On the Lunar Atmospheric Tide at Singapore

IX. On the Lunar Atmospheric Tide at Singapore. By Captain C. M. Elliot, Madras Engineers, F.R.S. Received December 18, 1851,—Read March 11, 1852. At the commencement of the year 1847, a paper by Colonel Sabine, R.A., V.P.R.S., was read before the Royal Society on the Lunar Atmospheric Tide at St. Helena. The influence of the moon upon the barometer, although small in amount, was shown in a very striking and decided manner; for after eliminating the regular diurnal variation, the differences arranged in lunar tables showed a decided maximum, both at the superior and inferior culmination of the moon, and a decided minimum at its rising and setting. The effect which the moon’s position, relatively to the meridian of the place, had upon the barometric pressure, was publicly noticed, about the middle of 1842, by Captain Lefroy, R.A., who appears to have had his attention directed to it from the first establishment of the observatory at St. Helena. On the receipt of Colonel Sabine’s paper, I was anxious to ascertain if the fact of the moon’s influence, so clearly and decidedly shown at St. Helena, could be similarly proved by the Singapore barometric observations. I therefore determined, before leaving England for India, to proceed upon the plan adopted by Colonel Sabine, and in order that a comparison might be made between the results at Singapore and at St. Helena, have copied to a considerable extent the form of the different lunar tables drawn up by him in his very valuable paper. The observatory at Singapore was in latitude $1^\circ 18' 32''$ north, and longitude $103^\circ 56' 30''$ east of Greenwich. The cistern of the barometer was a few feet above high-water mark: the barometer was made by Newman: the diameter of the tube = $0.532$ inch. The observations of the barometer, by my assistants, were made at every two hours during the whole of 1841, the early part of 1842, and that of 1843; during the rest of the time, to the close of 1845, at every hour. In making out the Tables, showing the moon’s effect upon the barometer, I have only taken complete astronomical days, from noon to noon; and as Sundays were omitted, and as the observations commenced at midnight on Sunday and terminated at 11 p.m. on Saturday, the broken portions of Monday and of Saturday have not been taken into consideration; the mean, however, of the entire month has been assumed to be identical with the mean of these complete days. The Barometer Tables, corrected to $32^\circ$, having been made out, the mean monthly height of the barometer at each hour was deducted from the height given by observation at the corresponding hours during the month; if the height of the barometer, at any hour of observation, was less than the mean height at that hour, the difference was put down with the sign—; if greater, with the sign +. By this process the diurnal variation was eliminated. The residual quantities were then arranged in Tables, and the observation corresponding the nearest in time to the moon's culmination being marked for each day, the whole were again re-arranged in lunar tables as follows: The moon's superior culmination was assumed as 0 hour of lunar time, and the differences corresponding to that hour placed in the first column; the remaining columns were similarly formed. The means of the sums of these differences are exhibited in Table I., which consists of two parts, the first part containing the barometric differences at the lunar hours from the superior to the inferior passage, and the second part, from the inferior to the superior passage; the means for each period of six months are shown in the final column of the second part of the Table. Table II. shows the differences between the mean results and the several numbers in Table I. It must be borne in mind, that had the sets of weekly observations been complete, the sum of the minus differences would have equalled the plus ones: this, however, is not the case owing to the omissions above noted, and an inequality is thereby produced which occasioned the formation of Table I., in which the range of the mean