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the West. Nearly all our clouds come from some westerly direction, and since they pass over one of the driest areas in the world, depositing very little moisture on the way, it follows that they must be nearly or quite as rich in moisture as when they left the high levels over the Atlantic. Therefore such difference as there is between the absorption and radiation over land and sea must be more pronounced in the lower levels than in the upper.
Regarding the curious diurnal variations of pressure characteristic of valleys and mountains, it has long been recognised that it is a thermal result quite independent of the primary causes of the general barometric oscillations over the earth's surface.
Recently Prof. Bigelow has attempted a comprehensive theory of the diurnal oscillations of all the chief meteorological elements. Here again I quote at some length :
“ Let us illustrate the formation of the double diurnal period at the earth's surface and the single period in the cumulus level by considering the behaviour of the absolute humidity, that is, the number of grams of water vapor per cubic centimeter. The first diurnal effect of the radiation from the earth is to raise the vapor content of the atmosphere from the low level occupied by it at night to a higher level during mid-day.
This absorbing screen of water vapor, visible or not, rises and falls once daily through 1000 or 2000 meters, taken as a whole. While the warm air rises by convection from the surface to the level of 1500 meters, the vapor rises with it and endeavours to saturate the unit volumes of the higher strata at the prevailing lower temperatures, the depleted lower volumes being partially filled up again by fresh evaporation from the water and land surfaces. There is a decrease in actual temperature with the elevation, and therefore the saturated unit-volume content decreases. The vapor sheet rises to higher levels, and this, together with the fresh supply by evaporation from the surface, can refill the depleted volume again, especially during the forenoon hours. After the noon hour the continued increase of temperature gives rise to larger vapor capacity per unit-volume.
But while the rising vapor sheet keeps the upper volumes filled, the lower, which are drained by the ascension of the water vapor, can not be supplied by evaporation at the surface at a sufficiently rapid rate to keep them full, because the prevailing surface moisture has been taken up at an earlier hour. The same remarks are true for the relative humidities. The result is that the upper volumes are always full or relatively full, and have an increasing actual content up to the early afternoon, about 2 p.m., so that the diurnal curve at some distance above the ground has a single maximum and minimum as observed. On the other hand, while the 10 a.m. surface volumes are kept filled, or relatively filled, they are actually depleted in the afternoon, and not replenished by evaporation up to the original relative humidity of the morning, and therefore the curve shows a depression in the early afternoon, and is doubly periodic. The second maximum
at the surface is due to a reversal of this process as the vapor settles back slowly to the ground during the afternoon and night. The additional lag of the evening maximum being four hours in the evening to about 10 p.m. is lue to the slow cooling of the ground after sunset, which continues to be a source of heat for several hours, and the slow conductivity of the heated atmosphere, which retains its heat even longer than the ground after the sun has set. This theory, if pursued into quantitative details, will evidently account for the entire series of observed phenomena. Analysing the diurnal barometric pressure by volume contents, we see that with the heating of the lower strata the denser air of night is replaced by contents of lower density after mid-day; taking into account the lag, the lower volumes are depleted and the upper are filled relatively, thus producing the two types of periods. This is entirely analogous to the barometric pressures of winter and summer, wherein the summer pressures are lower [than those of winter) at the surface of the earth, but greater at some such level as 1500 or 2000 meters, the summer pressure corresponding to that of the diurnal pressure in the afternoon.
It is inferred from these considerations that since the double diurnal period is confined to a thin sheet near the surface and does not extend throughout the atmosphere, Lord Kelvin's theory of a dynamic forced wave is not available for explaining this phenomenon."
There seem to me- I hope you will agree that I am speaking with all diffidence as one seeking rather than imparting informationthere seem to me great difficulties in Prof. Bigelow's exposition. In the absence of direct proof it is surely difficult to believe that there can be such an enormous vertical circulation of air extending from the bottom to an altitude of upwards of 10,000 feet as seems to be implied. Then there is the circumstance that over the ocean the vapour tension varies with the temperature and has only a single maximum and minimum in the day, whereas the pressure of the air has a semi-diurnal period as strongly pronounced as it is over the land, in spite of the almost uniform temperature of the lower air and of the floor upon which it rests.
