On a Cycle of Eighteen Years in the Mean Annual Height of the Barometer in the Climate of London, and on a Constant Variation of the Barometrical Mean according to the Moon's Declination

XIX. On a Cycle of Eighteen Years in the Mean Annual Height of the Barometer in the Climate of London, and on a constant variation of the Barometrical Mean according to the Moon's Declination. By Luke Howard, Esq., F.R.S. Received February 4,—Read March 11, 1841. I HAVE already treated this subject, partially and in detail, in the 'Climate of London*.' The further and full development of it in that way will be found an undertaking more of labour than of difficulty, the materials being already provided for doing this through a lunar cycle of eighteen years; but I am enabled, by means of these, to present to the Royal Society some general results, which will prove interesting, and probably important to the science to which they belong. The like method has been adopted in this paper as in my two former, read before the Society, on the connexion of the barometric variation with the Lunar Phases and Apsides. I have excluded, by appropriate averages, those effects of the lunar influence which belong not to the subject immediately before us. These, however, will require, whosoever we may think it time to form a theory, to be examined conjointly with the present and every other of the elements of this intricate subject. Table I. Barometrical Averages on successive Solar Years, from 1815 to 1832, constructed to show the Moon's influence on the Mean Heights, varying according to her Declination: for the manner of forming which, see the remainder of this paper. | Year | Days' observations | Annual mean | Moon in or near the equator | Moon at or near her greatest north declination | Moon in or near the equator | Moon at or near her greatest south declination | Averages on nine years | |------|-------------------|-------------|-----------------------------|-----------------------------------------------|-----------------------------|-----------------------------------------------|-----------------------| | 1815 | 370 | 29-766 | 29-8391 | 29-7819 | 29-7947 | 29-8880 | | | 1816 | 368 | 29-648 | 29-7883 | 29-7128 | 29-7046 | 29-8357 | | | 1817 | 362 | 29-733 | 29-7908 | 29-8590 | 29-8420 | 29-7499 | | | 1818 | 369 | 29-836 | 29-8116 | 29-8649 | 29-8363 | 29-8348 | | | 1819 | 361 | 29-831 | 29-7930 | 29-8168 | 29-9287 | 29-7106 | | | 1820 | 369 | 29-839 | 29-8014 | 29-8020 | 29-9363 | 29-8622 | | | 1821 | 362 | 29-805 | 29-8206 | 29-9085 | 29-7880 | 29-7044 | | | 1822 | 362 | 29-889 | 29-8543 | 29-8472 | 29-9354 | 29-9426 | | | 1823 | 369 | 29-763 | 29-8040 | 29-8436 | 29-6741 | 29-7203 | | | 1824 | 368 | 29-878 | 29-9788 | 29-9126 | 29-9129 | 29-7546 | | | 1825 | 362 | 29-987 | 30-0823 | 30-0285 | 29-8932 | 29-9933 | | | 1826 | 369 | 30-033 | 30-0899 | 30-0213 | 29-9959 | 29-9910 | | | 1827 | 362 | 29-938 | 29-9374 | 29-8875 | 29-9218 | 29-9829 | | | 1828 | 363 | 29-814 | 29-8590 | 29-7532 | 29-7990 | 29-8608 | | | 1829 | 363 | 29-688 | 29-6838 | 29-6563 | 29-6857 | 29-7002 | | | 1830 | 368 | 29-671 | 29-7404 | 29-6902 | 29-6604 | 29-6900 | | | 1831 | 362 | 29-653 | 29-6351 | 29-6310 | 29-6700 | 29-5968 | | | 1832 | 363 | 29-702 | 29-6480 | 29-8210 | 29-7293 | 29-6830 | | The averages on successive periods of nine years in the last column exhibit the barometrical mean, increasing and decreasing, as follows:—29·8111 + 0124 + 0266 + 0222 + 0125 = 29·8848 — 0019 — 0168 — 0149 — 0262 = 29·8250 inch. Then, to complete the cycle, 29·8250 — 0139 = 29·8111 inch. * Vol. i. p. 172. 2nd Edition. ### Table II. Barometrical Averages on successive Cycles of nine Solar Years, classed according to the Moon’s place in Declination. | Periods taken | 1. Moon at or near equator, and going north. | 2. Moon at or near her greatest north declination. | 3. Moon at or near equator, and going south. | 4. Moon at or near her greatest south declination. | 5. Averages on whole periods of nine years. | 6. Averages on the four results preceding. | |---------------|---------------------------------------------|-------------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------|---------------------------------------------| | | in. | in. | in. | in. | in. | in. | | 1815–23 | 29·8114 | 29·8263 | 29·8267 | 29·8054 | 29·8173 | 29·8174 | | 1816–24 | 29·8270 | 29·8408 | 29·8398 | 29·7794 | 29·8059 | 29·8218 | | 1817–25 | 29·8596 | 29·8759 | 29·8608 | 29·8081 | 29·8366 | 29·8511 | | 1818–26 | 29·8929 | 29·8939 | 29·8779 | 29·8349 | 29·8577 | 29·8749 | | 1819–27 | 29·9069 | 29·8964 | 29·8873 | 29·8513 | 29·8696 | 29·8856 | | 1820–28 | 29·9142 | 29·8927 | 29·8729 | 29·8680 | 29·8691 | 29·8870 | | 1821–29 | 29·9011 | 29·8765 | 29·8451 | 29·8500 | 29·8518 | 29·8682 | | 1822–30 | 29·8922 | 29·8523 | 29·8304 | 29·8484 | 29·8372 | 29·8560 | | 1823–31 | 29·8678 | 29·8282 | 29·8014 | 29·8100 | 29·8123 | 29·8269 | | 1824–32 | 29·8505 | 29·8257 | 29·8076 | 29·8058 | 29·8076 | 29·8225 | Mean by the columns: 29·8724 29·8608 29·8450 29·8261 29·8365 29·8511 The averages presented at the foot of columns 1 to 4, show a decrease in the barometrical mean, consequent on the moon’s varying positions in declination, which may be thus stated: 29·8724 in. on equator, minus by north place, ‘0116 in.; again, minus by passage of equator south, ‘0158 in.; again, minus by south place, ‘0189 in.; lastly, plus by return north over equator, ‘0463 in. The averages in columns 5 and 6 exhibit the barometrical mean, increasing and decreasing with great regularity, during the course of a lunar cycle of eighteen years. The averages which form the two Tables before us were obtained in the following manner: 1. The year was divided, by an ephemeris, into periods of lunar declination, the whole set in each case including not less than 361, nor more than 370 days. 2. These periods of declination were subdivided into weeks (or spaces of from six to eight days, generally seven) with the moon’s extreme north, her extreme south, and her respective positions on the equator, coming and going, placed as nearly as might be in the midst of the space on which the average was taken—to wit, the average of the medium heights of the barometer for each twenty-four hours of the space. 