Observations Made with the Invariable Pendulum (No. 4. Jones), at the Royal Observatory, Cape of Good Hope, for the Purpose of Determining the Compression of the Earth

XI. Observations made with the invariable pendulum (No. 4. Jones), at the Royal Observatory, Cape of Good Hope, for the purpose of determining the compression of the earth. By the Rev. Fearon Fallows, F.R.S. Astronomer of the Cape Observatory. Communicated by the Lords Commissioners of the Admiralty. Read February 18, 1830. The important problem of ascertaining the ellipticity of the earth has, for a long time past, drawn forth the talents and labours of some of the most scientific men in Europe; and it still continues to be deemed an object of especial regard by all who feel an interest in the promotion of natural knowledge. To attempt to depict the strenuous exertions, the innumerable fatigues, the ardour for the improvement of science, which actuated so many illustrious persons in endeavouring to discover the true figure of the earth, would only be a waste of time; as learned Societies have always recognised and stamped the due meed of merit to each, and invariably appreciated and published to the world the valuable results which have with so many difficulties been obtained. The nations of Europe, emulous of each other in a work which particularly distinguishes the acquirements of modern times, have encouraged and laudably given their protection and sanction to eminent individuals engaged in undertakings so conducive to the honour of an enlightened community. Whatever difference of opinion may exist as to the respective values to be attached to observations in the admeasurement of an arc of the meridian, or by the variation in the lengths of the seconds pendulum made in different latitudes, there can be no doubt that the former has this paramount advantage; that certain fixed points are determined, by which the geography of a country is considerably promoted, and at length brought as nearly as possible to perfection: whilst the latter method possesses a superiority in being able to concentrate under the immediate eye of the observer the results of his inquiries, which are readily obtained, and easily performed and accomplished. The Lords Commissioners of the Admiralty having furnished this observatory with the invariable pendulum (No. 4. Jones), which had for several years been most strictly examined by Captain Sabine at Mr. Browne's, in Portland Place, London, and subsequently by the same learned gentleman in the course of his inquiries in different parts of the earth, I wished at the earliest opportunity to have a series of experiments made upon it, which might unite every possible degree of accuracy on the part of the observers, as well as the utmost stability in the structure intended for supporting the pendulum. From many unforeseen circumstances, I found at length that the completion of this observatory would be delayed for a considerable time, though previously I had, too fondly perhaps, anticipated finishing it at a much earlier period; and I therefore took advantage of a small out-house (then of no further use) within a short distance of the building, to erect a stout brick pier, well bonded, for the support of the small transit instrument; the same which I used in forming my catalogue of 273 southern stars reduced to the beginning of 1824. Temporary chases were made for meridian observations; and the recess for the clock (Molyneux's*) and pendulum was soon constructed in a most substantial manner within a few feet of the transit. The top of this recess consisted of a thick strong Robben-Island stone, perforated in the middle, and chiselled out at the upper part, for the reception of the brass plate containing the agate planes upon which the knife-edges of the pendulum rest. This plate was securely fastened to the stone with cement; and I found that when the agates were once truly adjusted to level, they remained (with one exception only, and I think this might be attributed to some error in one of the small levels,) during the whole of the observations that succeeded. It is hardly worthy of remark that at the end of each day's work the knife-edges were screwed up from the agates, and remained so till the commencement of another series on the first favourable opportunity. The clock (adjusted to sidereal time and corrected for rate by the stars,) was placed in the recess, having the bottom of the case resting upon a large block of stone embedded in well-wrought clay, and the back of the case was tightly screwed to a strong piece of well seasoned * The new clock, not the old one. wood let into the wall. I have little doubt but that the good going of the clock was by these means in a great measure secured. On each side of the pendulum, somewhat above the middle of it, were suspended two of Jones's thermometers. The disk was formed of a small circle of card paper about three-tenths of an inch in diameter, this measure being found to be the best and most convenient. Instead of the wooden stand for supporting the small telescope, through which the coincidences, or rather the disappearances and re-appearances of the pendulum-rod and the disk are noted, as well as the magnitude of the arc of vibration, a small thick brick pier was raised so as to receive the plate to which the telescope is attached. The usual adjustments of the clock, pendulum and telescope, being completed, we were now ready to commence. I here deem it right to notice the very able assistance which I received from Captain Ronald: his exertions were truly praiseworthy; I cannot recommend them too highly. I likewise avail myself of paying a just tribute to the aid which was afforded by Lieutenant Johnson, of the Honourable East India Company's Service, now superintendant of the observatory at St. Helena. This gentleman being on a visit to me, very kindly at my request took an active part in all the observations. The sheets accompanying this short paper must be considered as the united labours of Captain Ronald, Mr. Johnson, and myself, and the responsibility of each as to accuracy must depend upon the papers signed with the observer's name. As far as I am able to judge of these things, the near agreement of three independent series of observations is no small argument of their accuracy. It must not for a moment be conceived that I reckon our results as in any way final in the determination of the compression of the earth, inasmuch as it would be advisable