AND ON THE DIURNAL INEQUALITY. 
9 
Fig. 6. 
M./' 
the result of a sea with considerable tides in some parts, and with spaces of no-tide. 
This may happen by the interference of two different tides ; for instance, if two tide- 
waves differing six hours in the hour of high water arrive at any place, the two tides 
will destroy each other, and there will be no tide. And this may occur in a more 
complex manner. Thus, as Mr. Airy has remarked 
if two equal rectilinear waves, transverse to each other, 
travel across the same ocean, in directions AB and 
AC, the result will be that compound waves will 
travel in the direction AP which makes equal angles 
with the two directions AB and AC. But in this 
case there will be certain lines MN, M'N', parallel to 
AP, along which there will be no tide. And though 
the lines which mark the compound waves may be 
considered as the cotidal lines, these lines will be dis- 
continuous, and the parts outside of the space MN, 
M'N' will be separated by six hours from the parts 
within that space. This example shows also how 
partial and limited cotidal lines may be, and how precarious m.ust be all inferences 
on that subject from a few points to wide oceans. 
23. The complex cases of tides appear at first sight to be interpreted in a different 
manner when we draw complex cotidal lines, as in Article 15, and when we suppose 
a combination of simple undulations, as in the last Article. But this difference of 
interpretation does not necessarily exist, if we conceive the cotidal lines to be mere 
geometrical diagrams, not lines marking the progress of a wave by motions of the 
particles perpendicular to the line of the wave. With this extension of the notion of 
a cotidal line, such lines may still be used to represent, in the first instance, the 
results of tide observations made at a series of places in the same seas ; nor does it 
appear that there can be at present devised any better method of bringing tide ob- 
servations into geographical combination, than this method of drawing cotidal lines. 
The case of the tides of the German ocean, for instance, where the order of the tide- 
hours had led me to draw the cotidal lines as converging to a centre of no-tide (as 
in Article 15), has been differently explained by Mr. AiRy-f'. He conceives that 
these tides arise from the combination of a tide running along the eastern coast of 
England to the south, with a tide coming through the Straits of Dover to the east. 
But the combination of these two tides would, in fact, produce such cotidal lines as 
I have drawn, with a point of no-tide where I had predicted it, and where it was 
found by Capt. Hewett. It is true, that on this supposition the point of no-tide 
would not be a point of rest of the ocean ; nor did I ever suppose that it would be so. 
There is, at the point of no-rise- and-fall of the surface, a considerable stream of tide 
alternately north-east and south-west, as Capt. Hewett found. And the same will 
* Tides and Waves, Art. 367. t Ibid. 526. 
MDCCCXLVIII. C 
