of Edinburgh, Session 1878-79. 97 
Using these in (7) we find that v vanishes throughout if we 
make 
2 com 
a 
• ( 14 ); 
and with this value for l in (12), we find, by (7), 
u = H — c~ l v cos (mx - at) . . . (15) : 
and using (14) and (13) we find 
• ( 16 ), 
from which we infer that the velocity of propagation of waves is 
the same for the same period as in a fixed canal. Thus the 
influence of rotation is confined to the effect of the factor € -2«m/<r.y. 
Many interesting results follow from the interpretation of this 
factor with different particular suppositions as to the relation 
between the period of the oscillation the period of the rota- 
tion (—\ and the time required to travel at the velocity — across 
\oi J m 
the canal. The more approximately nodal character of the tides 
on the north coast of the English Channel than on the south or 
French coast, and of the tides on the west or Irish side of the 
Irish Channel than on the east or English side, is probably to be 
accounted for on the principle represented by this factor, taken 
into account along with frictional resistance, in virtue of which the 
tides of the English Channel may be roughly represented by more 
powerful waves travelling from west to east, combined with less 
powerful waves travelling from east to west, and those of the 
southern part of the Irish Channel by more powerful waves tra- 
velling from south to north combined with less powerful waves 
travelling from north to south. The problem of standing oscillations 
in an endless rotating canal is solved by the following equations — 
h = H {e~ ly cos (mx - at) - e ly (cos mx + at)} \ 
u — H— {e~^ cos (mx — at) + d y cos (mx - at)} > . (17) 
v = 0 