to begin a new series of observations (say) in the midst of winter, or what would be better, in different seasons of the year, lest the coefficient for temperature might require some correction; though even this test can hardly be supposed, from the experiments made by Captain Sabine on this very pendulum in London, to be required. I have ever been of opinion, (how far correct or not, I leave others to judge,) that the invariable pendulum ought to be a standard instrument in an observatory; that it should be swung at all seasons of the year; that it would be proper to forward it on authorized occasions to the various fixed observatories now situated in the northern and southern hemispheres; that the instrument should return again to the same stations as before, and the observations be renewed; that, finally, after each circuit it should undergo a strict examination at the spot where it was first tried, in order that it might proceed again as before. Should any harm take place from improper packing or accidental circumstances, the evil would be soon discovered, and the instrument repaired. The pendulum is of a very delicate construction, and consequently it is the more necessary that it should be as often as possible compared at those points where it has previously been used. Formulæ used in computing the Observations. \[ a = \text{greater, and } b \text{ the lesser arc observed at the beginning and end of each set of coincidences.} \] \[ t = \text{mean of the thermometers immediately adjacent to the pendulum.} \] \[ H = \text{height of the barometer.} \] \[ \tau = \text{height of the attached thermometer.} \] It must be remarked that the sidereal day is reduced to a mean solar day for comparison in London. \[ \begin{align*} \log (\text{reduct. for arc}) &= 9.55132 + \log (a + b) + \log (a - b) - \log \{\log a - \log b\} \\ \text{Reduct. for temp.} &= (t - 62^\circ) \times 0.421. \\ \log (\text{reduct. for vacuum}) &= 9.31083 + \log H. \\ &- \{\log (1 + 0.002083 \cdot t - 53^\circ) + \log (1 + 0.0001 \cdot \tau - 53^\circ)\} \end{align*} \] The specific gravity of the pendulum is assumed . . . 8.6 Sabine. The expansion for 1° of the pendulum . . . . . . . . . . 0.421 — The temperature assumed as the standard for spec. grav. = 53° — The temperature assumed as the standard for pendulum = 62° — Specific gravity of the air (water = 1) . . . . . . . . . . \( \frac{1}{8.3} \) — The height of barometer assumed as standard for spec. grav. = 29.27 inches. The height of the pendulum above the mean level of the sea in Table Bay was found to be 32 feet nearly, and above the low-water mark 34 feet, on the day when it was determined. Hence \[ \begin{align*} \text{For 34 feet at the Cape} & \quad \text{Reduction} = 0.14 \\ \text{For 83 feet in London} & \quad \text{Reduction} = 0.34 \\ \text{Difference} & = 0.20 \end{align*} \] This quantity 0.20 vibration is additive to the difference between the number of vibrations (in a mean solar day) at Mr. Browne's and the Cape. **Brief statement of the final results.** 1st,—Captain Ronald. Observations made in London.—Pendulum (No. 4. Jones). \[ \begin{align*} \text{Vibrations in a Mean Solar Day.} \\ \text{Mean of 100 coincidences} & = 86164.62 \end{align*} \] Observations made at the Cape of Good Hope. \[ \begin{align*} \text{Vibrations in a Mean Solar Day.} \\ \text{Mean of 270 coincidences} & = 86097.64 \\ \text{Mean of 160} & = 86097.88 \\ \text{Mean of 200} & = 86097.74 \\ \text{True Mean of 630} & = 86097.73 \end{align*} \] 2nd,—Mr. Johnson. \[ \begin{align*} \text{Vibrations in a Mean Solar Day.} \\ \text{Mean of 240 coincidences} & = 86097.792 \\ \text{Mean of 180} & = 86097.898 \\ \text{True Mean of 420} & = 86097.83 \end{align*} \] 3rd,—Mr. Fallows. | Mean of 401 coincidences | = 86097.67 | |--------------------------|------------| | Mean of 419 | = 86097.66 | | Mean of 507 | = 86097.70 | | Mean of 81 | = 86097.69 | | True Mean of 1408 | = 86097.68 | Summary at the Cape. | Captain Ronald | True Mean of 630 coincidences = 86097.73 | | Mr. Johnson | True Mean of 420 = 86097.83 | | Mr. Fallows | True Mean of 1408 = 86097.68 | | True Mean of 2458 | = 86097.72 | From this last conclusion, compared with that obtained by Captain Sabine at Mr. Browne's, in Portland Place, and which only differs $\frac{1}{50}$th of a vibration in a day from Captain Ronald's subsequent determination, the compression of the earth is very readily ascertained. Let $n =$ the difference in the number of vibrations of the pendulum at London and the Cape. Then for $$\begin{align*} \text{Compression} & \quad n = 65.752 \\ & \quad n = 67.344 \\ & \quad n = 68.828 \end{align*}$$ London. No. of vibrations in a mean solar day = 86164.64 Sabine. Cape. No. of vibrations in a mean solar day = 86097.72 Reduction due to difference of level from low-water mark = 0.20 True difference in the No. of Vibns in a mean solar day = 67.12 This quantity gives the compression of the earth = $\frac{1}{66.92}$ I am aware that this compression somewhat differs from that obtained in the Southern Hemisphere by Sir Thomas Brisbane, at Paramatta, though it is nearly in accordance with M. Freycinet's observations in Cape Town. The documents, however, are here given, and I have every hope that they may meet the public eye, and undergo the usual test of candid and liberal criticism. Fearon Fallows. Royal Observatory, Cape of Good Hope, May 19th, 1829. P. S. The latitude of the Observatory is not yet ascertained by actual observation with the new mural circle. This instrument has been attached to its pier for several months past; but from some discrepancies in reading, the cause of which is not yet discovered, I am under the necessity of assuming $33^\circ 55' 56''$ as a very near approximate latitude*. The examination of the mural will go on, and the conclusions be forwarded home when some definite opinion may be formed of it. * I connected the Observatory with my former temporary one in Cape Town, by a survey over the intermediate ground. ### Appendix. Observations made by Captain Ronald with the invariable pendulum (No. 4. of Sabine), in Portland Place, London. Lat. 51° 31' 8" N. | 1825 | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coincidence. | Arc. | |------|--------|--------|--------------|---------|---------|---------------------|------| | | inches.