ON THE TIDES OF THE FRITH OF FORTH. 111 
those published formerly in the Transactions being on a similar plan, but in 
this case it had been more fully carried out, and found of greater importance 
than in former cases. This plan was to carry on simultaneously at the places 
examined, a series of continuous observations every five minutes night and 
day, by successive observers, without intermission, for the period of a month, 
or of several months, as might be required. Printed forms were sent to all 
the stations, and in them the observer simply noted down every five minutes 
the height of the tide on a graduated scale placed before him. Every day 
at noon all these papers were sent by post to the central station, and im- 
mediately on their arrival the papers of the different stations were compared 
and their observations laid down on paper, so as to give a graphical repre- 
sentation to the eye of all the observations, by means of which they were at once 
verified and compared with great facility ; and accuracy of observation was 
by this means made very certain, as carelessness or incorrectness in the ob- 
servations was at once manifest to the eye. 
These tide-waves were represented to the eye in the following way. A 
horizontal line is divided into equal parts, which represent time or hours, 
thus,—VI, VII, VIII, IX, X, XI, XU, I, &c.; and these spaces are again 
subdivided into twelfth parts of an hour; a scale of feet is placed vertically, 
and numbered 1, 2, 3, 4, 5, &c.; then the observations are taken, and if 
is found that at VI o'clock the water stood at 0, and then was low water ; 
at VII the water had risen to 1 foot, and a mark is made one foot high above 
the hour VII ; at VIII a mark is made at the corresponding height of 23 feet ; 
at IX a mark is placed above it to the corresponding height. When this 
has been done for every hour and also for every five minutes, these points 
form a line, which exhibits the form of the tide-wave as it passed that station 
on the day of observation; in this way are laid down on the same paper all 
the observations of the same day at the different stations. : 
From the examination of the form of these tide-waves thus laid down, cer- 
tain characters of the tide-wave peculiar to each locality had been discovered. 
As in the former observations of the Clyde and the Dee, so in this series it had 
been found that the form and dimensions of a channel produce important: 
changes on the form of the tide-wave. Where the sea was deep and the shore 
open and abrupt, the tide-wave was symmetrical, and of the form predicted 
by Laplace, when he says that in rising and falling the water covers in equal 
times equal arcs of a vertical circle. This is the form of the ocean tide-waye ; 
but on approaching a shallow shore and travelling along a shelving coast, the 
tide-wave undergoes two changes; its summit hecomes displaced forwards 
in time, its horizontal chords become dislocated, and the wave ceases to be 
symmetrical. This peculiar dislocation and displacement are characteristic 
of a littoral tide, and in the case of running streams, the currents still further 
affect the tide-wave, and give to it a peculiar distortion characteristic of flu- 
vial tides. To these were further added the exaggeration and elevation of the 
tide by means of narrow channels, All these phenomena were fully proved 
by the present series of observations. : 
The author also considers it to have been fully established, by the obser- 
vations on the Frith of Forth, that there exists on the eastern coast satisfac- 
tory evidence of the presence of a second tide-wave in that part of the German 
Ocean, and that the southern tide-wave, a day older than the northern tide- 
wave, sensibly affects the phenomena of that part of the coast. To this he 
attributes the double tides of the Frith of Forth, the nature of which he fully 
explained. Regarding these double tides various theories had been formed ; 
and there were various ways in which such tides might happen, whenever 
tide-waves arrive by different paths in different times. But this kind of double 
