux | 11 5 | | Boulogne | 11 25 | | Cape Grisnez | 11 27 | | Calais | 11 49 | | Dunkirk | 12 8 | For the places not otherwise marked in these Tables, the tides were referred to the transit immediately preceding, as giving sufficient exactness for general maritime purposes: but observations received at the Admiralty since the above laws were discovered, have been referred to the third, fourth, or fifth preceding transit, according to their place in Table B. The Devonport tides discussed some years ago, apart from those of neighbouring places, appeared to give the greatest exactness with the fourth preceding transit, which has accordingly been used in the Admiralty Tables. There can be no doubt at present that the third preceding transit is more correct for this port; but the labour of recalculating new Tables would be great, and the difference of the result would never be more than one minute in the time and one inch in the height. MDCCCL.