Now, I have troubled you at so much length with these various theories because each one seems to me to contain something worth attention. Certainly they all display a certain amount of irresponsible slurring over difficulties, and base their strongest pretensions on what we know least about ; nevertheless they are not to be entirely rejected on that account. They compare very favourably, at any rate, with some of the theories that have attained transient currency in other sciences.
The most important contribution so far made to the theory of the diurnal oscillation of barometric pressure is due to Hann. This renowned meteorologist has done a vast amount of work in classifying and generalising the harmonic elements of the pressure variations for a great number of stations, and has succeeded in establishing a number of results of the first importance. Harmonic
analysis, as it is called, is of considerable importance in many branches of physics. It is based on the principle that the summation of any number of harmonic curves is a periodic curve. The task of the meteorologist is the laborious inverse process: the separation of the various periodic curves met with in meteorology into their harmonic constituents as far as possible. Most of the diurnal meteorological curves well repay analysis as far as the fourth harmonic, the curve of diurnal barometric variation in particular. The periodic formula as it is usually employed in meteorology is, for hourly observations
a = p + u, sin (V1 + 11150)
+ u, sin (V2 + 2n 15°)
V2, V2 V3.............the epochs
Now, Hann has established that in the case of the barometric pressure, up to latitude 48° at least, u, is greater than U., and, indeed, considerably the greater over the tropical oceans. Also that the flood-time of the semi-diurnal barometric wave is very constant over pretty well the entire globe. The flood-time of the diurnal wave, however, varies widely according to the latitude and topography of the station.
Table 3 gives the various harmonic elements for the four barometer curves of Fig. 1, together with one or two others for comparison. I have also added harmonic elements of vapour tension for Kimberley, Lisbon, Córdoba, and Hong Kong. You will see from these that the epoch of the semi-diurnal wave of pressure comes later on the whole (i.e., the constant angle gets smaller) as the latitude increases, saving in the case of the station near the Arctic Circle.
Let me now quote a passage or two from a comparatively recent paper by Hann as expressing some of his latest views :
“I was myself convinced that all the attempts to explain the diurnal barometric oscillation by means of the daily variations of the meteorological elements at any one place. . . . could lead to no conclusion; and I have published a series of papers giving a precise description of the phenomenon as manifested over the whole earth, ai sea-level as well as at all elevations for which observations exist, and I have endeavoured to give the results in such a form as would be suited for the basis of a physicomathematical theory. With this object I have represented all the results of observations in periodic functions.
“I am of opinion that, speaking generally, the observed daily variation of wind and temperature do not stand in as close a relation to the diurnal barometric oscillation as has hitherto been assumed. ..... We had better deal with the action of the sun on the upper strata of the atmosphere, and treat this as the principal cause. The actinometrical observations show us that
these upper strata absorb a considerable amount of heat. This diurnal heating action of the sun on the upper strata would harmonise far better with the general uniformity of the daily barometric oscillation along the different parallels of latitude, as well as with its general independence of weather. We need not quite exclude local influences, but these seem to be more of a secondary character.
“ Inasmuch as the periodical action of the sun's rays on the upper strata of the atmosphere, recurring day by day, must produce periodical movements of great regularity (an oscillation of the entire mass of the atmosphere), it is easy to see that this can explain the typical character of the diurnal barometric oscillation, while the local differences of the earth's surface represent the modifying element.
“ If a limited mass of fluid is set in simple pendulum-like oscillations, their amplitudes are governed by the given conditions of the fluid or the gas (dimensions, temperature). If the impulse is a single powerful one, such as that which gives rise to seiches in lakes, it is perfectly immaterial how it goes on : the mass of water takes up always the same pendulum movement in which it can move in virtue of its dimensions (the length and depth of its basin).