3. These weekly averages, obtained generally from the curves inscribed by the barometer, on the face of a clock by Cumming, in my possession, were then placed under their respective heads of the four positions of the moon above-mentioned. 4. They were then laid together for the whole year, or for the number of days necessarily so accounted, which numbers make an average of 365½ days to the year. 5. Averages were, lastly, taken under the respective heads of north, south, &c. on successive periods of nine years, as 1815–23, 1816–24, &c., the series beginning 23rd December 1814, and ending 19th December 1832. These results occupy the four leading columns of the second Table; the preceding are in Table I. 6. The leading column in Table I. contains a set of annual barometrical means taken (with the exception of the last) from those I have already published in the 'Climate of London.' These are calculated from the Tables for each month in the ordinary way, and not on the solar years. I have given them as they stand in that work, though in the years from 1815 to 1817 they ought possibly to be higher by a tenth of an inch, from the too high placing the scale in those years; but this (with other like inaccuracies which may be hereafter found and rectified) I do not consider as affecting much the proportions found among the results in any given year. In calculating the set of averages on periods of nine years, placed in the last column of this Table, I have, however, to prevent discrepancies, added this tenth of an inch upon each of the three years. 7. The fifth column of Table II. contains the barometrical mean, calculated upon the whole period of solar years, which, in the four preceding columns, are averaged under the respective lunar positions of north, south, &c. The sixth column of this Table shows a mean founded on a direct average of the four results placed under these heads. I have noticed some features of the variation at the foot of the Tables. I shall proceed now to state some general results, of course as to the barometer alone. The effects on the mean temperature and rain must for the present be left unnoticed. The barometrical mean in our climate is depressed (on an average of years) by the moon's position in south declination. In every one of these averages upon periods of nine years, in Table II., the mean under south is lower than that under north declination; the difference being in some cases between six and seven hundredths of an inch: and it is larger on the averages in the fore-part than on those in the latter part of the series. The mean under south declination is also lower than either of the other three; with exception of the four latter averages, in which it exceeds a little that of the position "going south." This depression is gradual: it commences with the moon in full north declination, and proceeds through her remaining positions to the time when she again crosses the equator to return north; at which season the whole weight that had been abstracted is suddenly restored—this of course must be understood of the small differences in the mean here treated. There will be found, in the observations employed, an abundance of particular cases of variation which contradict such a rule, but the compensations, it appears, cover these in its favour. We have here, I think, evidence of a great tidal wave or swell in the atmosphere, caused by the moon's attraction, preceding her in her approach to us, and following slowly as she departs from these latitudes. Were the atmosphere a calm fluid ocean of air of uniform temperature, this tide would be manifested with as great regularity as are those of the ocean of waters. But the currents, uniformly kept up by the sun's varying influence, effectually prevent this, and so complicate the problem. There is also manifest in the lunar influence a gradation of effects, which is here shown, as it is found to operate through a cycle of eighteen years. In these, the mean weight of our atmosphere increases through the fore-part of the period; and, having kept for a year at the maximum it has attained, decreases again through the remaining years to a minimum; about which there seems to be some fluctuation, before the mean begins to rise again. This result is brought out in different ways by all the averages upon years; and it pervades, though with less of uniformity, those upon the quarter periods or weeks of declination. The study of these, with a view to theory, rude and imperfect as they are, may become, I would willingly hope, an occupation for those more capable and better prepared than myself to grapple with the subject. February 3, 1841. L. H.