ON THE HYDRODYNAMICAL THEORY OF SEICHES. 611 
by Du Boys, entitled “Essai Théorique sur les Seiches” (Arch. d. Sc. Phys. et Nat. 
Genéve, t. xxv., June 15, 1891). In this paper he reproduces the well-known theory 
for a lake of uniform depth and section. Then, by a confessedly inexact application of 
‘the theory of progressive waves (‘‘onde solitaire de translation”), he arrives at the 
formula T, = (2/v) i dl/,/(gh), to which we have already referred. Dv Boys’ theory gives, 
for reasons explained elsewhere,* a good approximation in certain cases for 'T,, and 
also for the position of the uninode, but it gives no account of the incommensurability 
M@uenerseiche periods (it would give T,:T,:T,:.... = 1:1/2:1/8:.... in all 
eases); nor does it lead to a correct determination of the binodes. Moreover, no good 
reason can be given for the fact that in order to get a good approximation for T, we 
must integrate along the line of greatest depth, instead of using Ketianp’s formula t 
for the wave velocity, and putting T, =2 | dl,/(b/ag), where b is the surface breadth, 
and a the area of the cross section. Nevertheless Du Boys’ work was a notable initial 
step in a difficult investigation. 
§ 19. In an address, an abstract of which was published in IJ Nuovo Cimento, 4, 
yol. vill. p. 270, 1898, VoLTERRa, at the instigation of Forex, pointed out the great 
interest of the phenomena of seiches from a physico-mathematical point of view; and 
promised to develop a mathematical theory in a separate paper. It is, however, 
impossible to gather the exact nature of his views from the brief abstract referred to ; 
and his promised memoir has not, so far as I can learn, yet appeared. 
At a meeting of the Royal Society of Edinburgh on 16th February 1903, I gave, 
at the request of Sir Joun Murray, and chiefly for the sake of his Lake Surveyors, a 
similar address, in which I stated most of the general principles above enunciated on 
the strength of approximative calculations, which I have since replaced by the more 
rigorous and more effective methods of the present paper. During this address, Mr E. 
Maciacan-WeEDDERBURN demonstrated the uninodal and binodal standing waves in a 
long rectangular trough by means of the following elegant apparatus devised by 
himself. 
CP is a long rectangular trough, in which there is a fixed partition, D, pierced at 
the bottom, dividing C P into a small and a large compartment, with a communication 
at the bottom of moderate size. E is a movable partition, by means of which the 
longer part of the trough can be shortened at will. A strong spiral spring, 8, suitably 
supported and weighted with a heavy ball, B, to give sufficient inertia, is used to make 
4 plunger execute a vertical simple harmonic motion, of period T, in the compartment 
CD. So long as DE is not adjusted so that the period of the standing wave in that 
part of the trough is T or a multiple of T, the forced oscillations in DE attain no 
particular magnitude; but when E is so adjusted that the periods are very nearly 
equal, or the one double the other, a large standing wave is set up, which can be 
Maintained for any length of time by giving properly timed impulses to B. In this 
* See Proc, R.S.E., vol. xxv. p. 646 ; also § 49 below. + Trans, Roy. Soc. Edin., xiv. p. 524, 1839. 