| | | | | | | | July 31 | 29.950 | 70.48 | 1 | 31 21 | 31 28 | 1 31 24.5 | 1.185 | | | 29.934 | 70.50 | 11 | 28 03 | 28 18 | 3 28 10.5 | .610 | | Aug. 1 | 29.944 | 69.75 | 1 | 13 35 | 13 45 | 11 13 40.0 | 1.110 | | | 29.942 | 70.25 | 11 | 10 34 | 10 49 | 1 10 41.5 | .575 | | | 29.942 | 70.35 | 1 | 33 55 | 34 01 | 1 33 58.0 | 1.320 | | | 29.941 | 70.65 | 11 | 30 31 | 30 45 | 3 30 38.0 | .670 | | 2 | 29.950 | 71.00 | 1 | 49 29 | 49 36 | 10 49 32.5 | 1.225 | | | 29.944 | 71.90 | 11 | 45 59 | 46 15 | 0 46 7.0 | .640 | | | 29.944 | 71.90 | 1 | 58 01 | 58 08 | 0 58 4.5 | 1.305 | | | 29.944 | 71.80 | 11 | 54 26 | 54 41 | 2 54 33.5 | .665 | | 3 | 29.952 | 71.00 | 1 | 9 39 | 9 44 | 11 9 41.5 | 1.370 | | | 29.952 | 71.80 | 11 | 6 02 | 6 14 | 1 6 8.0 | .695 | | | 29.953 | 71.80 | 1 | 18 47 | 18 55 | 1 18 51.0 | 1.180 | | | 29.924 | 72.00 | 11 | 15 16 | 15 29 | 3 15 22.5 | .605 | | 4 | 29.584 | 72.20 | 1 | 52 51 | 52 57 | 0 52 54.0 | 1.310 | | | 29.574 | 72.00 | 11 | 49 11 | 49 24 | 2 49 17.5 | .665 | | 5 | 29.500 | 70.30 | 1 | 33 38 | 33 44 | 10 33 41.0 | 1.290 | | | 29.520 | 70.75 | 11 | 30 18 | 30 30 | 0 30 24.0 | .640 | | | 29.522 | 70.80 | 1 | 36 24 | 36 31 | 0 36 27.5 | 1.370 | | | 29.530 | 71.05 | 11 | 32 51 | 33 03 | 2 33 57.0 | .685 | | 6 | 29.628 | 67.20 | 1 | 46 11 | 46 16 | 11 46 13.5 | 1.315 | | | 29.616 | 68.60 | 11 | 43 21 | 43 34 | 1 43 27.5 | .650 | Mean = 29.804 ### Observations computed. | Observations | Mean Temp. | Interval | Vib* in 24 Mean Solar Hours. | Corr. for Arc. | Reduct. to 70° 82' Fahr. | Reduced Vib* in 24 Mean Solar Hours at 62° Fahr. | |--------------|------------|----------|-----------------------------|----------------|-------------------------|--------------------------------------------------| | 1 | 70.49 | 1 56 46.0 | 86153.354 | +1.277 | -0.139 | 86154.492 | | 2 | 70.00 | 1 57 01.5 | 86153.899 | 1.124 | 0.345 | 86154.678 | | 3 | 70.50 | 1 56 40.0 | 86153.143 | 1.568 | 0.135 | 86154.576 | | 4 | 71.45 | 1 56 34.5 | 86152.949 | 1.378 | +0.265 | 86154.592 | | 5 | 71.85 | 1 56 29.0 | 86152.754 | 1.534 | 0.434 | 86154.722 | | 6 | 71.40 | 1 56 26.5 | 86152.666 | 1.685 | 0.244 | 86154.595 | | 7 | 71.90 | 1 56 31.5 | 86152.843 | 1.260 | 0.455 | 86154.558 | | 8 | 72.10 | 1 56 23.5 | 86152.560 | 1.541 | 0.539 | 86154.640 | | 9 | 70.52 | 1 56 43.0 | 86153.249 | 1.467 | -0.126 | 86154.590 | | 10 | 70.92 | 1 56 29.5 | 86152.772 | 1.665 | +0.042 | 86154.479 | | 11 | 67.90 | 1 57 14.0 | 86154.336 | +1.521 | -1.229 | 86154.629 | Mean = 70.82 Correction for rate ........... +0.441 Correction for buoyancy ...... +5.873 Reduction to 62° Fahr....... +3.713 86164.622* *Note.—The accordance of this result with that obtained by Captain Sabine, is sufficient to show that the instrument remained unaltered, and warrants the comparison of any future observations with those obtained by former observers; subject, of course, to any change, which it may have undergone since that period, or that it may yet meet with, which can only be satisfactorily ascertained, when another series shall have been made with it, in London, where its rate is probably better known, than at any other of Captain Sabine's stations. Mr. Browne, at whose house these observations were made, favoured me with the rate of the clock, as follows: | 1825. | July 31 | Cumming with Molyneux set = | Molyneux with Mean Time. | |-------|---------|-----------------------------|--------------------------| | | | s | s | | Aug. 1| noon | +0.2 | July 30th, fast .......... 0.26 | | | 12 p.m. | +0.2 | Aug. 6th, ............... 0.55 | | | noon | 0.4 | ½)0.29 | | | 12 p.m. | 0.6 | 0.042 per diem. | | | noon | 0.8 | Cumming gains 0.400 | | | 12 p.m. | 1.0 | Gains on Mean Time.. 0.442=rate. | | | noon | 1.2 | | | | 12 p.m. | 1.4 | | | | noon | 1.6 | | | | 12 p.m. | 1.8 | | | | noon | 2.0 | | | | 12 p.m. | 2.2 | | | | noon | +2.4 | | Observations made with the pendulum (No. 4, of Sabine). Observatory, Cape of Good Hope. Lat. 33° 55' 56". By Captain Ronald. | 1828. | Barometer. | Thermometers. | No. of Coin. | Disapp. | Re-app. | Time of Coincidence. | Arc. | |-------|------------|---------------|--------------|---------|---------|----------------------|------| | Nov. 23 | inches. | A. | B. | | | | | | | 29.906 | 72.2 | 73.2 | 1 | 4 53 | 5 9 | 12 5 1.0 | 1.03 | | | 29.917 | 74.7 | 75.7 | 31 | 42 5 | 42 17 | 14 42 11.0 | .48 | | | 29.917 | 75.7 | 74.6 | 1 | 50 2 | 50 15 | 14 50 8.5 | 1.11 | | | 29.947 | 71.3 | 72.3 | 31 | 27 13 | 27 26 | 17 27 19.5 | .51 | | | 29.956 | 67.8 | 68.4 | 1 | 56 22 | 56 35 | 12 56 28.5 | 1.215 | | | 29.983 | 71.2 | 71.8 | 31 | 33 57 | 34 9 | 15 34 3.0 | .520 | | | 29.986 | 70.2 | 70.9 | 1 | 14 13 | 14 27 | 16 14 20.0 | 1.27 | | | 29.951 | 69.3 | 69.9 | 31 | 51 50 | 52 2 | 18 15 56.0 | .52 | | | 29.951 | 69.3 | 69.9 | 1 | 57 45 | 57 59 | 18 57 52.0 | 1.27 | | | 29.964 | 68.1 | 68.9 | 31 | 35 23 | 35 36 | 21 35 29.5 | .53 | | | 29.966 | 66.3 | 67.2 | 1 | 55 49 | 56 1 | 9 55 55.0 | 1.175 | | | 29.998 | 67.5 | 68.2 | 31 | 33 44 | 33 59 | 12 33 51.5 | .495 | | | 29.998 | 67.5 | 68.1 | 1 | 41 20 | 41 33 | 12 41 26.5 | 1.32 | | | 30.006 | 70.6 | 71.4 | 31 | 19 5 | 19 17 | 15 19 11.0 | .54 | | | 29.997 | 72.7 | 73.4 | 1 | 25 52 | 26 8 | 16 26 0.0 | 1.200 | | | 29.966 | 72.3 | 73.0 | 31 | 3 8 | 3 22 | 19 3 15.0 | .515 | | | 29.963 | 71.7 | 72.6 | 1 | 19 7 | 19 21 | 19 19 14.0 | 1.20 | | | 29.966 | 71.9 | 72.8 | 31 | 56 31 | 56 44 | 21 56 37.5 | .50 | Mean. 29.963 MDCCCXXX. Observations computed. The clock making on the 23rd, 86636.826*, on the 24th, 86636.916*, and on the 25th, 86637.024* sidereal vibrations in a mean solar day. | Number of Observations | Mean Temp. | Interval | Vibns in 24 Mean Solar Hours | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vibns in 24 Mean Solar Hours at 62° F. | |------------------------|------------|----------|-----------------------------|-----------------|-------------------|-----------------------------------------------| | 1 | 73.95 | h m s | 86085.584 | + 0.891 | + 5.031 | 86091.506 | | 2 | 73.47 | 2 37 11.0 | 86085.643 | 1.024 | 4.829 | 86091.496 | | 3 | 69.80 | 2 37 34.5 | 86087.102 | 1.164 | 3.284 | 86091.550 | | 4 | 70.02 | 2 37 36.0 | 86087.189 | 1.232 | 3.376 | 86091.794 | | 5 | 69.05 | 2 37 37.5 | 86087.276 | 1.249 | 2.968 | 86091.493 | | 6 | 67.30 | 2 37 56.5 | 86088.486 | 1.077 | 2.231 | 86091.794 | | 7 | 69.40 | 2 37 44.5 | 86087.790 | 1.329 | 3.115 | 86092.234 | | 8 | 72.85 | 2 37 15.0 | 86086.073 | 1.138 | 4.568 | 86091.779 | | 9 | 72.25 | 2 37 23.5 | 86086.569 | + 1.114 | + 4.315 | 86091.998 | Mean .. 70.90 Mean . . . 86091.738 Correction for buoyancy . . . . . . . + 5.900 Number of Vibrations in vacuo, in 24 Mean Solar Hours.. 