If the impulse recurs periodically, then oscillations of that period are forced to occur, even if these do not coincide with any any of the forms of oscillation which belong to free waves.
This holds if the impulse represents a simple sine wave. In other cases the following must be considered. Fourier showed mathematically that any periodical form of oscillation (or wave of any form) can always be resolved into a sum of simple pendulum oscillations (waves), and that their number of oscillations are 1, 2, 3, times as great as the number of oscillations of the given form of movement, and only in one single manner. When any periodically recurring impulse of any form is resolved by Fourier's harmonic analysis into pendulum oscillations, each portion of these produces a forced oscillation of the same period in the mass of fluid. But the amplitudes of these forced waves do not preserve the same proportion to each other as those of the waves which produce them. If the period of an exciting wave is nearly the same as that of a free wave in the liquid, the resulting forced oscillation will attain a disproportionally great amplitude.
'This principle may be applied to the constant oscillations of our atmosphere which are produced by a periodical impulse, i.e., by the variation of temperature which recurs uniformly day by day. If the atmospherical envelope of our earth, with its conditions of space and of temperature, is most easily set in oscillations of a semi-diurnal period, the semi-diurnal portion of its exciting cause, the diurnal temperature wave, will be the most active. It does not matter whether this semi-diurnal temperature wave has a real independent existence."
That is to say, if I interpret this quotation aright, the semidiurnal oscillation of the barometer is to be regarded as mainly a forced wave of pressure of 12 hours period due to the harmonic component wave of temperature of the same period. There have been many adverse criticisms of this view. Hann himself notices one to the effect that,
“ There is, in reality, no daily variation of temperature with two maxima and minima ; and if we, in spite of this, obtain a double daily temperature wave, because we insist on representing the daily march of temperature by a series of sines, this forced methematical form can serve to explain an observed phenomenon, whereas for this some real natural process must be sought for as a cause."
Such an objection would only be valid if the diurnal variation of temperature were a simple impulse of 24 hours' period. In reality it is anything but that. It is itself the result of a train of acting and reacting processes, due largely to the presence of great water areas over the earth's surface, and to the presence of aqueous vapour in the atmosphere. Before the final result of a temperature impulse upon the air can be considered, we have to take into account the fact that the temperature impulse itself is largely modified by the train of operations set agoing by itself. Thus, for example, the diurnal variation of temperature gives rise to a diurnal variation of aqueous vapour. This aqueous vapour absorbs and radiates heat, thus disturbing the otherwise simple curve of temperature. Then, again, clouds are formed, and these shew a tendency to two, or, perhaps, three maxima in the day. These also regulate the temperature.
Then, as Hann has observed, insolation by day and radiation by night combine to made the diurnal curve of temperature asymmetrical, and composed of two parts which do not follow the same law of variation. For all these reasons it seems clear that the various harmonics are not necessarily figments of the mathematical imagination. The strongest objection, to my mind, against the second harmonic wave of temperature being the ultimate cause of the semi-diurnal oscillation of pressure, is that for all altitudes known to us the variation of the one month by month differs considerably from that of the other. Taking Kimberley as an example, we find that the maximum phase of the second harmonic wave of pressure comes earliest in October and latest in February, the difference in time being almost exactly one hour; whereas the same epoch in the second harmonic wave of temperature is earliest in October and latest in July, the difference in time being more than two hours. And nearly the same rule holds up to altitudes of 15,000 feet, if not more. A second objection takes the form of a query : Have we exhausted every other possible source having an indubitable 12-hour period? There is, for example, the evaporation of water from the surface of the earth, which, as I have tried to explain before to-day, and as you will also see from the harmonic constants of vapour tension given above, shews strong barometric affinities. Is the semi-diurnal curve of vapour tension over the land due, as Bigelow says, to the displacement of the lower damp air by