values is shown, the lowest number being assumed as zero. The means of the complete years 1841, 1844 and 1845, are shown in Table III.; and as two-hourly observations were taken during the first six months of 1842 and of 1843*, and hourly observations during the latter portions of those years, the results of the first six months of 1842 have been combined with the first six months of 1843, and the hourly observations of the latter halves of these years have been combined for the same reason. In Table IV. the whole of the two-hourly observations, for a period of twenty-four months, have been added together for a general mean, and similarly the whole of the hourly observations for a period of thirty-six months. The results are exhibited in Plate X., which is drawn to '001 of barometric pressure to 0'74 of an inch of scale. Finally, Table V. exhibits the observations of three years combined, so as to show the effect upon the barometer of the moon when similarly situated both in its superior and inferior passage; and in a column in juxtaposition is placed a similar table derived from two years' observation at St. Helena, extracted from Colonel Sabine's valuable paper on the subject; from which it will be observed that the effect produced by the moon upon the barometer at Singapore, in the vicinity of the Equator, is slightly greater than at St. Helena, more distant by $14\frac{1}{2}$ degrees of latitude. * In 1843, in consequence of a deficiency in the number of assistants. With respect to the oceanic tide, the difference between rise and fall at spring tides varies from 9 to 12 feet. The establishment of the port is about 10\(^{h}\) 50\(^{m}\) A.M. ### Table I. Mean Barometrical Differences at the several Lunar Hours. #### 1st Part. From the Superior to the Inferior Passage. | Mean of each of the Lunar Hours. | 0. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | |---------------------------------|----|----|----|----|----|----|----|----|----|----|-----|-----| | First part of 1841 | -00603 | -00540 | -00107 | -00077 | -00176 | -00332 | | Second part of 1841 | -00619 | -00442 | -00239 | -00184 | -00369 | -00445 | | First part of 1842 | -00599 | -00470 | -00214 | -00075 | -00000 | -00264 | | Second part of 1842 | -00796 | -00685 | -00568 | -00473 | -00315 | -00085 | -00061 | -00000 | -00103 | -00326 | -00355 | -00625 | | First part of 1843 | -00372 | -00411 | -00191 | -00020 | -00031 | -00039 | | Second part of 1843 | -00728 | -00612 | -00502 | -00391 | -00365 | -00135 | -00000 | -00129 | -00138 | -00324 | -00199 | -00278 | | First part of 1844 | -00551 | -00533 | -00405 | -00376 | -00304 | -00050 | -00000 | -00030 | -00141 | -00365 | -00509 | -00739 | | Second part of 1844 | -00882 | -00827 | -00702 | -00641 | -00390 | -00173 | -00004 | -00064 | -00128 | -00215 | -00273 | -00351 | | First part of 1845 | -00674 | -00440 | -00253 | -00150 | -00113 | -00000 | -00100 | -00025 | -00114 | -00277 | -00305 | -00422 | | Second part of 1845 | -00774 | -00829 | -00611 | -00571 | -00280 | -00199 | -00024 | -00015 | -00161 | -00341 | -00411 | -00526 | #### 2nd Part. From the Inferior to the Superior Passage. | Mean of each of the Lunar Hours. | 12. | 13. | 14. | 15. | 16. | 17. | 18. | 19. | 20. | 21. | 22. | 23. | |---------------------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | First part of 1841 | -00468 | -00500 | -00539 | -00069 | -00000 | -00000 | -00397 | -00294 | | Second part of 1841 | -00723 | -00394 | -00113 | -00000 | -00097 | -00040 | -00358 | | First part of 1842 | -00431 | -00552 | -00286 | -00178 | -00092 | -00490 | -00321 | | Second part of 1842 | -00807 | -00734 | -00625 | -00499 | -00409 | -00325 | -00253 | -00313 | -00456 | -00567 | -00690 | -00446 | | First part of 1843 | -00301 | -00505 | -00278 | -00000 | -00000 | -00052 | -00163 | -00261 | | Second part of 1843 | -00618 | -00915 | -00424 | -00600 | -00444 | -00344 | -00178 | -00156 | -00265 | -00179 | -00513 | -00303 | | First part of 1844 | -00812 | -00592 | -00671 | -00501 | -00290 | -00000 | -00065 | -00171 | -00271 | -00353 | -00471 | -00356 | | Second part of 1844 | -00505 | -00456 | -00348 | -00192 | -00100 | -0008 | -00000 | -00162 | -00229 | -00338 | -00428 | -00315 | | First part of 1845 | -00553 | -00411 | -00282 | -00286 | -00269 | -00110 | -00086 | -00158 | -00116 | -00288 | -00406 | -00530 | | Second part of 1845 | -00641 | -00555 | -00333 | -00200 | -00111 | -00014 | -00000 | -00031 | -00043 | -00259 | -00437 | -00546 | ### Table II. Numerical Values of the excess or defect of the Barometric Differences at the several Lunar Hours. #### 1st Part. From the Superior to the Inferior Passage. | Lunar Hours. | 0. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | |--------------|----|----|----|----|----|----|----|----|----|----|-----|-----| | First part of 1841 | +0031 | +0025 | -0020 | -0022 | -0012 | +0004 | | Second part of 1841 | +0026 | +0008 | -0006 | -0017 | +0001 | +0010 | | First part of 1842 | +0028 | +0015 | -0011 | -0005 | -0039 | -0006 | | Second part of 1842 | +0033 | +0024 | +0012 | +0003 | -0036 | -0045 | -0012 | -0009 | +0018 | | First part of 1843 | +0011 | +0015 | -0007 | -0006 | +0005 | +0011 | | Second part of 1843 | +0040 | +0029 | +0018 | +0007 | +0004 | -0019 | -0018 | -0010 | -0012 | -0004 | | First part of 1844 | +0019 | +0018 | +0005 | +0002 | -0005 | -0031 | -0036 | -0053 | -0021 | +0001 | +0020 | +0038 | | Second part of 1844 | +0055 | +0049 | +0057 | +0031 | +0006 | +0016 | +0053 | +0027 | -0021 | -0012 | -0006 | -0002 | | First part of 1845 | +0041 | +0017 | -0002 | -0012 | -0015 | -0027 | -0011 | -0024 | -0015 | +0001 | +0004 | +0016 | | Second part of 1845 | +0044 | +0049 | +0028 | +0024 | -0006 | -0014 | -0031 | -0032 | -0017 | +0001 | +0008 | +0019 | 2nd Part. From the Inferior to the Superior Passage. | Lunar Hours | 12. | 13. | 14. | 15. | 16. | 17. | 18. | 19. | 20. | 21. | 22. | 23. | |-------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | First part of 1841 | +0017 | +0021 | +0003 | -0022 | -0029 | +0010 | | Second part of 1841 | +0036 | +0024 | -0024 | -0036 | -0026 | -0005 | | First part of 1842 | +0011 | +0023 | -0003 | +0005 | -0004 | -0012 | -0019 | -0013 | +0001 | +0024 | | Second part of 1842 | +0036 | +0029 | +0018 | +0018 | +0005 | -0012 | -0019 | -0013 | +0001 | +0024 | | First part of 1843 | +0004 | +0025 | -0002 | -0026 | -0021 | -0013 | | Second part of 1843 | +0005 | +0009 | +0002 | +0028 | +0012 | +0002 | -0014 | -0019 | -0017 | -0006 | -0014 | +0019 | | First part of 1844 | +0046 | +0034 | +0028 | +0023 | +0001 | +0016 | -0027 | -0035 | -0017 | -0008 | -0002 | +0002 | | Second part of 1844 | +0003 | +0012 | +0001 | -0014 | -0023 | -0025 | -0032 | -0017 | -0001 | -0000 | +0009 | +0028 | | First part of 1845 | +0029 | +0014 | +0002 | +0002 | +0000 | -0016 | -0018 | -0011 | -0015 | +0002 | +0013 | +0026 | | Second part of 1845 | +0031 | +0022 | 0000 | -0013 | -0022 | -0032 | -0033 | -0028 | -0029 | -0008 | +0010 | +0031 | Table III. Excess or Defect of the Barometric Differences at the several Lunar Hours shown in Annual Means. 1st Part. From the Superior to the Inferior Passage. | Lunar Hours | 0. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | |-------------|----|----|----|----|----|----|----|----|----|----|-----|-----| | 1841 | +0028 | +0016 | -0013 | -0020 | -0005 | +0007 | | First part of 1842, and first part of 1843 | +0020 | +0015 | -0009 | -0006 | -0013 | +0003 | | Second part of 1842, and second part of 1843 | +0036 | +0026 | +0015 | +0005 | -0008 | -0027 | -0035 | -0032 | -0026 | -0011 | -0010 | +0007 | | 1844 | +0037 | +0032 | +0021 | +0016 | -0000 | -0024 | -0034 | -0030 | -0021 | -0005 | +0007 | +0020 | | 1845 | +0042 | +0033 | +0014 | +0006 | -0010 | -0020 | -0021 | -0028 | -0016 | +0001 | +0006 | +0018 | 2nd Part. From the Inferior to the Superior Passage. | Lunar Hours | 12. | 13. | 14. | 15. | 16. | 17. | 18. | 19. | 20. | 21. | 22. | 23. | |-------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | 1841 | +0026 | +0022 | -0010 | -0029 | -0027 | +0007 | | First part of 1842, and first part of 1843 | +0008 | +0024 | -0003 | -0024 | -0022 | +0002 | | Second part of 1842, and second part of 1843 | +0020 | +0019 | +0010 | +0023 | +0008 | -0001 | -0013 | -0019 | -0015 | -0003 | -0001 | +0002 | | 1844 | +0021 | +0023 | +0013 | +0004 | -0011 | -0020 | -0030 | -0026 | -0009 | -0004 | +0004 | +0015 | | 1845 | +0030 | +0018 | +0001 | -0005 | -0011 | -0024 | -0026 | -0020 | -0022 | -0003 | +0012 | +0029 | Table IV. Excess or Defect of the Barometric Differences at the several Lunar Hours as severally deduced from Hourly and 2-Hourly Observations. 