86097.638 Rate of the Sidereal Clock. | Nov. 22nd. | Stars. | Rates. | Nov. 24th. | Stars. | Rates. | Nov. 25th. | Stars. | Rates. | |------------|--------|--------|------------|--------|--------|------------|--------|--------| | | α Pegasi | + 0.10 | α Arietis | + 0.10 | | α Pegasi | + 0.35 | | | | α Andromedæ | .07 | α Ceti | .29 | | α App. Sc. | .40 | | | | γ Pegasi | .04 | γ Eridani | .42 | | β Arietis | .45 | | | | β Arietis | .12 | Aldebaran | .35 | | α | .24 | | | | α | .13 | | | | ρ Ceti | .49 | | | | γ Ceti | .17 | | | | δ | .36 | | | | α | .28 | | | | γ | .43 | | | | γ Eridani| .37 | | | | α | .69 | | | | Aldebaran| + .23 | | | | γ Eridani| .55 | | | | | | | | | Aldebaran| + .63 | | Here the rate appears to have been increasing, and therefore a proportion was made for each day's observations, thus: For the observations of the 23d, Rate + 0.270 24th, . . . + .360 25th, . . . + .468 * Note.—In these numbers, both in this and the two following series, the rate of the clock is included, being = 86636.556 + rate. ### Observations with the pendulum (Continued). | 1829 | Attached Therm. | Barom. | Thermometers. | No. of Coin. | Disapp. | Re-app. | Time of Coincidence. | Arc. | |------|----------------|--------|---------------|--------------|---------|---------|---------------------|------| | Jan. 7 | 72.0 | 30.035 | inches. | 72.4 | 73.0 | 1 | m s | m s | h m s | 15 51 23.5 | 1.12 | | | 73.5 | 30.020 | 73.0 | 73.6 | 21 | 36 20 | 36 34 | 17 36 27.0 | .62 | | | 77.5 | 29.964 | 76.2 | 76.8 | 1 | 34 22 | 34 36 | 21 34 29.0 | 1.18 | | | 77.0 | 29.919 | 74.8 | 75.2 | 21 | 19 10 | 19 25 | 23 19 17.5 | .66 | | | 77.5 | 29.919 | 75.6 | 76.0 | 1 | 30 4 | 30 18 | 23 30 11.0 | 1.37 | | | 76.5 | 29.900 | 74.5 | 75.1 | 21 | 14 46 | 15 2 | 1 14 54.0 | .73 | | 8 | 69.0 | 29.952 | 69.0 | 69.6 | 1 | 45 56 | 46 11 | 15 46 3.5 | 1.30 | | | 69.6 | 29.951 | 70.6 | 71.1 | 21 | 31 3 | 31 18 | 17 31 10.5 | .71 | | | 72.0 | 29.951 | 70.6 | 71.2 | 1 | 36 41 | 36 56 | 17 36 48.5 | 1.26 | | | 72.5 | 29.932 | 72.0 | 72.6 | 21 | 21 45 | 21 58 | 19 21 51.5 | .69 | | | 72.5 | 29.932 | 72.0 | 72.7 | 1 | 27 44 | 27 58 | 19 27 51.0 | 1.23 | | | 74.0 | 29.925 | 72.6 | 73.4 | 21 | 12 43 | 12 58 | 21 12 50.5 | .66 | | | 74.0 | 29.925 | 72.3 | 73.0 | 1 | 24 10 | 24 22 | 21 24 16.0 | 1.49 | | | 73.0 | 29.926 | 72.4 | 73.1 | 21 | 8 59 | 9 15 | 23 9 7.0 | .83 | | | 73.0 | 29.926 | 72.3 | 72.9 | 1 | 14 46 | 15 2 | 23 14 54.0 | 1.19 | | | 73.0 | 29.918 | 70.9 | 71.5 | 21 | 59 45 | 0 0 | 0 59 52.5 | .66 | Mean.. 73.54 29.943 On the morning of the 9th the clock was found stopped, which prevented the continuance of this series. Observations computed. The clock making on the 7th, 86636.306, and on the 8th, 86636.215 sidereal vibrations in a mean solar day. | Number of Observations. | Mean Temp. | Interval. | Vibns in 24 Mean Solar Hours. | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vibns in 24 Mean Solar Hours at 62° F. | |------------------------|------------|-----------|-------------------------------|-----------------|------------------|---------------------------------------------| | 1 | 73.00 | 1 45 3.5 | 86086.539 | +1.206 | +4.631 | 86092.376 | | 2 | 75.75 | 1 44 48.5| 86085.228 | 1.349 | 5.789 | 86092.366 | | 3 | 75.30 | 1 44 45.5| 86084.746 | 1.794 | 5.599 | 86092.139 | | 4 | 70.08 | 1 45 7.0 | 86086.756 | 1.607 | 3.402 | 86091.765 | | 5 | 71.60 | 1 45 3.0 | 86086.408 | 1.513 | 4.042 | 86091.963 | | 6 | 72.67 | 1 44 59.5| 86086.058 | 1.418 | 4.492 | 86091.968 | | 7 | 72.70 | 1 44 51.0| 86085.359 | 2.145 | 4.505 | 86092.009 | | 8 | 71.90 | 1 44 58.5| 86086.015 | +1.363 | +4.168 | 86091.546 | Mean .. 72.88 Correction for buoyancy ..... + 5.866 Number of Vibrations in vacuo, in 24 Mean Solar Hours.... 86097.882 ### Rate of the Sidereal Clock | Stars | Rates | Stars | Rates | |-------------|-------|-------------|-------| | α Ceti | -0.32 | α Ceti | -0.40 | | α Persei | .10 | γ Eridani | .43 | | γ Eridani | .30 | γ Cali Sc. | .10 | | θ | .28 | Capella | .50 | | X | .04 | Rigel | .30 | | 43d | .40 | γ Orionis | .20 | | ψ | .30 | | .30 | | γ Cali Sc. | .47 | β Aurigæ | -.50 | | γ Orionis | .52 | Mean | -.341 | | ε | .08 | | | | ζ | .28 | | | | η | .12 | | | | β Aurigæ | -.04 | | | Mean: -.250 ### Observations with the pendulum (Continued) | 1829 | Attached Therm. | Barom. | Thermometers | No. of Coin. | Disapp. | Re-app. | Time of Coincidence | Arc. | |------|-----------------|--------|--------------|--------------|---------|---------|--------------------|------| | Jan. 16 | 78.0 | 29.986 | 80.1 | 1 | 57 22 | 57 34 | 20 57 28.0 | 1.41 | | | 78.0 | 29.998 | 73.2 | 21 | 41 55 | 42 9 | 22 42 2.0 | .77 | | | 78.0 | 29.998 | 74.0 | 1 | 47 16 | 47 30 | 22 47 23.0 | 1.30 | | | 76.0 | 29.990 | 72.7 | 21 | 32 2 | 32 16 | 0 32 9.0 | .71 | | | 76.0 | 29.990 | 72.8 | 1 | 37 44 | 37 58 | 0 37 51.0 | 1.11 | | | 76.0 | 29.990 | 72.4 | 21 | 22 40 | 22 55 | 2 22 47.5 | .59 | | | 70.0 | 29.988 | 71.0 | 1 | 32 32 | 32 44 | 13 32 38.0 | 1.46 | | 17 | 72.0 | 30.014 | 71.3 | 21 | 17 32 | 17 47 | 15 17 39.5 | .73 | | | 72.0 | 30.014 | 71.3 | 1 | 20 39.5 | 20 54 | 15 20 46.25 | 1.42 | | | 74.0 | 30.026 | 71.8 | 21 | 5 39 | 5 55 | 17 5 47.0 | .75 | | | 74.0 | 30.026 | 72.0 | 1 | 9 4 | 9 18 | 17 9 11.0 | 1.22 | | | 75.5 | 30.025 | 72.6 | 21 | 54 6 | 54 21 | 18 54 13.5 | .64 | | | 75.6 | 30.025 | 73.0 | 1 | 57 1 | 57 14 | 18 57 7.5 | 1.24 | | | 75.6 | 30.023 | 72.9 | 21 | 41 59 | 42 13 | 20 42 6.0 | .70 | | | 75.6 | 30.023 | 73.6 | 1 | 45 54 | 46 8 | 20 46 1.0 | 1.35 | | | 76.0 | 30.006 | 73.1 | 21 | 30 47 | 31 0 | 22 30 53.5 | .72 | | | 76.0 | 30.006 | 74.0 | 1 | 35 49 | 36 2 | 22 35 55.5 | 1.30 | | | 75.0 | 29.990 | 73.3 | 21 | 20 43 | 20 57 | 0 20 50.0 | .70 | | | 75.0 | 29.990 | 73.6 | 1 | 24 34 | 24 48 | 0 24 41.0 | 1.44 | | | 72.0 | 29.988 | 73.0 | 21 | 9 25 | 9 40 | 2 9 32.5 | .74 | Mean: 75.01 30.005 Observations computed. The clock making on the 16th, 86636.057, and on the 17th, 86636.027 sidereal vibrations in a mean solar day. | Number of Observations | Mean Temp. | Interval | Vib's in 24 Mean Solar Hours | Corr. for Arc. | Reduc. to 62° FAHR. | Reduced Vib's in 24 Mean Solar Hours at 62° F. | |------------------------|------------|----------|-----------------------------|---------------|-------------------|-----------------------------------------------| | 1 | 76.95 | h m s | 86083.707 | +1.890 | +6.294 | 86091.891 | | 2 | 73.62 | 1 44 46.0| 86084.762 | 1.607 | 4.892 | 86091.261 | | 3 | 72.85 | 1 44 56.5| 86085.681 | 1.146 | 4.568 | 86091.395 | | 4 | 71.45 | 1 45 1.5 | 86086.088 | 1.890 | 3.978 | 86091.956 | | 5 | 71.85 | 1 45 0.75| 86086.022 | 1.867 | 4.147 | 86092.036 | | 6 | 72.60 | 1 45 2.5 | 86086.175 | 1.370 | 4.463 | 86092.008 | | 7 | 73.20 | 1 44 58.5| 86085.826 | 1.501 | 4.715 | 86092.042 | | 8 | 73.62 | 1 44 52.5| 86085.301 | 1.700 | 4.892 | 86091.893 | | 9 | 73.92 | 1 44 54.5| 86085.476 | 1.589 | 5.018 | 86092.083 | | 10 | 73.75 | 1 44 51.5| 86085.214 | +1.879 | +4.947 | 86092.040 | Mean ... 