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it will gradually reduce the temperature of the surface waters in the western part of the North Atlantic Ocean. These waters are slowly carried towards our shores by the agency of the Gulf Stream and the Gulf Stream drift, where they appear to arrive some four months later. Cold surface waters off the British Isles tend to increase the atmospheric pressure, and so to produce anticyclonic conditions with fine, sunny weather. This year the average wind over the Davis Strait region from January to March was southerly, instead of northerly, which is its normal direction. Such a reversal would reduce considerably the strength of the Labrador current, and consequently it might be anticipated that the Gulf Stream waters on this account would be warmer than usual. That would create low pressure, with cloudy or rainy weather during April to June in the British Isles. Other variations of the kind have been shown to be related to the character of the seasons in this country. While these researches are likely to prove of the greatest use in forecasting seasons, it will be evident that they do not satisfy the natural desire to know the ultimate cause of the bad weather. If our lack of summer was connected with a south wind in Davis Strait in the early spring, what was the cause or causes of that wind? And are the causes developed out of a natural succession of events taking place on this planet, or can they be ascribed to external influences, presumably in the sun? These are natural and important questions to which no adequate replies can at present be given.
Investigations of the nature described, which prove that two or more variable quantities fluctuate similarly (or dissimilarly) in sympathy with one another in point of time, or separated by a definite interval, do not of themselves indicate which of the variable quantities may be said to control the other, or, indeed, whether there is any causal relationship whatever between them. For the investigations are purely statistical in form: they start with two sets of numbers, representing two series of numerical measures of the intensity of the two variable quantities, the measures being taken at equal intervals of time. Whether or not a relationship exists between these two sets can be determined, quite independently of any arguments about cause and effect, by
a relatively simple arithmetical operation called 'correlation,' which is well known to statisticians. If there is a time-interval between the two variables, as in the example cited, then it will probably be agreed that, at any rate, the variable which comes later in point of time cannot be the cause of that which precedes it. But, in any case, it does not follow that one variable is the cause of the other related variable, even if the former precedes the latter in time. It may be that both variations are subject to an outside control, the nature of which may or may not be known.
Let us take a simple example by way of illustration. It is recognised that the temperature of the air is, on the average, higher at midday than at midnight. It is equally well known that the intensity of sunlight is greater at midday than at midnight; further, that solar radiation is appreciable at midday but not at midnight in these latitudes. The three variable quantities, temperature, sunlight, and solar variation, are, therefore, closely related in the statistical sense-they all increase and decrease together. But this fact will not, of itself, enable us to decide whether the variations in one quantity (say sunlight) are produced by the variations in one of the others, or whether they are due to some other cause. It is the application of other facts of a physical, as opposed to a statistical nature, which enables us to affirm that the fluctuations of solar radiation are the cause of the fluctuations both of temperature and of sunlight. The statistical correlation which exists between temperature and sunlight is merely a consequence of that fact, and does not signify that sunlight causes temperature or temperature sunlight.
Although these facts seem self-evident when applied to a case of which the mechanism' is obvious, they are liable to be set in the background when a discussion is proceeding in regard to the statistical correlation between two variable quantities, if it is not known whether any physical relation in the nature of cause and effect exists between them. Indeed, cases have occurred in which the existence of a high correlation between two quantities has been taken to prove the coexistence of a physical causal relation between those quantities. No doubt each case must be considered in the setting of its attendant
circumstances; but, apart from that, it is very undesirable to assume causal relationships without further investigation, merely on the strength of statistical correlations. It is, of course, legitimate to explore the possibility of the existence of such relationship, and to test the hypothesis by noting whether physical deductions drawn therefrom are in accord with observed facts. Should the hypothesis emerge unscathed from that test, its probability is considerably enhanced.