1st Part. From the Superior to the Inferior Passage. | Lunar Hours | 0. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | |-------------|----|----|----|----|----|----|----|----|----|----|-----|-----| | Mean of two years | +0024 | +0015 | -0011 | -0013 | -0009 | +0005 | | Mean of three years | +0038 | +0030 | +0017 | +0009 | -0006 | -0024 | -0030 | -0021 | -0005 | +0001 | +0015 | 2nd Part. From the Inferior to the Superior Passage. | Lunar Hours | 12. | 13. | 14. | 15. | 16. | 17. | 18. | 19. | 20. | 21. | 22. | 23. | |-------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | Mean of two years | +0.017 | +0.023 | -0.007 | -0.0025 | -0.0025 | -0.0025 | -0.0005 | +0.0004 | +0.0022 | | Mean of three years | +0.024 | +0.0020 | +0.0008 | +0.0007 | -0.0005 | -0.0015 | -0.0023 | -0.0022 | -0.0015 | -0.0003 | +0.0004 | +0.0022 | Table V. Mean Variation of Barometric Pressure deduced from the Hourly Observations. | Moon's distance from the meridian | Variations of barometric pressure | Hourly variations | |----------------------------------|----------------------------------|------------------| | | At the hours following the meridian passage. | At the hours preceding the meridian passage. | | | From the observations at the hours following the meridian passage. | From the observations at the hours preceding the meridian passage. | | | Mean of three years at Singapore. | Mean of two years at St. Helena. | | | Moon's distance from the meridian. | | h | h in. in. | h in. in. | in. in. | in. in. | in. in. | in. in. | | 0 | 0 +0.0038 | +0.0031 | 0 +0.0038 | +0.0031 | +0.0057 | +0.0057 | +0.00570 | +0.00365 | 0 | | 1 | 12 +0.0024 | +0.0031 | 12 +0.0024 | +0.0031 | +0.0057 | +0.0057 | +0.00570 | +0.00365 | 1 | | 2 | 13 +0.0020 | +0.0025 | 13 +0.0020 | +0.0025 | +0.0051 | +0.0044 | +0.00475 | +0.00336 | 2 | | 3 | 2 +0.0017 | +0.0012 | 2 +0.0017 | +0.0012 | +0.0038 | +0.0028 | +0.00330 | +0.00275 | 3 | | 4 | 3 +0.0009 | +0.0008 | 3 +0.0009 | +0.0008 | +0.0034 | +0.0022 | +0.00280 | +0.00158 | 4 | | 5 | 4 +0.0007 | +0.0008 | 4 +0.0007 | +0.0008 | +0.0034 | +0.0022 | +0.00280 | +0.00158 | 5 | | 6 | 5 +0.0005 | +0.0005 | 5 +0.0005 | +0.0005 | +0.0021 | +0.0008 | +0.00145 | +0.00110 | 6 | | | 6 +0.0004 | +0.0004 | 6 +0.0004 | +0.0004 | +0.0021 | +0.0008 | +0.00145 | +0.00110 | 7 | | | 7 +0.0003 | +0.0003 | 7 +0.0003 | +0.0003 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 8 | | | 8 +0.0002 | +0.0002 | 8 +0.0002 | +0.0002 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 9 | | | 9 +0.0001 | +0.0001 | 9 +0.0001 | +0.0001 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 10 | | | 10 +0.0000 | +0.0000 | 10 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 11 | | | 11 +0.0000 | +0.0000 | 11 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 12 | | | 12 +0.0000 | +0.0000 | 12 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 13 | | | 13 +0.0000 | +0.0000 | 13 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 14 | | | 14 +0.0000 | +0.0000 | 14 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 15 | | | 15 +0.0000 | +0.0000 | 15 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 16 | | | 16 +0.0000 | +0.0000 | 16 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 17 | | | 17 +0.0000 | +0.0000 | 17 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 18 | | | 18 +0.0000 | +0.0000 | 18 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 19 | | | 19 +0.0000 | +0.0000 | 19 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 20 | | | 20 +0.0000 | +0.0000 | 20 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 21 | | | 21 +0.0000 | +0.0000 | 21 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 22 | | | 22 +0.0000 | +0.0000 | 22 +0.0000 | +0.0000 | +0.0018 | +0.0008 | +0.00145 | +0.00110 | 23 |