SEPTEMBER 4, 1902 | 
NATURE 
445 
the physical conditions are adequately represented in 
this way. 
He desires to find a solution when the period of the 
external disturbing force is the same as that of a free 
standing oscillation of the type of a seiche ina lake. For 
a seiche with-a single central node the length of the tank 
must be equal to half the distance traversed by a long 
wave in the period of the external force. Thus the size 
of the tank is determined by the period of the external 
force and by the depth of the water. ' In the detailed 
treatment of the problem the depth is supposed to be 
uniform. Mr. Harris writes his equation of motion in the 
form of an equation of virtual work; he reverses the 
forces of inertia, adds them to the impressed forces and 
equates the virtual work to zero. Lagrange made the 
displacements arbitrary, and thus his equation of virtual 
work was exactly equivalent to as many differential 
equations of motion as there were variables ; but Mr. 
Harris takes the displacements as proportional to the 
actual displacements per unit time and obtains a single 
equation. This is permissible, but the result cannot be 
anything but an equation of energy. I am unable to see 
any advantage in this procedure. He then assumes 
that the type of oscillation will be the same as in free 
oscillations, but this is surely a quite unwarrantable 
assumption. If the periodic forces have the same period 
as the free oscillation the oscillations will be large, but 
the type will in general be different. Does not this error 
vitiate his whole treatment of the problem? -.However, 
let us proceed. The type and period being the same as 
those of a free oscillation in the absence of friction, the 
periodic sustaining forces must’ exactly balance . the 
frictions, and the frictional forces are proportional to the 
velocities. Now the motion being ofthe same type as in 
a free oscillation, the displacements are all simple har- 
monic functions of the time, and at any instant are all in 
the same phase. Hence the frictional forces, and there- 
fore also the sustaining forces, are all in a phase differing 
from that of the displacements by a quarter period. 
Thus all the sustaining forces vanish at the instant 
when the displacement is a maximum, and we get nothing 
out of the equation of virtual work but what was put into 
it by dubious assumptions.! 
_ Asa result of this discussion the following rule (p. 621) 
is given :— 
“Project the force arrow” (of a number of tidal-force 
diagrams giving the direction and magnitude of the 
forces at various parts of the basin at successive hours) 
“belonging to the assumed time in each diagram upon 
the line of motion passing through it; the aggregate of 
the elementary masses, each tultiplied by the intensity 
of the tidal force in the direction of the displacement, 
and again by a quantity proportional to the value of the 
maximum displacement (since the oscillation is harmonic), 
must be zero at the time of high and low water. The 
algebraic sum of these products for any given hour 
should be plotted as an ordinate at that hour. Where 
the curve thus constructed crosses the time axis denotes 
the time of high and low water.” 
Besides the objection to the proposition raised above 
in the case of the canal of uniform depth with synchro- 
nous disturbing force, I fail to see any adequate con- 
sideration of the variability of depth, of the absence of 
synchronism in the component disturbing force in the 
direction of the canal, or of the effects of the component 
transverse to the canal. 
But even if it were possible to assent to this rule, it 
appears to me that there are other still more doubtful 
assumptions. On p. 624 we read :— 
“ Considering the actual distribution of land and water, 
1 A considerable portion of this criticism is due to Prof. Love, with whom 
I have had the advantage of discussing the matter. He points out, further, 
that Mr. Harris's equation (308), p. 619, which forms the key-note of the 
whole, is really identically satisfied by the ; ssumptions. 
NO. 1714, VOL. 66] 
| 
a few computations upon hypothetical cases will suffice 
to convince one that as a rule the ocean tides, as we 
know them, are so great that they can be produced only 
by successive actions of the tidal forces upon oscillatory 
systems, each having, as free period, approximately the 
period of the forces, and each perfect enough to pre- 
serve the general character of its motion during several 
such periods were the forces to cease their action. This 
greatly simplifies matters. . . .” Undoubtedly the sim- 
plification is great, but is it true? 
Then later :—“ The paths of the particles being practi- 
cally fixed and determined by the boundary conditions, 
it becomes possible to disregard the forces arising from 
the earth’s rotation.” 
Now Lord Kelvin has concluded that “the oscillations 
of water in a rotating rectangular trough are not of the 
simple harmonic type in respect to form, and the problem 
of finding them remains unsolved” (PAz/. Mag., vol. x., 
1880, p. 113). He has, however, solved the case of a 
rotating endless canal with straight sides, and adduces 
his results as probably dominating some remarkable 
characteristics of the tides of the English Channel. It 
seems to follow that either Lord Kelvin or Mr. Harris is 
wrong. j 
I gather that the free period of oscillation in the 
several basins into which the ocean is partitioned is the 
same as that of the tidal force. Now it is surely pro- 
foundly improbable that any large portion of our curiously 
shaped oceans should possess even approximately the 
critical free period, yet unless this is so the theory 
seems to be inapplicable. Finally, I think that the pro- 
cess of partition should receive an elaborate and critical 
discussion as to each basin; but I do not find that this is 
given in the book. 
I can, in conclusion, only express a hope that I am not 
doing an injustice to Mr. Harris in dissenting so abso- 
lutely from his views. No one would have welcomed 
more warmly than I a new clue to our treatment of this 
difficult problem. I venture to express my admiration at 
the courage of the attempt, and although, as I think, it is 
a failure, yet it may inspire others to more successful 
attacks. G. H. DARWIN. 
NOTES. 
Tue hundredth anniversary of the birth of Abel, the great 
Norwegian geometrician, is on the point of being celebrated 
at Christiania. Representative men of science from many 
countries are expected to be present. The interest which His 
Majesty King Oscar II. has manifested in this centenary cele- 
bration is another proof of his continued sympathy with mathe- 
matical work and scientific research generally. It is announced 
that the Paris Academy of Sciences will be represented by 
M. Darboux and the Paris University by M. Emile Picard. 
Ir is announced in Scéence that at a recent meeting of the 
| corporation of the Marine Biological Laboratory at, Woods 
Holl it was voted to transfer the Laboratory and its equipment 
to the Carnegie Institution.: This action was taken after it had 
been stated to the members of the corporation that the executive 
committee of the Carnegie Institution would recommend to the 
trustees that the Laboratory should be accepted, that its debts 
should be paid, that new buildings should be erected, that 
20,000 dollars a year should be allowed for maintenance and 
that the scientific management should rest as heretofore with the 
naturalists of the United States. 
Tue Cape Town correspondent of the 7zes states that great 
interest is being manifested there in the suggested visit of the 
3ritish Association in 1905. As a preliminary measure, free 
passes on all the South African railways are promised for the 
