(7.8231) 
XXXII.—Calculation of the Periods and Nodes of Lochs Earn and Treig, from the 
Bathymetric Data of the Scottish Lake Survey. By Professor Chrystal and 
Ernest Maclagan-Wedderburn, M.A. (With Two Maps.) 
(Read July 17, 1905, Issued separately November 7, 1905.) 
§ 1. In a paper* published in the present volume of the Zransactions of the 
Society (p. 659, 3rd July 1905), one of the authors of this communication has given 
a Hydrodynamical Theory of Seiches, and deduced formule with a view to particular 
applications. The object of the present paper is to give some account of a series of 
calculations on which we have been occupied for some time, with a view to work out, 
a prior, from the Bathymetric Data of the Lake Survey, the Seiche Constants for the 
three seiches of lowest nodality in Lochs Earn and Treig. 
§ 2. As this is the first time that any attempt has been made to solve completely 
a problem of the kind, we naturally selected lakes having as simple a configuration as 
possible. A general idea of the shape of the two lakes, and also of the nature of the 
data from which we have worked, will be obtained from the 3-in. maps reproduced 
in figures (3) and (4). 
The numbers on the maps indicate the depths in feet. They are mostly arranged 
in lines (numbered from the deeper to the shallower end, and spoken of as “ sounding 
lines”) nearly perpendicular to the longitudinal direction of the lake. 
§ 3. The first step is to construct the Normal Curve of the Lake (H.-S. § 20). 
The line A’ A, drawn as nearly as possible through the deepest soundings, is straightened 
and taken as the x-axis of the theory. For convenience in identifying sounding lines 
and intermediate sections, 7, measured in arbitrarily chosen units, fixes the distance 
of any section from the deeper end A’ of the lake. The area, A(x), of the vertical 
section through each sounding line was calculated or measured by the planimeter. 
This multiplied by b(«), the breadth of the section at the surface, the units in both 
cases being feet, gives = A(x) d(x), the. ordinate of the normal curve corresponding 
to each section. The section for which o is greatest (No. 10 in Karn, No. 5 in Treig) 
was chosen for the origin, O, of the variable, v. Thus in Karn v is the area between the 
sounding line No. 10 and the surface line of the section corresponding to x, the sign of 
v being positive or negative according as the corresponding section is towards the 
shallower or the deeper end of the lake. The values of v for A and A’ are denoted by 
a and a’; these and the values corresponding to the various sounding lines were found 
from the map by means of the planimeter. 
The next step was to fix upon two parabolas having a common vertex immediately 
under O, each passing through one of the ends of the c-v-curve, so as to get as 
* Denoted hereafter by the letters H.T.S. 
TRANS. ROY. SOC. EDIN., VOL, XLI. PART III. (NO. 32). 121 