73.38 Mean ... 86091.860 Correction for buoyancy ....... + 5.876 Number of Vibrations in vacuo, in 24 Mean Solar Hours.... 86097.736 Rate of the Sidereal Clock. | Jan. 16th. | Stars. | Rates. | Compared with Observations of the 15th. | |------------|--------|-------|----------------------------------------| | | α Persei | -0.60 | | | 17 Eridani | .50 | | | γ Orionis | .65 | | | δ Aurigae | .59 | | | ε Geminor | .58 | | | ε Can. Min. | .74 | | | μ Columbae | .60 | | | β Aurigae | .33 | | | θ Leporis | .50 | | | ε Can. Maj. | .50 | | | δ Geminor | .48 | | | δ Can. Min. | .57 | | | Procyon | .47 | | | Pollux | -.58 | Mean ... - .499 | Jan. 17th. | Stars. | Rates. | Compared with Observations of the 15th and 16th. | |------------|--------|-------|----------------------------------------| | | α Persei | -0.60 | | | 17 Eridani | .50 | | | γ Orionis | .65 | | | δ Aurigae | .59 | | | ε Geminor | .58 | | | ε Can. Min. | .74 | | | μ Columbae | .60 | | | β Aurigae | .33 | | | θ Leporis | .50 | | | ε Can. Maj. | .50 | | | δ Geminor | .48 | | | δ Can. Min. | .57 | | | Procyon | .47 | | | Pollux | -.58 | Mean ... - .529 Abstract of Captain Ronald's observations. London. Mean of 110 coincidences = 86164.62 Cape. Mean of 270 coincidences = 86097.64 160 = 86097.88 200 = 86097.74 True Mean of 630 coincidences at the Cape = 86097.73 ### Cape of Good Hope: Observer, Mr. Johnson. | Year | Attached Therm. | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coin. | Arc. | Remarks | |------|-----------------|--------|--------|--------------|---------|---------|---------------|-----|----------| | Dec. | | | | | | | | | | | 15 | 68.5 | 30.224 | 67.3 | 67.7 | 1 | 15 | 48 | 16 | 4 | 15 15 56.0 | 1.20 | | | 68.7 | 30.220 | 67.9 | 68.2 | 21 | 1 | 9 | 1 | 27 | 17 1 18.0 | 0.67 | | | 68.8 | 30.220 | 68.3 | 68.6 | 1 | 22 | 22 | 22 | 38 | 17 22 30.0 | 1.28 | | | 69.5 | 30.215 | 68.4 | 68.9 | 21 | 7 | 41 | 8 | 0 | 19 7 50.5 | 0.68 | | | 69.5 | 30.215 | 68.4 | 68.9 | 1 | 24 | 9 | 24 | 27 | 19 24 18.0 | 1.07 | | | 69.5 | 30.204 | 68.4 | 68.7 | 21 | 9 | 31 | 9 | 53 | 21 9 42.0 | 0.56 | | | 69.5 | 30.204 | 68.4 | 68.7 | 1 | 20 | 38 | 20 | 54 | 21 20 46.0 | 1.32 | | | 69.0 | 30.205 | 68.2 | 68.7 | 21 | 5 | 53 | 6 | 13 | 23 6 3.0 | 0.70 | | 16 | 69.0 | 30.118 | 67.8 | 68.3 | 1 | 50 | 26 | 50 | 43 | 15 50 34.5 | 1.20 | | | 69.5 | 30.110 | 67.3 | 67.7 | 21 | 35 | 45 | 36 | 3 | 17 35 54.0 | 0.71 | | | 69.5 | 30.092 | 67.9 | 68.3 | 1 | 46 | 45 | 47 | 1 | 17 46 53.0 | 1.20 | | | 69.5 | 30.076 | 67.7 | 68.0 | 21 | 32 | 3 | 32 | 21 | 19 32 12.0 | 0.72 | | | 69.5 | 30.076 | 67.7 | 68.0 | 1 | 48 | 27 | 48 | 44 | 19 48 35.5 | 1.23 | | | 70.0 | 30.048 | 67.9 | 68.3 | 21 | 33 | 44 | 34 | 1 | 21 33 52.5 | 0.77 | | | 70.0 | 30.048 | 67.9 | 68.3 | 1 | 44 | 45 | 45 | 2 | 21 44 53.5 | 1.21 | | | 68.5 | 30.028 | 67.6 | 68.2 | 21 | 30 | 1 | 30 | 19 | 23 30 10.0 | 0.78 | | 17 | 68.5 | 30.028 | 67.5 | 68.0 | 1 | 39 | 34 | 39 | 50 | 14 39 42.0 | 1.20 | | | 69.5 | 30.022 | 67.8 | 68.3 | 21 | 24 | 51 | 25 | 9 | 16 25 0.0 | 0.72 | | | 69.5 | 30.022 | 67.8 | 68.3 | 1 | 35 | 45 | 36 | 1 | 16 35 53.0 | 1.12 | | | 70.5 | 30.016 | 68.5 | 69.0 | 21 | 20 | 58 | 21 | 15 | 18 21 6.5 | 0.68 | | | 70.5 | 30.016 | 69.0 | 69.5 | 1 | 37 | 33 | 37 | 50 | 18 37 41.5 | 1.12 | | | 71.5 | 30.009 | 69.5 | 69.8 | 21 | 22 | 41 | 22 | 58 | 20 22 49.5 | 0.67 | | | 71.5 | 30.009 | 68.5 | 68.8 | 1 | 34 | 1 | 34 | 17 | 20 34 9.0 | 1.30 | | | 70.0 | 30.004 | 69.0 | 69.5 | 21 | 19 | 8 | 19 | 25 | 22 19 16.5 | 0.79 | ### Observations computed. | No. of Observ. | Mean Temp. | Interval | Uncorrected Number of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Red. Vibns in 24 Mean Solar Hours at 62° Fahr. | |----------------|------------|----------|---------------------------------|--------------|------------------|---------------------|------------------------------------------------| | 1 | 67.78 | h m s | 86088.392 | 0.39 | 1.394 | 2.432 | 86091.828 | | 2 | 68.60 | 1 45 20.5| 86088.275 | 0.39 | 1.524 | 2.779 | 86092.188 | | 3 | 68.73 | 1 45 24.0| 86088.568 | 0.39 | 1.052 | 2.833 | 86092.063 | | 4 | 68.70 | 1 45 17.0| 86087.960 | 0.39 | 1.622 | 2.821 | 86092.013 | | 5 | 67.78 | 1 45 19.5| 86088.198 | 0.21 | 1.461 | 2.433 | 86091.882 | | 6 | 67.97 | 1 45 19.0| 86088.137 | 0.21 | 1.482 | 2.513 | 86091.922 | | 7 | 68.15 | 1 45 17.0| 86087.960 | 0.21 | 1.609 | 2.589 | 86091.948 | | 8 | 68.10 | 1 45 16.5| 86087.920 | 0.21 | 1.597 | 2.568 | 86091.875 | | 9 | 67.90 | 1 45 18.0| 86088.059 | 0.21 | 1.482 | 2.484 | 86091.815 | | 10 | 68.63 | 1 45 13.5| 86087.660 | 0.21 | 1.300 | 2.791 | 86091.541 | | 11 | 69.45 | 1 45 8.0 | 86087.180 | 0.21 | 1.284 | 3.136 | 86091.390 | | 12 | 68.95 | 1 45 7.5 | 86087.120 | 0.21 | 1.753 | 2.925 | 86091.588 | Mean... 68.39 Correction for buoyancy ... +5.956 Number of Vibrations in vacuo, in 24 Mean Solar Hours .. 86097.794 Rate of the Sidereal Clock. | Dec. 14th | Dec. 15th | |-----------|-----------| | By α Arietis | -0.53 | By α Ceti | -0.74 | | Aldebaran | 0.26 | Aldebaran | 0.28 | | Capella | 0.50 | Capella | 0.50 | | Rigel | 0.12 | Rigel | 0.14 | | β Tauri | 0.34 | β Tauri | 0.44 | | ζ Orionis | 0.60 | ζ Orionis | 0.30 | | β Aurigae | 0.74 | ζ | 0.39 | Mean Rate.. | -0.44 | Mean Rate.. | -0.39 | Mean Rate on the 18th by Mr. Fallows's Observations 0.03 Remark.