Journals (continued). Symons's Monthly Meteorological Magazine. January to June, 1888. 8vo. London. Mr. Symons, F.R.S. Zeitschrift für Biologie. Bd. XXIV. Heft 3. 8vo. München 1888. The Editors. Brodie (Rev. P. B.) On the Range, Extent, and Fossils of the Rhætic Formation in Warwickshire. 8vo. Warwick [1888]; On the Discovery of a New Species of Fish. 8vo. Warwick [1888]. The Author. Chadwick (Edwin), C.B. [A series of pamphlets on Education, Sanitary Science, Local Government, &c.] 8vo. London 1857-88. The Author. Dallas (W. L.) Memoir on the Winds and Monsoons of the Arabian Sea and North Indian Ocean. 4to. Calcutta 1887. The Author. Dawson (Sir J. W.), F.R.S. Modern Science in Bible Lands. 8vo. London 1888. The Author. Engelmann (G.) Botanical Works. Edited by W. Trelease, and Asa Gray. 4to. Cambridge, Mass. 1887. Mr. Henry Shaw, St. Louis. Grimaux (E.) Lavoisier 1743-1784. 8vo. Paris 1888. Prof. E. Grimaux. Huygens (C.) Œuvres Complètes de Christiaan Huygens. Tome I. 4to. La Haye 1888. Société Hollandaise des Sciences. Jones (T. R.), F.R.S., and C. D. Sherborn. On some Ostracoda from the Fullers-Earth Oolite and Bradford Clay. 8vo. [Bath 1888.] The Authors. Martone (M.) Dimostrazione della Trascendenza del Numero. 8vo. Napoli 1888; Nota ad una Dimostrazione di un Celebre Teorema del Fermat. 8vo. Napoli 1888. The Author. Scott (A.), and L. Atkinson. A Short History of Diamond Cutting. 12mo. London [1888]. The Authors. Vial (E.) La Ramie et son Traitement. 8vo. Paris 1888. The Author. Wimshurst (J.) Electric Influence Machines. 4to. London 1888. The Author. VOL. XLIV. 2 H "On the Relations of the Diurnal Barometric Maxima to certain critical Conditions of Temperature, Cloud, and Rainfall." By HENRY F. BLANFORD, F.R.S. Received March 30,--Read May 3, 1888. It is not my purpose in this paper to discuss the general problem of the diurnal barometric variation. It is certainly a very complex phenomenon, and one of which no satisfactory analysis has yet been made. The atmospheric stress (whatever be its nature) that originates the oscillation, is followed by movements which alter both the vertical and horizontal distribution of the gravitating mass, and the striking differences that characterise the diurnal curve of pressure on mountain peaks, plains, and valleys, and on the ocean as compared with the land, are doubtless due in a large measure to these resulting redistributions of the mass. Amid all the recorded variations of the oscillation as a whole, the feature that displays the greatest constancy is the occurrence of a maximum in some hour of the forenoon, and of a second maximum one or two hours before midnight. The exceptional cases, in which these two critical phases are much shifted from their normal positions, are but few, and may probably all be explained by gravitation effects being superadded to the normal semidiurnal oscillation. One of the most anomalous forms of the diurnal oscillation yet recorded is that given by Professor Mohn, for the North Atlantic, between latitudes 62° and 80°, in the summer months.* The general form of this pressure curve is similar to that of the diurnal temperature curve. It falls to a minimum in the early morning hours, and rises to a maximum between 1 h. and 3 h. 30 m. P.M. But of the three curves for different years and latitudes given by Professor Mohn, two show, as a subordinate feature, a small rise to a secondary maximum, between 10 and 11 P.M., and two an irregularity in the morning rise, such as would result from a small wave with a maximum about 7 or 8 A.M., in combination with the principal oscillation of twenty-four hours' period. At Christiania and Upsala the phases of the single period oscillation are reversed, the maximum being in the night, the minimum in the day, but the semidiurnal element exhibits characters similar to those of the North Atlantic curve. This comparative constancy of the semidiurnal element of the oscillation, which was originally pointed out by Lamont,t seems to indicate that it depends more directly on the action of the sun than * Norske Nordhavs Expedition,' 1876–1878. +Sitzungsber. d. Bayerisch. Akademie,' 1862, vol. 1, p. 89. does the diurnal element, and that its explanation is a first necessary step to that of the whole phenomenon. The object of the present paper is to draw attention to the approximate coincidence of its maximum phases with certain critical phases of temperature, cloud, and rainfall, which may at least help to throw some light on its physical causes. Forenoon Maximum. It was noticed independently by Espy, in 1840, Davies, in 1859,† and Kreil, in 1861, that the forenoon maximum of the barometric oscillation approximately coincides with the most rapid rise of temperature, and each of these writers attributed the rise of pressure to the reactionary effect of the heated and expanding atmosphere. The only data, however, given by any of them in support of the statement are the horary variations of the temperature and pressure at Prague, by Kreil, and a rough diagram of the diurnal curves at Padua, by Davies; and shortly after the publication of Kreil's paper, the subject was very fully discussed by Lamont, in the paper already referred to in the Sitzungsberichte' of the Bavarian Academy, wherein he showed that, on the ordinary assumption that the atmosphere is free to expand in a vertical direction, against no other resistance than the static pressure of the superincumbent mass, the supposed reactionary effect would be inappreciable. Since the publication of Lamont's paper, I am not aware that any physicist has paid further attention to the hypothesis in question, or thought it worth while to appeal to further evidence in verification of the observation on which it is based, until quite recently. But in 1876, in noticing the subject of the barometric oscillation in the 'Indian Meteorologist's Vade Mecum,' it occurred to me that Lamont's assumption that the atmosphere is free to expand vertically, lifting the superincumbent mass, is