It is not necessary, however, for the physical nature of the connexion between two correlated variables to be known before use can be made of the correlation. For many years, forecasts of the rainfall during the season of the south-west monsoon in India have been prepared and published by the Indian Meteorological Department. The forecasts are based entirely on statistical correlations which have been proved to exist between the monsoon rainfall and such widely differing quantities as the atmospheric pressure in Argentine and in Siberia in a previous season, the extent of the Nile flood, etc. There is no question that the forecasts are much superior to pure guesses, although it must be admitted that they do not always produce even the correct sign for the computed divergence of the monsoon rainfall from the average. Such discrepancies are probably explained, not by faults in the method, but by the fact that the quantities which affect the monsoon are not all known. This is not surprising when it is remembered that no one has yet constructed and published a complete physical picture of the manner in which the quantities which are used operate to affect the rainfall in India. The fact that the variables mentioned were associated with the monsoon rainfall was known long before the amount of the correlation was computed. It was discovered by inspection and comparison of a large number of curves, one of which showed the fluctuations in the serial values of the monsoon rainfall from year to year, and the others showed similar fluctuations of other quantities of which regular observations were available. To the physicist, who likes to trace cause and effect in every stage of his work, this method of discovering significant variables may seem crude; nevertheless, the method is truly scientific; for it consists in sifting out from a mass of
observational data those series of observations which show promise of correlation, in investigating each one of these by strict statistical methods; and finally, in utilising those which display a satisfactory numerical degree of correlation.
The monsoon forecasts of India, as developed in recent years by Sir Gilbert Walker, are cited as the best-known and best-developed example of seasonal correlation. It must be remembered that conditions in India are more regular and stable than in this country; hence the problem of seasonal forecasting in India is more likely to yield to solution than is the corresponding problem here. Moreover, our seasons are characterised by variable weather rather than by persistent cold or heat, rain or drought; so that day-to-day forecasts of weather are of greater general utility in this country than forecasts of seasons which frequently cannot be adequately described by means of average values.
As the sun is acknowledged to be the primal cause of the weather, it is natural to look to him for an explanation of abnormal seasons. Those manifestations of solar activity called sunspots are known to exhibit a period of about eleven years, and it is recognised that a corresponding period of eleven years in terrestrial magnetism is directly connected with the sunspot period. Many investigators have sought to trace a similar period in meteorological phenomena. Such a period has been found; but its magnitude is small, and, in consequence, it is far more elusive than the magnetic period. Still, it is now fairly generally agreed that the eleven-year period in meteorology is real. When we come to inquire how the variation is shown, the remarkable result appears that during years of considerable solar activity, as evidenced by the presence of many sunspots, air temperature is lower than the average; and, conversely, when solar activity is feeble, temperature is relatively high. Paradoxes of this kind are not unusual in meteorology: we cannot, therefore, dismiss the matter as unreal or inconsequential merely because it appears improbable at first sight.
It must suffice to mention, in explanation, that some observers have affirmed that high cirrus clouds and cirrus haze occur more frequently during the periods of Vol. 244.-No. 483.
sunspot maxima than of sunspot minima. Such cloud or haze would tend to reduce the temperature. Prof. W. J. Humphreys, of the United States, has, on the other hand, essayed to prove that at times of sunspot minima the sun emits radiation which is comparatively intense in the ultra-violet part of its spectrum. The effect of this would be to increase the concentration of ozone in the upper layers of the earth's atmosphere. Now ozone absorbs terrestrial radiation much more readily than solar radiation, which it transmits without difficulty; the result is that the relative concentration of ozone acts like the glass of a greenhouse, which transmits solar radiation into the greenhouse but fails to transmit outward radiation of longer wave-length from the heated objects inside. In this way the higher temperature at sunspot minima is explained. It is interesting to note that the year 1924 was at, or very close to, a period of sunspot maximum. Consequently, it may be inferred that, other things being equal, world temperature during 1924 was likely to be rather lower than normal. The amount is not great, being on the average from one-half to a whole Fahrenheit degree. This amount, though small, is persistent day and night, from month to month, and it probably exercises an appreciable effect upon the human race, as well as upon the boundaries of areas suitable for different kinds of growing crops.
It is also worthy of remark that a connexion appears to have been traced between records of temperature and the incidence of those volcanic eruptions which are of the explosive type, and project large quantities of very fine dust into the upper layers of the atmosphere. The dust is so excessively fine that it requires a very long time to settle. It is carried about by the upper winds, and becomes distributed throughout the upper atmosphere, causing coronæ around the sun. It may persist for months and even years after the eruption. The great eruptions of Krakatoa in 1883, of Mont Pelée in 1902, and of Katmai in 1912, were of this type. The dust-cloud, though exceedingly attenuated, probably causes a reduction in air temperature at the surface of the earth during the time that it persists. Whether recent volcanic eruptions may have contributed to the causes of the cold summer is a question which cannot be