A FEW QUESTIONS IN HYDRODYNAMICS. 
99 
ably look for wave motion more or less complete. The case 
worked out by Airy must be subject to the restriction that 
the length of the strait shall not be too short; for, he has em¬ 
ployed the Lagrangian form of the determining equations 
and assigned simple harmonic motions to the individual 
particles. His case also must be subject to the restriction 
that the outside waters be so deep that their horizontal mo¬ 
tions are small. For, suppose but one of the bodies to have 
a tide; the wave in the strait becomes by theory stationary. 
The particles of the strait have their greatest outward elon¬ 
gation—and so have no velocity—at the time of high water. 
Now, if the outer or tided body be so shallow that a wave 
progresses to the shore and has a considerable current velocity, 
this horizontal motion (great at the time of high water) will 
have a profound influence upon the motion in the strait. 
In fact, unless a strait having sufficient shallows at either 
end be exceedingly short and narrow, a partially progressive 
wave through the strait will be the result. 
Other questions concerning periodic motions in straits are 
readily suggested. 
It is hardly necessary to add, in conclusion, that the chief 
aim of this paper has been to point out a few of the tolerably 
definite unanswered questions in hydrodynamics which must 
be investigated before satisfactory progress can be made in 
the theory of tides. 