subject to an important modification which may greatly alter the conditions of the problem as contemplated by him. These conditions take no account of the resistance to expansion that must be opposed by the highly attenuated but extremely cold external atmospheric strata of great but unknown thickness, the existence of which is proved by the phenomena of luminous meteors. If a sheet of the atmospheric envelope, of indefinite horizontal extent, resting on the earth's surface, be heated and charged with vapour, the first effect will be an increase of its elastic tension, which will be relieved by a wave of elastic compression transmitted to the Brit. Assoc. Rep.,' 1840, Part II, p. 55. + Edinburgh Phil. Journ.,' vol. 10, 1859, p. 225. overlying strata. Having regard to the slow rate at which this wave is generated, the rise of temperature, even in such a climate as that of Northern India, not exceeding 5° or 6° in the hour of most rapid heating, equivalent to an increment of less than th of the initial pressure, it appears to me that the rate of propagation will be sensibly that due to half the height of a homogeneous atmosphere, or a little more than two-thirds the rate of the sound-wave. This rate will be continually retarded as the wave advances through the loftier and colder strata, being proportional to the square root of the absolute temperature of each stratum. And it will depend on the thickness of the atmospheric sheet heated, the amount of the heating, and on the thickness and temperature of the cold external strata, whether the retardation may not be such as to allow of the tension of the lower strata becoming such as is indicated by the barometer at the time of the forenoon maximum, Under such circumstances, the instant of maximum pressure should coincide with that of the most rapid rise of temperature and vaporisation. I do not think that our knowledge of any of these fundamental conditions is such as to justify a rejection of the hypothesis on à priori grounds, and it may therefore be worthy of inquiry how far it is in accordance with verifiable observation. At Calcutta, the atmospheric pressure at 9 h. 30 m, A.M. is about th greater than at the time of the morning minimum; an increase which would be produced by heating the air in a closed vessel less than 2°. A retardation of about half an hour in the dissipation of the increased pressure produced by heating and evaporation would suffice to produce the observed effect. Dr. Sprung, in his admirable manual, the 'Lehrbuch der Meteorologie,' published in 1885, has referred to the above hypothesis, and has tested the coincidence of the critical phases of temperature and pressure by the summer results of the hourly observations and autographic registers of the Prague Observatory, from 1842 to 1861, which have been recomputed by Professor Augustin. The result of this test appears to be satisfactory. At Prague, on the mean of the summer months, the forenoon barometric maximum occurs a little after 8 A.M., and nearly coincides with the most rapid rise of temperature.t In India there is no station at which the forenoon maximum falls at so early an hour at any season; but at Yarkand and Kashghar, according to Dr. Scully's valuable observations, in the summer, it occurs even earlier than at Prague, while in the winter it is as late as the mean epoch at Calcutta. It is true we have only fifteen series of *Op. cit., p. 336. + As computed from the figures given by Dr. Sprung, by the application of the method of differences (see footnote below), the barometric maximum occurs nineteen minutes later than the instant of most rapid heating. hourly readings for the winter months, November to February, taken at intervals of seven or eight days, and but eight series for June and July, but so regular is the march of the diurnal variation both of temperature and pressure in this climate, that even these suffice to show the distinctive characters of the curves at both seasons. The observations have been published at length in the first volume of the 'Indian Meteorological Memoirs.'* To eliminate small irregularities, corrected hourly values have been computed from these by means of the harmonic formula. A very exact determination of the critical phases cannot of course be expected from such data, but according to the method of computation adopted,† the epochs of the forenoon pressure maximum and of most rapid heating are as follow at the two * Op. et vol. cit., p. 94, et seq. + Throughout this paper the time of most rapid heating has been determined in the following manner: in general, from the uncorrected means of the observations, which, for the reasons shown by Dr. Bergsma ('Batavia Mag. and Met. Obs.,' vol. 1, p. xvii) and in accordance with my own experience and that of other Indian meteorologists, if the observations are sufficiently extensive, are more trustworthy than the so-called corrected values obtained by computing them from three or four terms of the harmonic formula. The instant of most rapid rise of temperature may be ascertained by twice differentiating for the values of t the formula which expresses the temperature as a function of the time t, and putting The most convenient formula for this purpose is that of the method of differences employed by Dr. Jelinek for obtaining the approximate times of the maximum and minimum phases of temperature, pressure, &c. On taking the first, second, and third differences of the temperatures at the clock hours, two before and two after the instant of most rapid rise, the hour in which this occurs is shown by the change of algebraical sign of the second order of differences. Denoting that which precedes this change by ▲, and the differences of the first and third order next following in order of sequence by A' and A'3, the second differentiation of the formula which value of t reckons from the clock hour corresponding to A2. The epoch thus obtained has an error of a few minutes only, and is quite accurate enough for the present purpose. |