564 
first 24 hr it was more likely to be good for subsequent 
time intervals. In spite of the obvious advantage of 
avoiding the necessity for determining continuity, it is 
felt that this method, unlike that used by Bortman [6] 
places too heavy requirements on the theory, and makes 
the determination of empirical corrections difficult. 
A similar study has been made by Fultz [23] who 
also used trajectories computed on daily 10,000-ft 
charts, and in addition estimated the true trajectory of 
the air parcels. Such a method could obviously lead to 
quantitative empirical corrections to the vorticity paths 
in many different geographical areas. However, the 
number of cases studied by Fultz was small (largely 
because of the length of time necessary to compute true 
paths) and the corrections were apparently so complex 
that the author confined his practical results to a 
number of valuable qualitative rules. 
Among recent studies designed to avoid the problems 
of determining continuity perhaps the most important 
is the work of Charney and Eliassen [11, 12] mentioned 
previously. This represents a considerable refinement 
of the simple planetary wave formula particularly as it 
applies to the determination of local pressure (or height) 
changes. Several empirical studies are currently under- 
way to test and expand this theory. 
- Before concluding this brief review of quantitative 
studies of circulation patterns it is necessary to say a 
few words about the accuracy that has been attained. 
It must be confessed that in spite of the fact that they 
seem to fit into a logical pattern which can be explained 
on physical grounds, these empirical results represent 
only the average behavior of circulation features. For 
example, the largest correlation coefficient found be- 
tween theoretical and observed wave displacement rep- 
resents a degree of success accounting for perhaps only 
50 per cent of the variability of observed motions. These 
meager results are probably due in part to the great 
complexity of the atmosphere which makes it impossible 
for any single factor, such as a wave length, a vorticity 
path, or a region of confluence to be responsible for 
more than a small part of the subsequent circulation 
changes. Only by integrating in some way all the many 
processes taking place throughout the whole atmosphere 
can one hope to approximate a complete solution. Such 
a desirable goal can be obtained only through con- 
tinued close collaboration between theoretical and syn- 
optic meteorologists. 
Another contributing factor lies in the limits of ob- 
servational accuracy. Because of instrumental errors, 
sparseness of upper-air reports, and analytical diffi- 
culties it is not generally possible to define a trough or 
ridge at 45°N any closer than about four degrees of 
longitude. Because of this one source of error (even 
supposing that a perfect linear relationship exists be- 
tween wave length and trough speed), the highest corre- 
lation that could be attained is —0.85. This result 
suggests that in meteorology, as in other sciences, it is 
highly desirable to include in any quantitative compari- 
son of theoretical and empirical findings a careful analy- 
sis of errors. 
Statistical Studies of the General Circulation. Me- 
THE GENERAL CIRCULATION 
teorology has always been a fertile field for statistics. 
It contains numbers of observations perhaps equal to or 
in excess of those in any science. The number of com- 
binations of elements making use of different places and 
different time intervals is well nigh infinite. Partly for 
this reason, meteorology has encouraged the use of the 
correlation technique for discovering significant rela- 
tionships between meteorological elements or between 
one and the same element in space or in time. While this 
statistical procedure has its secure place in meteor- 
ological research, it has probably been the cause of 
more heated controversy among meteorologists than 
any other research tool. Owing to the amazingly large 
mass of correlations to be found in the literature and 
the lack of general agreement as to tests of significance 
to apply to such statistics, it becomes exceedingly dif- 
ficult at this time to portray or evaluate the role of sta- 
tistical studies of the general circulation. Perhaps the 
most indefatigable worker along these lines has been 
Sir Gilbert Walker, whose statistical studies of con- 
temporaneous and lag correlations form the basis of 
many interesting and informative papers [52]. For the 
most part these papers have been reviewed at length 
elsewhere [40] and thus the present brief survey will 
not attempt to treat this work but instead will con- 
centrate on the work of Willett [57, 59] who, perhaps 
next to Walker, has given the atmosphere its most 
vigorous statistical workout. Besides, Willett had the 
distinct advantage of having hemisphere-wide maps 
at the surface and aloft and could thereby obtain inte- 
grated indices of the general circulation which Walker 
had to estimate by values of elements chosen at selected 
points. Moreover, Willett’s work is of particular in- 
terest inasmuch as it ties in with, and indeed, forms 
some of the basis of, the material discussed in earlier 
portions of this article. 
The principal meteorological material upon which 
this work was based consists of daily analyzed charts 
at sea level and at 10,000 ft over the entire Northern 
Hemisphere for the cold months of the year from Oc- 
tober through March for the seven years 1932-39. 
From these charts, five-day mean maps were prepared 
twice a week (so that there was one or two days overlap 
between five-day periods) as well as a host of statistical 
derivatives. A list of the complete number of these 
“tdices” of the general circulation would in itself 
occupy considerable space, even without the addition 
of the vast number of correlations computed between 
pairs of indices. The principal indices considered on a 
hemisphere-wide scale can be relegated to three types: 
zonal, meridional, and solenoidal. The zonal indices 
have been defined on page 555. 
The meridional indices used by Willett express the 
mean (over space and time) of the north-south com- 
ponent of geostrophic flow averaged for each of the 
latitudes 30°N, 45°N, and 60°N. This quantity was 
necessarily obtained from values taken from daily syn- 
optic charts and, as in the case of the zonal indices, 
was obtained for both sea-level and 10,000 ft. 
The solenoidal index measures the poleward gradient 
of mean virtual temperature between sea level and 