—On the 16th and 17th the weather was unfavourable for observation; the quantity assumed for the rate of the clock on those days is a mean of its rate on the 15th and 18th: probably on the 17th the rate was less than that which has been assigned. Observations with the pendulum (Continued). | 1829 | Attached Therm. | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coin. | Arc. | Remarks | |------|----------------|--------|--------|--------------|---------|---------|---------------|------|----------| | Jan. 20. | inches, | | | | | | | | | 68.5 | 29.972 | 68.6 | 69.0 | 1 | 9 46 | 9 55 | 17 9 50.5 | 1.67 | The Pendulum was not stopped between these Observations. | | 73.7 | 30.017 | 73.0 | 73.6 | 21 | 54 19 | 34 35 | 18 54 27.0 | 1.12 | | " | 73.7 | 30.017 | 72.8 | 73.4 | 1 | 59 34 | 59 49 | 18 59 41.5 | 1.12 | | " | 71.7 | 30.010 | 71.7 | 72.0 | 21 | 44 22 | 44 37 | 20 44 29.5 | 0.83 | | " | 71.7 | 30.010 | 71.8 | 72.0 | 1 | 1 55 | 2 5 | 21 2 0.0 | 1.60 | | " | 73.5 | 30.003 | 73.0 | 73.5 | 21 | 46 18 | 46 33 | 22 46 25.5 | 1.31 | | " | 73.5 | 30.003 | 73.2 | 73.7 | 1 | 51 31 | 51 45 | 22 51 38.0 | 1.31 | | " | 74.5 | 30.003 | 73.5 | 74.0 | 21 | 36 6 | 36 22 | 24 36 14.0 | 0.90 | | 21. | 67.0 | 30.137 | 68.8 | 69.0 | 1 | 14 28 | 14 37 | 15 14 32.5 | 1.68 | | " | 70.0 | 30.145 | 69.4 | 69.9 | 21 | 59 25 | 59 41 | 16 59 30.0 | 0.91 | | " | 70.0 | 30.145 | 69.4 | 69.9 | 1 | 4 41 | 4 57 | 17 4 49.0 | 0.90 | | " | 72.0 | 30.145 | 70.0 | 70.4 | 21 | 50 1 | 50 17 | 18 50 9.0 | 0.50 | | " | 72.0 | 30.145 | 70.6 | 71.0 | 1 | 7 6 | 7 17 | 19 7 11.5 | 1.60 | | " | 73.0 | 30.137 | 70.2 | 70.6 | 21 | 52 3 | 52 17 | 20 52 10.0 | 0.87 | | " | 73.0 | 30.137 | 70.5 | 70.8 | 1 | 57 18 | 57 34 | 20 57 26.0 | 0.86 | | " | 72.0 | 30.116 | 70.3 | 70.6 | 21 | 43 34 | 43 49 | 22 43 41.5 | 0.48 | | " | 72.0 | 30.116 | 70.7 | 71.3 | 1 | 59 40 | 59 49 | 22 59 44.5 | 1.70 | | " | 71.0 | 30.114 | 69.9 | 70.2 | 22 | 49 51 | 50 9 | 0 50 0.0 | 0.87 | Observations computed. | No. of Observ. | Mean Temp. | Interval | Uncorrected No. of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced No. of Vib. in 24 Mean Solar Hours at 62° Fahr. | |---------------|------------|----------|-----------------------------|--------------|-----------------|-------------------|--------------------------------------------------| | 1 | 71.05 | 1 44 36.5 | 86084.431 | +0.54 | +3.148 | +3.810 | 86091.929 | | 2 | 72.50 | 1 44 48.0 | 86085.440 | +0.54 | 1.547 | 4.421 | 86091.948 | | 3 | 72.57 | 1 44 25.5 | 86083.460 | +0.54 | 3.458 | 4.454 | 86091.912 | | 4 | 73.60 | 1 44 36.0 | 86084.392 | +0.54 | 1.978 | 4.883 | 86091.793 | | 5 | 69.27 | 1 45 0.5 | 86086.529 | -0.410 | 2.666 | 3.061 | 86091.846 | | 6 | 69.93 | 1 45 20.0 | 86088.216 | -0.410 | 0.781 | 3.338 | 86091.924 | | 7 | 70.60 | 1 44 58.5 | 86086.373 | -0.410 | 2.425 | 3.620 | 86092.008 | | 8 | 70.55 | 1 45 15.5 | 86087.823 | -0.410 | 0.716 | 3.600 | 86091.729 | | 9 | 70.52 | 1 50 15.5 | 86086.529 | -0.410 | +2.609 | +3.587 | 86092.315 | Mean... 86091.934 Correction for buoyancy ... +5.944 Number of Vibrations in vacuo, in 24 Mean Solar Hours .. 86097.878 Rate of the Sidereal Clock. | Jan. 20th. | Jan. 21st. | |------------|------------| | By β Tauri | By β Tauri | | δ Orionis | δ Orionis | | ξ | ζ | | α | α | | Procyon | Procyon | | Pollux | Pollux | | Mean Rate..| Mean Rate..| Remark.—From the above result, it appears that the rate varied nearly a second in the space of 24 hours: there is reason to suppose that the change was owing to some sudden derangement which the clock might have suffered on the night of the 20th. From the tolerable accordance with each other of the pendulum observations of the 21st, it may be presumed that the rate was equable during that day. Abstract of Mr. Johnson’s observations. Mean of 240 coincidences = 86097.792 Mean of 180 coincidences = 86097.878 True mean of 420 coincidences = 86097.829 General Remark.—During both series of experiments, the observatory was kept in the same state, the North shutter being open during the day, and the door of the recess, in which the clock and pendulum stood, constantly closed, with the exception of the two small openings made in it for the purpose of showing the dial plate, and the graduated arc of the pendulum. During the second series, the weather was particularly favourable, both for observations of the transit instrument and pendulum. --- Cape of Good Hope; Observer Mr. Fallows. First Series. | Year | Attached Therm. | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coin. by the Sidereal Clock. | Arc. | Remarks | |------|----------------|--------|--------|--------------|---------|---------|-----------------------------------|------|----------| | Dec. | | | | | | | | | | | 2 | 66.5 | 30.205 | 68.2 | 69.1 | 1 | 50 41 | 50 56½ 16 50 48¾ 1.38 | | This day very favourable for observation; little wind—the Observatory chase shut, except when observing. The Thermometers read off before the North chase was opened. | | | 67.0 | 30.205 | 68.0 | 68.9 | 31 | 28 31 | 28 51 19 28 41 0.51 | | | | | 67.1 | 30.205 | 68.0 | 68.9 | 1 | 33 50 | 34 4½ 19 33 57¼ 1.48 | | | | | 67.5 | 30.207 | 67.1 | 68.0 | 31 | 11 44 | 12 1 22 11 52½ 0.61 | | | | | 66.0 | 30.205 | 67.1 | 68.0 | 1 | 38 1 | 38 16 14 38 8½ 1.38 | | | | | 68.5 | 30.205 | 69.6 | 70.5 | 31 | 15 56 | 16 13 17 16 4½ 0.57 | | | | | 68.7 | 30.205 | 70.1 | 71.2 | 1 | 43 43½ | 42 59 17 42 51½ 1.20 | | | | | 68.5 | 30.175 | 70.2 | 71.2 | 31 | 20 24 | 20 44½ 20 20 34¾ 0.50 | | | | | 68.6 | 30.174 | 70.2 | 71.3 | 1 | 30 6 | 30 22 20 30 14 1.22 | | | | | 68.0 | 30.151 | 68.0 | 69.0 | 31 | 7 57 | 8 15 23 8 6 0.49 | | | | | 65.0 | 30.102 | 64.2 | 65.0 | 1 | 3 18 | 3 32 12 3 25 1.38 | | | | | 67.5 | 30.139 | 66.9 | 67.6 | 31 | 41 31 | 41 49 14 41 40 0.57 | | | | | 67.6 | 30.140 | 66.9 | 67.6 | 1 | 47 24 | 47 40 14 47 32 1.20 | | | | | 68.5 | 30.165 | 69.1 | 70.0 | 31 | 25 26½ | 25 41½ 17 25 34 0.51 | | | | | 68.6 | 30.166 | 69.1 | 70.0 | 1 | 31 10 | 31 26 17 31 18 1.35 | | | | | 68.5 | 30.120 | 68.3 | 69.1 | 31 | 9 0 | 9 18 20 9 9 0.58 | | | | | 68.5 | 30.120 | 67.0 | 67.8 | 1 | 19 40 | 19 54 20 19 47 1.41 | | | | | 68.0 | 30.108 | 67.3 | 68.0 | 31 | 57 33 | 57 52 22 57 42½ 0.58 | | | | | 64.0 | 30.125 | 63.0 | 63.6 | 1 | 40 18 | 40 34 10 40 26 1.42 | | | | | 64.5 | 30.127 | 64.0 | 64.8 | 31 | 18 32 | 18 49 13 18 40½ 0.68 | | | | | 64.5 | 30.127 | 64.1 | 64.8 | 1 | 24 13 | 24 28 13 24 20½ 1.29 | | | | | 66.4 | 30.127 | 65.8 | 66.4 | 31 | 2 31 | 2 46 16 2 38½ 0.56 | | | | | 66.3 | 30.127 | 66.3 | 67.0 | 1 | 13 24 | 13 32 16 13 28 1.72 | | | | | 68.0 | 30.200 | 68.4 | 69.2 | 42 | 49 5½ | 49 22½ 19 49 14 0.50 | | | | | 68.0 | 30.200 | 68.1 | 68.9 | 1 | 54 25 | 54 41 19 54 33 1.13 | | | | | 68.0 | 30.115 | 68.0 | 68.5 | 31 | 32 20 | 32 36 22 32 28 0.49 | | | Mean 67.23 30.1594 MDCCCXXX. First Series computed. | 1829 | Mean Temp. | Interval | Uncorrected No. of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vib.ns in 24 Mean Solar Hours | |------|------------|----------|------------------------------|--------------|-----------------|-------------------|-------------------------------------| | | | | | | | | | | 68.550 | 2 37 52½ | 86087.78 | -0.52 | +1.354 | +2.758 | 86091.37 | | 68.000 | 2 37 55½ | 86087.94 | 0.52 | 1.682 | 2.526 | 86091.63 | | 68.800 | 2 37 56 | 86087.98 | 0.41 | 1.464 | 2.863 | 86091.50 | | 70.540 | 2 37 43 | 86087.24 | 0.41 | 1.114 | 3.595 | 86091.54 | | 69.625 | 2 37 52 | 86087.76 | 0.41 | 1.121 | 3.210 | 86091.68 | | 65.925 | 2 38 15 | 86089.08 | 0.26 | 1.464 | 1.652 | 86091.94 | | 68.400 | 2 38 2 | 86088.34 | 0.26 | 1.362 | 2.694 | 86092.14 | | 69.125 | 2 37 51 | 86087.70 | 0.26 | 1.442 | 3.000 | 86091.88 | | 67.525 | 2 37 55½ | 86087.98 | 0.26 | 1.564 | 2.326 | 86091.61 | | 63.850 | 2 38 14½ | 86089.06 | 0.26 | 1.730 | 0.779 | 86091.31 | | 65.275 | 2 38 18 | 86089.26 | 0.26 | 1.326 | 1.379 | 86091.69 | | 67.725 | 3 35 46 | 86088.24 | 0.26 | 1.797 | 2.410 | 86092.15 | | 68.375 | 2 37 55 | 86087.94 | -0.26 | +1.017 | +2.684 | 86091.38 | Mean... 67.824 Buoyancy .............. 