96 
HARRIS. 
of obtaining a solution for a body sufficiently resembling 
the body in question is very great. 
In long-wave motion the depth is assumed to be small in 
comparison w r ith a wave length or with most of the hori¬ 
zontal dimensions. When, however, the relative depth is 
not sufficiently small, the motion is spoken of as ordinary, 
oscillatory, surface, or deep-water waves. Solutions of prob¬ 
lems in wave motion for a vessel of any uniform depth (and 
with vertical side walls) can be obtained from the solutions 
of corresponding problems in long-wave motion,—as was first 
noticed by Poisson and Ostrogradsky. This fact is of great 
importance in making experiments upon waves, because in 
nearly all cases it is convenient, if not absolutely necessary, 
to make use of a body of water whose relative depth is too 
great for the requirements of long-wave motion, and long 
waves are what the experimenter usually wishes to study 
upon a greatly reduced scale. 
When the depth is variable and equal to a considerable 
fraction of a wave length, the question of free oscillation be¬ 
comes much more difficult than for a body of uniform depth ; 
in fact, we now have to find a function satisfying Laplace’s 
equation and the boundary condition, and also to make use 
of a surface condition in determining an admissible period of 
oscillation. But few cases have been worked out. 
Problems of the classes referred to above should admit of 
solutions were the powers of the mathematician adequate to 
the task. But there are important problems which, if capa¬ 
ble of solution at all, certainly involve determining condi¬ 
tions less simple and satisfactory in their character; and, 
strange to say, no person seems to have given them much 
consideration. I refer first and chiefly to a branch of a long¬ 
wave motion, viz., the imperfect free oscillation of a body of 
water but partially surrounded by rigid boundaries. Such 
bodies are certain harbors, bays, and portions of the common 
ocean. Experience tells us that seiches may be found in 
harbors and bays as well as in lakes, and there is evidence 
to show that frequently, if not generally, the tides originate 
