DR. HAROLD JEFFREYS ON TIDAL FRICTION IN SHALLOW SEAS. 
245 
on the other. The two side-pieces are the Gulf of Siam and the Java Sea. The data 
for it are obtained from the ‘ China Sea Pilot,’ volumes 3 and 4, except the depths, 
which are taken from the Admiralty Charts. The tides are affected by a large diurnal 
inequality due to the inclination of the Equator to the ecliptic. When the moon is 
north of the Equator it tends to raise two tidal protuberances in the ocean, one 
exactly below it and the other exactly opposite to it. Owing to the earth’s rotation 
each of these moves round the earth once a day, keeping the same distance north or 
south of the Equator. Thus if a place is not on the Equator, they pass at different 
distances from it, so that the two tides in the lunar day are unequal in height. 
The variation in the level of the water thus caused can be described as a semi-diurnal 
change, on which a diurnal change is superposed. 
Now the rate of travel of a tidal wave is practically independent of its period, but 
if the depth and the form of the coast are such that the waves starting from the north 
and south sides of the Equator take different times to reach the place of observation, 
their combined effect may be remarkable. In particular, if the wave from the south 
arrives a quarter of a lunar day after or before the other, the semi-diurnal part of the 
one wave will correspond to high water while that of the other corresponds to low 
water, and if the amplitudes are equal the two will neutralize each other. In other 
words, there will be a node of the semi-diurnal tide. The diurnal parts, however, will 
not neutralize each other, their phases being only a quarter of a period apart. Thus 
at such a place there will be a diurnal tide and no semi-diurnal tide. Several places 
are known where there is only one high water in each lunar day; among them are 
parts of the South China Sea, the Gulf of Carpentaria, and Bering Sea. The tides in 
these require special discussion before they can be considered in the present problem, 
because the diurnal tide depends essentially on the inclination of the Equator to the 
plane of the moon’s orbit and would not exist if this were zero. The dissipation of 
energy in it must therefore arise from the motion of the moon in declination and not 
in right ascension, and will affect mainly the inclinations of the Equator and the 
moon’s orbit to the ecliptic, while producing little effect on the earth’s rotation and 
the motion of the moon in longitude. In discussing the secular acceleration of 
the moon it can therefore be ignored. If observations of the diurnal tide in the 
places where there are two high waters in the day were more numerous it might be 
possible to determine the dissipation in it, and from it the secular changes in the 
inclinations, but at present this is impossible. 
In the Java Sea, between Borneo and Java, the tide is mainly diurnal; in fact 
according to the ‘ Eastern Archipelago Pilot,’ part 3, the semi-diurnal tide is not 
appreciable on the north coast of Java till east of Surabaya, which is itself almost at 
the eastern end. On the south coast of Borneo the observations are not so numerous, 
but it seems clear that there also the tide is mainly or entirely diurnal. The tidal 
currents are described as weak. We can accordingly neglect the dissipation in the 
Java Sea. At its western end this sea is connected to the South China Sea by two 
