816 
ing examples: According to Pettersson [43], the tem- 
perature variations of the Gulf Stream are faithfully 
reflected in the simultaneous variations of the air tem- 
perature on the west coast of Scandinavia. Furthermore, 
Meinardus [38] showed that, during the years 1862-97, 
in 92 per cent of the cases the mean temperature for 
February and March in Berlin changed, relative to 
the preceding year, in the same direction as the mean 
temperature for the previous November, December, 
and January in Kristiansund had changed relative to 
the preceding year. This result seemed, indeed, useful 
for prognostic purposes and was mentioned to that 
effect in textbooks for several decades. However, a 
new investigation [11] showed that the correlation co- 
efficient between these quantities was +0.73 for the 
period 1862-90, but was only —0.30 for the subse- 
quent period 1891-1920. 
For many years J. W. Sandstrém was of the opinion 
that a warm Gulf Stream would bring a mild winter 
to northern Europe. In the year 1939, however, the 
Gulf Stream temperatures reached a record height, but 
northern and central Europe experienced the coldest 
winter in 110 years. 
A relationship between ice conditions and the general 
weather, particularly in northern Russia, has been 
shown by Wiese in several papers [56]. Undoubtedly, 
ice conditions and ocean currents are interrelated with 
the general atmospheric circulation in many ways. 
However, these interrelations exist mainly in the form 
of simultaneous correlations. The significant correla- 
tion coefficients between ice conditions and meteoro- 
logical elements in subsequent time intervals, that were 
computed from long series of observations, were, at 
best, of the magnitude |r| = 0.5. Thus, the ocean cur- 
rents and the ice conditions are never decisive, but 
only of contributory significance. 
Motions of the Pole. The quasi-periodical displace- 
ments of the rotational axis of the earth which have 
been found by observations of polar motion are com- 
posed of a period of approximately 434 days (Chan- 
dler’s period), caused by the unequal mass distribution 
of the solid terrestrial body, and of an irregular annual 
period caused by the air-mass displacements in the 
course of the seasons. The displacements of the rota- 
tional axis cause, in turn, changes in the centrifugal 
force and thereby a transport of air masses. These dis- 
placements of the earth’s axis, however, are only very 
small. On the average, the amplitude of the oscillation 
amounts to 0.2-0.3 seconds of arc, 0.5 seconds of are 
at the most. Thus, the pole deviates only about 9 m 
from its mean position. It has recently been found that 
over a forty-year period, a high pressure over northern 
Sweden was followed 434 days later by another high 
pressure with a relative frequency of 59 per cent [17, 
pp. 72-73]. Although this frequency, which was de- 
rived from 382 cases, exceeds the limit of chance, it is 
nevertheless much too small to be considered of prac- 
tical importance for extended-range weather forecast- 
ing. 
The Problem of Rhythms. Pressure Waves. The ques- 
tion regarding the existence of periods other than the 
WEATHER FORECASTING 
well-known daily and annual periods of weather phe- 
nomena is of great importance to extended-range 
weather forecasting. It was hoped, above all, that 
periods or waves in the fluctuations of atmospheric 
pressure would be found, which, when extrapolated, 
would permit the computation of the future pressure 
trend for a given location. By using this process for 
several stations, one would be able to calculate the 
development of pressure patterns, at least for a limited 
number of days in advance. When V. Bjerknes and his 
co-workers [28, 30] showed that waves, subsequently 
developing into cyclones, can form along surfaces of dis- 
continuity in the troposphere, a mathematical-physical 
basis was established for the problem of atmospheric 
pressure waves. Others, Exner [33, pp. 383-388] for in- 
stance, consider the thermal contrast of continents and 
oceans as a cause of the formation of forced oscillations. 
At any rate, regardless of the explanation offered for the 
formation of pressure waves, they can exist for a longer 
period of time only if they coincide approximately 
with the free oscillations of the atmosphere. Progress 
has also been made in the exploration of free atmos- 
pheric oscillations during the last two decades. While 
Y. Bjerknes [80] neglected the vertical acceleration 
(quasi-static method) and considered the earth’s sur- 
face as plane, Wiimsche [58] treated the free oscillations 
of a compressible medium as a spatial problem in polar 
coordinates, and thus neglected neither speed nor ac- 
celeration in a vertical direction. However, his compu- 
tations were still based on the assumption that the 
oscillations occur as isothermal changes of state in an 
isothermal atmosphere. This assumption naturally has 
an influence on the lengths of the resulting periods. 
The short-period waves to which the cyclones owe 
their formation are of no importance for extended- 
range forecasting. It would be erroneous to attempt 
computation of the pressure distribution for the next 
two days from extrapolation of these short-period 
waves, since this can be achieved more easily by the 
methods of synoptic analysis. The assumption of J. 
Bjerknes and H. Solberg [29] that the rhythm of pres- 
sure changes is the result of four cyclone families 
circulating with more or less constant velocity around 
the pole has been disproven by observational facts. 
As regards the longer waves, there is still no convincing 
proof of their existence. During World War II, more 
than one thousand analyses of rhythms were made at 
the Forschungsinstitut fiir langfristige Witterungsvorher- 
sage in Bad Homburg, Germany. Subsequent extra- 
polation of those resultant waves that were recognized 
as quasi-persistent on the basis of mathematical cri- 
teria, permitted prediction of the direction (sign) of 
atmospheric pressure changes to a definite date. These 
predictions were accurate more frequently than would 
have been possible by chance. However, the relative 
frequency of correct forecasts remained below 75 per 
cent and is therefore inadequate for practical purposes. 
If we determine how often in such analyses the in- 
dividual trial waves prove to be quasi-persistent, we 
find frequency maxima for European stations at 7 
and 8, 12 and 138, 20, 22 and 24, as well as 30 and 33 
ee 
