A—MATHEMATICAL AND PHYSICAL SCIENCES 27 
years of sixty-eight stations scattered over the world and drew attention 
to the relations between them: among these the opposition between 
Sydney in Australia and Buenos Aires was fated to have great influence : 
his subsequent studies involved temperature and rainfall also. In 1902 
the Lockyers confirmed the existence of the see-saw between pressure 
in the Argentine and in India or Australia ; and using graphical methods 
produced a world map, dividing areas in it according as their pressures 
varied with India or South America. ‘They were followed by Bigelow’s 
study of relationships with solar prominences. During recent years 
considerable development has followed the introduction of statistical 
methods, particularly in the hands of Exner, and of members of the 
meteorological services of England and India. 
It will be convenient if I may here introduce a technical phrase. If 
we have two series of numbers of which the variations are connected, 
there will be a certain proportion of the variations of each which are 
associated with those of the other, and this proportion is called the 
correlation coefficient between the series. If it is nearly unity the numbers 
vary closely together ; if it is small there is little relationship between 
them ; and if it approaches —1 the relationship is close, but one series 
goes up when the other goes down. 
Let us now consider some of the results of the analysis of seasonal 
features. It has long been known that in the North Atlantic Ocean there 
are two types of winter. In one pressure is high near the Azores and 
south-west Europe, and low in Iceland, while temperatures are high in 
north-west Europe; in the other type all these features are reversed. 
(See the three upper graphs in Fig. 1.) Let us suppose that we want 
to know the effect of these types on, say, temperature in Labrador. 
An obvious plan would be to plot the variations in successive winters, 
December to February, of the quantities which increase together, such 
as Vienna pressure and Stornoway temperature, and also of the quantities 
which decrease when the former increase, such as Iceland pressure, 
reversing these so as to secure similarity of the graphs. We could then 
draw a graph which is the mean of all these, and could regard it as 
expressing the variations of the North Atlantic fluctuation as a whole. 
(See the lowest graph of Fig 1.) If now we were to plot Labrador tem- 
perature below it we should see that its variations were, like those of 
Iceland pressure, strongly opposed: and on reversing Labrador there 
would be very strong similarity. So Labrador becomes a good example 
of the second group. Now we want to know the effect of the North 
Atlantic oscillation on the pressure temperatures and rainfall of a large 
number of places ; and if in this way we put a hundred graphs under one 
another, some easy to classify and some doubtful in character, it would 
be difficult to draw satisfactory conclusions in a manner capable of 
convenient and accurate expression. So instead of graphs we use 
numbers. Having found by preliminary investigation the stations which 
are most representative, we calculate the figures in successive years for 
the North Atlantic oscillation as a whole, and then work out the correlation 
coefficients of this with the pressures, temperatures and rainfalls of all 
the places in which we are interested. These coefficients are plotted 