86091.69 +5.98 (No. of Coincidences = 401) Number of Vibrations in vacuo, in 24 Mean Solar Hours... 86097.67 Rate of the Sidereal Clock. | Dec. 2nd. | Dec. 3rd. | Dec. 4th to Dec. 9th. | |-----------|-----------|-----------------------| | By α Arietis... | -0.38 | By α Ceti... | -0.24 | By α Ceti... | -0.33 | | α Ceti... | 0.52 | Capella... | 0.30 | Capella... | 0.26 | | Rigel... | 0.50 | β Tauri... | 0.50 | Rigel... | 0.22 | | β Tauri... | 0.70 | δ Orionis... | 0.58 | β Tauri... | 0.23 | | δ Orionis... | 0.50 | ξ... | 0.36 | δ Orionis... | 0.23 | | ξ... | 0.55 | β Aurigae... | -0.50 | β Aurigae... | 0.27 | | β Aurigae... | -0.46 | Mean Rate... | -0.41 | Sirius... | -0.28 | | Mean Rate... | -0.52 | Mean Rate... | -0.26 | ### Second Series | Year | Month | Day | Attached Therm. | Barom. | Thermometers | No. of Coin. | Disapp. | Re-app. | Time of Coincid. by the Sidereal Clock | Arc. | |------|-------|-----|-----------------|--------|--------------|-------------|---------|--------|--------------------------------------|------| | 1829 | Dec. 18 | | | | | | | | | | | | | | 66.1 | 30.022 | 65.2 | 65.7 | 1 | 15 26 | 15 38 11 15 32 | 1.78 | | | | | 69.5 | 30.053 | 68.1 | 68.7 | 53 | 49 17 | 49 35 15 49 26 | 0.39 | | | | | 70.0 | 30.053 | 71.2 | 71.7 | 1 | 0 9 | 0 13 16 0 11 | 1.87 | | | | | 72.0 | 30.016 | 72.2 | 72.4 | 59 | 4 21 | 4 37 21 4 29 | 0.40 | | | | | 72.1 | 30.015 | 72.2 | 72.4 | 1 | 25 47 | 26 4 21 25 55 1/2 | 1.12 | | | | | 71.0 | 30.024 | 71.0 | 71.5 | 16 | 44 30 | 44 47 22 44 38 1/2 | 0.76 | | | | | 71.0 | 30.025 | 71.0 | 71.4 | 1 | 55 5 | 55 22 22 55 13 1/2 | 0.89 | | | | | 71.5 | 30.054 | 70.1 | 70.5 | 18 | 24 26 | 24 42 0 24 34 | 0.55 | | | | | 67.5 | 30.165 | 68.0 | 68.3 | 1 | 56 39 | 56 47 12 56 43 | 1.72 | | | | | 72.0 | 30.185 | 71.5 | 72.0 | 58 | 16 5 | 16 18 17 56 11 1/2 | 0.37 | | | | | 72.0 | 30.185 | 71.6 | 72.2 | 1 | 1 37 | 1 45 18 1 41 | 1.79 | | | | | 72.5 | 30.102 | 70.6 | 71.2 | 54 | 39 43 | 39 57 22 39 50 | 0.39 | | | | | 72.5 | 30.101 | 71.2 | 71.7 | 1 | 44 54 | 45 11 22 45 2 1/2 | 0.92 | | | | | 71.0 | 30.086 | 69.8 | 70.2 | 20 | 24 48 | 25 7 0 24 57 1/2 | 0.58 | | | | | 67.5 | 30.023 | 67.2 | 67.8 | 1 | 19 24 | 19 31 11 19 27 1/2 | 1.77 | | | | | 72.0 | 29.995 | 73.8 | 74.2 | 63 | 44 56 | 45 7 16 45 1 1/2 | 0.34 | | | | | 72.5 | 29.994 | 74.9 | 74.9 | 1 | 51 39 | 51 47 16 51 43 | 1.74 | | | | | 75.0 | 29.909 | 76.8 | 77.1 | 52 | 18 26 | 18 44 21 18 35 | 0.44 | | | | | 75.0 | 29.908 | 77.0 | 77.0 | 1 | 30 29 | 30 46 21 30 37 1/2 | 1.31 | | | | | 74.5 | 29.901 | 74.8 | 75.3 | 36 | 33 38 | 33 55 0 33 46 1/2 | 0.50 | | Mean.. | | | 71.360 | 30.036 | | | | | | | ### Second Series computed | Year | Mean Temp. | Interval | Uncorrected No. of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vibns in 24 Mean Solar Hours | |------|------------|----------|------------------------------|--------------|------------------|-------------------|-------------------------------------| | 1829 | | | | | | | | | | 66.925 | 4 33 54 | 86088.34 | -0.03 | +1.628 | +2.073 | 86092.04 | | | 71.875 | 5 4 18 | 86086.14 | 0.03 | 1.757 | 4.157 | 86092.02 | | | 71.775 | 1 18 43 | 86086.28 | 0.03 | 1.427 | 4.115 | 86091.79 | | | 70.600 | 1 29 20 | 86087.04 | 0.03 | 0.849 | 3.621 | 86091.48 | | | 69.950 | 4 59 28 | 86086.90 | 0.17 | 1.505 | 3.347 | 86091.54 | | | 71.400 | 4 38 9 | 86086.30 | 0.17 | 1.641 | 3.957 | 86091.73 | | | 70.725 | 1 39 55 | 86087.40 | 0.17 | 0.906 | 3.673 | 86091.81 | | | 70.750 | 5 25 34 | 86086.59 | 0.08 | 1.499 | 3.684 | 86091.69 | | | 75.925 | 4 26 52 | 86084.68 | 0.08 | 1.689 | 5.862 | 86092.15 | | | 76.025 | 3 3 9 | 86084.68 | -0.08 | +1.248 | +5.905 | 86091.75 | | Mean.. | | | | | | | | | | | | | | | | | | | | | | | | | | (No. of Coincidences = 419) Number of Vibrations in vacuo, in 24 Mean Solar Hours... 86097.66 ## Rate of the Sidereal Clock. | Dec. 18th. | Dec. 19th. | Dec. 20th. | |------------|------------|------------| | **By β Aurigae** | -0.04 | **By α Ceti** | -0.28 | **By α Ceti** | +0.03 | | Sirius | -0.15 | Aldebaran | 0.00 | Aldebaran | -0.02 | | Procyon | +0.05 | β Tauri | 0.00 | Rigel | 0.22 | | Pollux | 0.00 | δ Orionis | 0.12 | β Tauri | 0.04 | | Mean Rate | -0.03 | ζ | -0.46 | δ Orionis | 0.07 | | | | Mean Rate | -0.17 | ζ | -0.20 | | | | Mean Rate | -0.08 | ### Third Series. | 1829 | Attached Therm. | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coin. by the Sidereal Clock. | Arc. | Remarks | |------|-----------------|--------|--------|--------------|---------|--------|-------------------------------------|------|----------| | Dec. 23 | 72.0 | 30.094 | 71.9 | 72.2 | 1 | 26 48 | 27 4 | 22 26 | 56 | 1.29 | | | 71.0 | 30.070 | 70.0 | 70.3 | 28 | 48 33 | 48 52 | 0 48 | 42 | 0.58 | | 24 | 66.0 | 30.095 | 65.0 | 65.5 | 1 | 45 0 | 45 5 | 11 45 | 2 | 1.84 | | | 70.0 | 30.094 | 69.1 | 69.6 | 62 | 5 59 | 6 10 | 17 6 | 4 | 0.34 | | | 71.1 | 39.094 | 71.9 | 72.4 | 1 | 10 37 | 10 52 | 17 10 | 44 | 1.31 | | | 74.0 | 30.072 | 74.3 | 75.0 | 24 | 10 14 | 10 33 | 19 10 | 23 | 0.68 | | | 74.0 | 30.072 | 76.0 | 76.6 | 1 | 16 1 | 16 17 | 19 16 | 9 | 0.92 | | | 74.0 | 30.055 | 75.0 | 75.7 | 31 | 53 20 | 53 32 | 21 53 | 26 | 0.40 | | | 74.0 | 30.054 | 75.4 | 76.0 | 1 | 59 12 | 59 26 | 21 59 | 19 | 1.38 | | | 73.0 | 30.080 | 72.9 | 73.1 | 33 | 46 48 | 49 4 | 0 46 | 56 | 0.50 | | 25 | 74.0 | 30.196 | 73.1 | 73.7 | 1 | 46 45 | 46 57 | 19 46 | 51 | 1.64 | | | 73.0 | 30.185 | 73.0 | 73.5 | 59 | 49 52 | 50 14 | 0 50 | 3 | 0.48 | | | 72.0 | 30.010 | 71.5 | 72.0 | 1 | 23 25 | 23 38 | 12 23 | 31 | 1.60 | | 26 | 77.0 | 30.060 | 76.2 | 76.9 | 65 | 58 42 | 58 59 | 17 58 | 50 | 0.28 | | | 79.0 | 30.061 | 79.9 | 79.9 | 1 | 9 1 | 9 19 | 18 9 | 10 | 0.98 | | | 82.0 | 30.020 | 81.6 | 81.9 | 