420 TRANSACTIONS OF SECTION A. 
observations at the centre showed no uninodal period, but did show the binodal 
eriod. 
: As the sides of the Madiisee were so shelving it was not possible to apply a 
mathematical theory to the calculation of the period of the oscillations which 
involved a rectangular approximation to the shape of the lake basin. The dis- 
continuity of temperature between the surface and bottom water was, however, 
very abrupt, and a mathematical theory was evolved on the assumption of a 
sudden discontinuity of temperature at a given depth, but applicable to a basin 
of variable depth and breadth. This theory gave excellent results when applied 
to the computation of the period for the Madiisee, and laboratory experiments 
with troughs of varying shapes gave conformable results. In Loch Earn, how- 
ever, the discontinuity was not very abrupt, and the theory did not give such 
good results. It was further extended to the cases of oscillations in a liquid 
of gradually varying density—the observed period of the uninodal temperature 
seiche for Loch Earn was 15:2 hours, and the period calculated according to 
the author’s theory was 15 hours. The following are the assumptions involved 
in the theory: (1) It was.assumed that in the oscillations (a) the motion of 
water particles was irrotational, (6) the amplitude was small, and (c) that there 
was no transverse motion of water particles. (2) A condition was imposed that 
at a certain depth there was no horizontal motion—which necessitated that 
above and below that depth the horizontal motion was in opposite directions, 
and that there was slipping at the boundary. There is a certain amount of 
arbitrariness in fixing the depth at which to assume this boundary, but it seems 
a reasonable supposition to fix the depth where the density gradient is greatest. 
With these assumptions the theory is found to depend on the differential 
equation 
where u is function depending on the contour of the lake and the horizontal 
displacement of water particles; v is a function depending on the contour of the 
lake and the depth chosen for the boundary; o(v) a function depending on 
» and the distribution of density; w== P sin n (t—r) where P is a function of 
v alone, tT is constant, and the value of n depends on the circumstances of each 
case. 
This equation is of exactly the same form as the equation arrived at by Pro- 
fessor Chrystal in the case of the ordinary seiche, and therefore the modes of 
computation and approximation elaborated by him are available. The similarity 
between the equations for the ordinary seiche and the temperature seiche also 
shows how close is the analogy between the two modes of oscillation. Given the 
period of the ordinary seiche and the distribution of density it is possible to 
give a close approximation to the period of the temperature seiche. 
2. Report on Magnetic Observations at Falmouth Observatory. 
See Reports, p. 103. 
3. On the Velocity and Direction of the Wind above Ground Level. 
By Miss Marcaret Waite, M.Sc. 
Conclusions are based on the results of kite and balloon ascents obtained daily 
at Glossop Moor, Derbyshire, over the two years 1908-1910, and comprising some 
thousand ascents. 
Wind velocities are measured in metres per second, heights in metres, and 
gradients of wind velocity in metres per second per 100 metres, an increase of 
wind velocity with height being accounted a positive gradient. 
Increase of Wind Velocity with Height.—Near the ground level the wind 
velocity increases very rapidly with height; the gradient decreases continuously 
to about 1,000 m., above which it is more or less constant, at about a tenth its 
value over the first level, ground to 500 m, : 
