610 PROFESSOR CHRYSTAL 
weight at the middle. The result is to lengthen the periods of the binodal, 
quadrinodal, etc. modes, but to leave unaltered the periods of the trinodal, quin- 
quinodal, ete. modes. Hence, if we start with a lake of uniform depth, and diminish 
its depth a little in the middle, the result will be to lengthen the periods of the 
uninodal, trinodal, etc. seiches, and to leave the periods of the binodal, quadrinodal, 
etc. seiches unaltered. One consequence of this is, that in the modified lake the 
period of the binodal seiche is less than half the period of the uninodal. This accords 
with what we have said before, since the lake is now convex. Similarly, by diminishing 
the density in the middle of the string, we get an explanation of the corresponding 
peculiarity of concave lakes. 
A slight modification of Merupr’s experiment will give us another illustration of 
the use of this acoustic analogy. Fix a tuning-fork with its prongs horizontal, so 
that it vibrates in a vertical plane. If we stretch a fine string vertically upwards from 
a point of attachment on one of the prongs, then, with the proper length and tension, 
when the fork is excited it will vibrate steadily with a beautifully sharp node in the 
middle, its lower ventral point being at a distance of about one-fourth of the length 
from the lower end. If a very small pellet of beeswax be fixed on the string at a 
distance of about one-eighth of its length from the lower end, it will be found, after 
slightly adjusting the tension, if necessary, so as to re-establish full resonance, that the 
string will vibrate with one node as before; but that node and also the lower ventral 
point will be nearer the lower end than before.* Hence, if we start with a lake of 
uniform depth, the nodes of the binodal seiche will be each at a distance of one-fourth 
of the length from its respective end; but if we make a shallow at one end, say about 
one-eighth of the length of the lake from that end, the corresponding node will be 
displaced towards the shallow. A depression of the lake bottom would, of course, 
have the opposite effect. 
In a similar way, we can see that an irregularity of the lake bottom will seriously 
disturb the seiches that have nodes there, while it may affect very little those seiches 
which have ventral points there. This suggests a very natural explanation why, of 
the many theoretically possible seiches for any given lake, we may find traces of only 
a limited number on the limnogram. To this point I shall return when we come to 
consider special lakes in detail, and the causes which may excite the seiches observed 
in them. 
A very important practical conclusion suggested by the acoustic analogy is that, 
while the boundary conditions at the end of the lake may seriously affect seiches of 
higher nodality, they have comparatively little influence on the seiches of lower nodality, 
in particular on the uninodal and binodal seiches. 
§ 18. So far as I am aware, the only serious attempt hitherto made to submit seiche 
phenomena in detail to mathematical calculation is contained in an interesting paper 
* With a Koenig’s fork (256 Ut,), 140 em. of No. 30 thread, which weighs 00058 gm. per cm., and a tension of 
45 gm., 2°5 mg. of wax produced a displacement of the ventral point exceeding 8 em. 
