426 SECTIONAL TRANSACTIONS.—A. 
Napier Shaw, the ascent of only 0.1 (km.)? of heated air per second over the 
tropics, rising to 15 km. moving polewards and descending in latitude 60°, 
would contribute work sufficient to make good the kinetic energy dissipated by 
turbulence. 
9. Dr. A. T. Doopson.—Meteorological Effects on Sea Level and 
Tides. 
The effect of the distribution of atmospheric pressure, statically and by the 
operation of the resulting wind, may have a magnitude of 3 feet or more on 
the sea-level at Liverpool. The greater part of the effect € can be expressed 
quantitatively by the relation 
(=«B+AE+p~N-+ constant, 
where «, A, » are constants, and B, E, N denote respectively the local atmo- 
spheric pressure and its gradients East and North. The constants are deter- 
mined from observational data. The correlation between fluctuations of sea- 
level and atmospheric pressure is greatest when the sea-level is taken three 
hours earlier than the atmospheric pressure, whereas the correlation between 
sea-level and the easterly gradient of pressure, corresponding, roughly, to a 
south wind, is greatest when the mean sea-level is taken about fifteen hours later 
than the corresponding pressure gradient. For the northerly gradient (easterly 
wind) the time difference for maximum correlation is practically zero. At 
Liverpool a §.W. wind, and not one blowing directly into Liverpool Bay, is 
most effective in raising sea-level. A quantitative separation of the relative 
effects of winds in the Atlantic and in the Irish Sea shows that the former 
are 50 per cent. more effective than the latter for a given pressure gradient, and 
that the most effective wind for raising sea-level at Liverpool is almost due south 
when operating in the Atlantic, and almost due west when operating in the 
Irish Sea. On the British coast of the North Sea the most effective wind- 
directions for raising sea-level are also from the west (i.e. off-shore). Local 
configuration of coast-line*plays only a small part in this phenomenon. 
The height and time of high-water are affected in a somewhat complex way, 
and no simple law has yet been formulated. 
10, Mr. T. Smiru.—Apocoptic Kxpansions. 
In the expansion of a general function, as by Taylor’s theorem, it is custo- 
mary to consider a number of leading terms and find limits between which the 
remainder lies for a definite range of the independent variable. The poly- 
nomial so obtained is in general not as close a representation of the function 
as is possible with a polynomial of that order. This and other expansions, 
as well as the usual formule for numerical interpolation, represent curves of 
order n, say, which pass through n+1 selected points on the fundamental curve. 
The polynomial of order n which represents the latter curve with the highest 
possible accuracy is constructed by causing it to pass through 2n+2 points, 
none of which lie on this curve. The coefficients are functions of n as well 
as of the derivatives of the function represented. 
11. Rev. A. L. Corrrs.—Series in Magnetic Disturbances. 
(1) The magnetic disturbance of 1923, March 24, during which the extreme 
range of declination was 66’, and in horizontal force 238y, was the greatest 
since the exceptionally violent storm of 1921, May 13-15. It was accom- 
panied by unusual earth-currents, and by displays of aurora borealis. It was 
preceded, at an interval of twenty-six days, by a disturbance somewhat less 
intense in 1923, February 26. This disturbance was alsc coincident with earth- 
currents and aurora borealis. These two were not isolate1 disturbances, for 
they were members of a series, at a mean interval of 27.2 days, from 1923, — 
January 30 to June 13. 
(2) The occurrence of this series of disturbances, and especially of the 
greater storm of March 24, is noteworthy, because the sun has been almost 
entirely free from spots and bright facule since the beginning of the year. 
