98 
HARRIS. 
are subjects of every-day experience ; but I am not aware of 
any investigation, theoretical or experimental, upon the mo¬ 
tions of the air particles which could be utilized in the ques¬ 
tion now under consideration. 
Another and quite different question of some importance 
and upon which no work appears to have been done may be 
stated as follows: Given a partially enclosed gulf or sea whose 
depth is sufficiently great for enabling the free surface of the 
same body of water were it totally enclosed by land to always 
remain sensibly normal to instantaneous gravity as disturbed 
by the moon and sun; required, the behavior of the partially 
enclosed body when acted upon by these disturbing forces. 
In particular, how large may the openings be and yet not 
cause the fluctuation of the surface in most places to differ 
much from the fluctuation which would exist were the open¬ 
ings to be all closed up ? 
Periodic tidal motion in straits has not received at the 
hands of mathematicians the attention which its importance 
demands. When a strait of small cross-section is so short 
that we can ignore the inertia of the water, we can, under cer¬ 
tain restrictions, apply Torricelli’s theorem, although the 
motion is steady for only a limited time. The narrowest part 
of East River, New York, Seymour Narrows, British Colum¬ 
bia, and Sergius Narrows, Alaska, are examples more or less 
satisfactory. But if the strait have any considerable length 
it will have a wave motion controlled by the bodies which 
it connects. The first question which suggests itself is, How 
long must this small strait be before the inertia of the water 
makes the application of Torricelli’s theorem unsatisfactory, 
assuming for simplicity that the bodies of water which it con¬ 
nects are comparatively deep ? The difficulty here lies, in 
the fact that the orbital motion of a water particle in a short 
strait varies much from its assumed simple, harmonic char¬ 
acter ; that is, the motion of a given particle is very different 
when in the strait than when out of it. If, however, the small 
strait be so long that the orbits of a considerable majority of 
the water particles do not extend beyond its ends, we can prob- 
