656 THE TRAVELLING CYCLONE [444
Hence
^X, i = ^-2«(£T-t2/) + £-2y, ...(6)
p ctx and on integration
(7)
As might have been expected, the last term in (7) is the same function of R as when U = 0, but R itself is now a function of U and t.
In the case considered by Sir N. Shaw, f is constant and may be removed from under the integral sign. Thus
(8)
P
If U — 0, R2 identifies itself with a2 + f, and we get
p/P = i(» + f)lO*' + 3/a) ............................ (9)
A constant as regards x and y, which might be a function of t, may be added in (8) and (9).
We see that if to + £= 0, that is if the original terrestrial rotation is annulled by the superposed rotation, p is constant, the whole fluid mass being in fact at rest. It was for the purpose of this verification that the terms in &r were retained. We may now omit them as representing a pressure independent of the motion under consideration. In the strictly two-dimensional problem there is a pressure increasing outwards due to " centrifugal force." In the application to the earth's atmosphere, this pressure is balanced by a component of gravity connected with the earth's ellipticity. Thus in Shaw's case we have
= const. + (o>£ + K2) y--ri + (*-Ut)*, ...... (10)
P (^ 0}<s ~i~ 2b ' )
showing that the field of pressure, though still circular, is no longer centred at 0 as when f=0, or even at C, where x = Ut,y = 0, but is displaced sideways to the point Avhere x — Ut, y = o)lTf(w^+ ^2). Shaw calls this the dynamic centre ; it is the point which is conspicuous on the weather map as the centre of the system of circular isobars.
As a case where the circular motion diminishes to nothing as we go outwards, let us now suppose that £= Ze-R'lar", falling off slowly at first but afterwards with great rapidity. We have
.' obesetting the acceptance of telepathy, biit I fully recognize that a strong case has been made out for it. I hope that more members of the Society will experiment in this direction. It is work that can be done at home, at odd times, and without the help of mediums, professional or other. Some very interesting experiences of this kind have been recorded by a former President, Prof. Gilbert Murray. With perhaps an excess of caution, he abstained from formulating conclusions that must have seemed to most readers to follow from the facts detailed. I trust we may hear still more from him.