ON TEMPERATURE OBSERVATIONS IN LOCH EARN. 647 
where wu is a function depending on the contour of the lake and the horizontal 
displacement of the water particles. 
Equation (4) may then be written as follows, after substituting for ¢’, and ¢, from 
equations (3’) and (3) 
ae Os = oo. = seis 
wis el 
e (ale } - #(A,(a)Ey} 
yg M506 (a) tr} (at re XC as) : : : : (7). 
But, as we are assuming that the motion is irrotational, we must have 
PAs) HAW} AAS) HAR Bw 
0{{6',(x)da}?  o{[B(w)da}? of {B(w)dax}? Of [b,(a)dx}? ev? 
when A’,(x) and A,(x) are the laminee adjacent on either side of boundary, B(«) is the 
breadth of A’,(~) and A,(x) at the boundary and v = {B(x)dx 
We may, therefore, neglecting quantities of the second order, write equation (7) in 
the following form :— 
@u ( SR’,A’,(z) 2B, A, (2 Cine 
EL Reet ape f —Ipgat See) + BeBe} 8) 
or 
Ou _ {2p’,}',(a) + 3B,,b, (ar) } au (10) 
we ISR’ nA ,(x)/A'(x)? + 2R,,A,(%)/A(x)? ov? ; 
= go(v)a : ; : (11), 
which is the same in form as the equation arrived at in our preliminary discussion, and 
as before, we find that the theory depends on the differential equation 
Ge, wb 
dv? * go(v) 
where u= =P sin n(t —T) : , : : (13), 
(12), 
and where P is a function of v alone and 7 is constant. Thus the methods used by 
Professor Curysrat,* in his discussion of the ordinary seiche, are available here also. 
For the evaluation of the periods of oscillation possible in any lake with a known 
density distribution we must proceed to evaluate o(v) at a number of positions. This 
See (as 1 2R,An(x 
Mar “hte sey ay 
error in making this assumption is small, as R,, and R’, are in nature always near unity, 
and it is only where their differences are concerned that we need take them into 
consideration. 
* “The Hydrodynamical Theory of Seiches,” Trans. Roy. Soc, Edin., xli. (iii.) p. 599. 
may be greatly simplified by assuming 