21 | 53 29 | 53 45 | 19 53 | 37 | 0.58 | | | 82.0 | 30.019 | 82.0 | 82.0 | 1 | 0 50 | 1 6 | 20 0 | 58 | 1.16 | | | 81.0 | 30.003 | 80.4 | 80.6 | 32 | 42 30 | 42 46 | 22 42 | 38 | 0.52 | | | 81.0 | 30.002 | 80.2 | 80.4 | 1 | 53 4 | 53 22 | 22 53 | 13 | 1.12 | | | 79.0 | 29.970 | 78.8 | 79.3 | 25 | 58 15 | 58 33 | 0 58 | 24 | 0.66 | | 27 | 74.0 | 29.942 | 74.0 | 74.0 | 1 | 40 47 | 40 55 | 12 40 | 51 | 1.83 | | | 79.0 | 29.965 | 79.8 | 80.1 | 65 | 15 26 | 15 36 | 18 15 | 31 | 0.28 | | | 80.0 | 29.975 | 80.0 | 80.1 | 1 | 21 4 | 21 22 | 18 21 | 13 | 1.28 | | | 80.0 | 29.976 | 80.6 | 80.8 | 28 | 41 54 | 42 12 | 20 42 | 3 | 0.58 | | | 81.0 | 29.976 | 81.0 | 81.3 | 1 | 47 44 | 48 0 | 20 47 | 52 | 1.34 | | | 80.0 | 29.930 | 80.0 | 80.1 | 29 | 13 43 | 14 1 | 23 13 | 52 | 0.60 | | | 80.0 | 29.928 | 80.0 | 80.2 | 1 | 23 52 | 24 10 | 23 24 | 1 | 1.13 | | | 78.0 | 29.962 | 78.0 | 78.5 | 19 | 57 46 | 58 8 | 0 57 | 54 | 0.68 | | Mean | 76.107 | 30.034 | ### Third Series computed. | Year | Mean Temp. | Interval | Uncorrected No. of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vib in 24 Mean Solar Hours | |------|------------|----------|------------------------------|--------------|-----------------|--------------------|----------------------------------| | 1829 | | | | | | | | | | h m s | | | | | | | | 71.100 | 2 21 46 | 86086.56 | -0.01 | +1.361 | +3.831 | 86091.74 | | | 67.300 | 5 21 2 | 86087.82 | +0.14 | 1.587 | 2.231 | 86091.78 | | | 73.400 | 1 59 39 | 86085.38 | +0.14 | 1.567 | 4.799 | 86091.89 | | | 75.825 | 2 37 17 | 86085.72 | +0.14 | 0.675 | 5.820 | 86092.35 | | | 74.350 | 2 47 37 | 86085.22 | +0.14 | 1.336 | 5.199 | 86091.89 | | | 73.325 | 5 3 12 | 86085.12 | +0.14 | 1.640 | 4.768 | 86091.67 | | | 74.150 | 5 35 20 | 86085.36 | -0.02 | 1.167 | 5.115 | 86091.62 | | | 80.825 | 1 44 27 | 86083.60 | -0.02 | 0.974 | 7.925 | 86092.45 | | | 81.250 | 2 41 40 | 86082.82 | -0.02 | 1.098 | 8.104 | 86092.00 | | | 79.675 | 2 5 11 | 86082.88 | -0.02 | 1.241 | 7.441 | 86091.54 | | | 76.975 | 5 34 40 | 86084.30 | -0.02 | 1.428 | 6.304 | 86092.01 | | | 80.375 | 2 20 50 | 86082.92 | -0.02 | 1.348 | 7.736 | 86091.98 | | | 80.600 | 2 26 0 | 86082.72 | -0.02 | 1.464 | 7.831 | 86091.99 | | | 79.175 | 1 33 53 | 86082.86 | -0.02 | +1.302 | +7.231 | 86091.37 | | Mean: 76.301 Buoyancy: +5.85 (No. of Coincidences = 507) Number of Vibrations in vacuo, in 24 Mean Solar Hours: 86097.70 ### Rate of the Sidereal Clock. | Dec 23rd. | Dec 24th. | Dec. 25th, 26th, & 27th. | |-----------|-----------|-------------------------| | By α Ceti | By α Ceti | By Rigel | | -0.02 | +0.02 | +0.09 | | Aldebaran | Aldebaran | β Tauri | | -0.01 | 0.26 | +0.01 | | Rigel | Rigel | δ Orionis | | -0.05 | 0.17 | -0.10 | | β Tauri | β Tauri | ζ | | -0.01 | 0.02 | -0.08 | | δ Orionis | δ Orionis | Mean Rate | | +0.01 | 0.00 | -0.02 | | ξ | ξ | | | -0.08 | +0.35 | | | Mean Rate | Mean Rate | | | -0.01 | +0.14 | | ### Fourth Series. | Year | Attached Therm. | Barom. | Therm. | No. of Coin. | Disapp. | Re-app. | Time of Coin. by the Sidereal Clock. | Arc. | Remarks | |------|-----------------|--------|--------|--------------|---------|---------|-------------------------------------|------|---------| | 1830 | | | | | | | | | | | Jan. 22 | 67.5 | 30.088 | 67.8 | 68.2 | 1 | 16 11 | 16 29 | 16 16 20 | 1.40 | Shut the clock door, and kept the Northern chase open. | | | 68.0 | 30.085 | 67.2 | 67.4 | 11 | 8 47 | 9 5 | 17 8 56 | 1.03 | | | 68.0 | 30.085 | 67.8 | 68.1 | 1 | 14 4 | 14 20 | 17 14 12 | 1.01 | | | 69.0 | 30.085 | 68.2 | 68.6 | 11 | 6 47 | 7 3 | 18 6 55 | 0.76 | | | 69.0 | 30.085 | 69.2 | 69.7 | 1 | 12 4 | 12 20 | 18 12 12 | 0.72 | | | 70.0 | 30.087 | 69.8 | 70.2 | 11 | 4 48 | 5 4 | 19 4 56 | 0.52 | | | 72.0 | 30.087 | 72.0 | 72.3 | 1 | 18 30½ | 18 36½ | 19 18 33½ | 1.91 | | | 72.0 | 30.084 | 71.5 | 71.7 | 11 | 10 47 | 11 2 | 20 10 54½ | 1.36 | | | 72.0 | 30.084 | 72.6 | 73.2 | 1 | 16 1 | 16 17 | 20 16 9 | 1.34 | | | 72.0 | 30.062 | 71.2 | 71.5 | 11 | 8 31 | 8 47 | 21 8 39 | 0.97 | | | 72.0 | 30.062 | 71.7 | 71.9 | 1 | 13 45½ | 14 21 | 21 13 54 | 0.93 | | | 72.0 | 30.055 | 70.5 | 70.8 | 11 | 6 20 | 6 36 | 22 6 28 | 0.71 | | | 72.5 | 30.037 | 71.2 | 71.5 | 1 | 10 21 | 10 37 | 23 10 29 | 1.47 | | | 72.5 | 30.035 | 70.2 | 70.4 | 12 | 8 1½ | 8 18½ | 0 8 10 | 1.06 | | | 72.5 | 30.035 | 71.2 | 71.5 | 1 | 13 17 | 13 33 | 0 13 25 | 1.02 | | | 72.5 | 30.043 | 70.0 | 70.3 | 11 | 5 51½ | 6 8½ | 1 6 0 | 0.78 | | Mean: | 70.844 | 30.063 | | | | | | | | ### Fourth Series computed. | 1830 | Mean Temp. | Interval | Uncorrected No. of Vibrations | Clock's Rate | Correc. for Arc. | Reduc. to 62° Fahr. | Reduced Vib. in 24 Mean Solar Hours | |------|------------|----------|------------------------------|--------------|-----------------|--------------------|-----------------------------------| | | | | | | | | | | 67.650 | h m s | 0 52 36 | 86087.52 | -0.93 | +2.481 | +2.379 | 86091.45 | | 68.175 | | 0 52 43 | 86088.76 | 0.93 | 1.275 | 2.600 | 86091.70 | | 69.725 | | 0 52 44 | 86088.90 | 0.93 | 0.624 | 3.252 | 86091.85 | | 71.875 | | 0 52 21 | 86084.94 | 0.93 | 4.340 | 4.157 | 86092.51 | | 72.125 | | 0 52 30 | 86086.48 | 0.93 | 2.168 | 4.263 | 86091.98 | | 71.225 | | 0 52 34 | 86087.18 | 0.93 | 1.095 | 3.984 | 86091.33 | | 70.825 | | 0 57 41 | 86085.86 | 0.93 | 2.600 | 3.715 | 86091.24 | | 70.750 | | 0 52 35 | 86087.34 | -0.93 | +2.053 | +3.684 | 86092.15 | Mean... 70.294 Mean... 86091.78 Buoyancy............. +5.91 (No. of Coincidences = 81) Number of Vibrations in vacuo, in 24 Mean Solar Hours... 86097.69 ### Rate of the Sidereal Clock. | Jan. 22nd. | s | |------------|---| | By Castor | -0.90 | | ε Geminor | 0.96 | | Sirius | 0.82 | | δ Geminor | 0.90 | | Castor | 0.80 | | Procyon | 1.02 | | Pollux | -1.08 | | Mean Rate | -0.93 | ### Abstract of Mr. Fallows’s observations. Mean of 401 coincidences = 86097.67 Mean of 419 coincidences = 86097.66 Mean of 507 coincidences = 86097.70 Mean of 81 coincidences = 86097.69 True Mean of 1408 coincidences = 86097.68 NOTE BY CAPTAIN SABINE. The observations which Mr. Fallows has communicated to the Society in this memoir, having been corrected for buoyancy and expansion, before the volume of the Phil. Trans. had reached the Cape, in which the true value of those corrections is assigned from experiments with a pendulum of the same materials and figure as that employed by Mr. Fallows, I have re-computed his results with the correct elements of reduction, and find the retardation of the vibrations at the Cape, compared with those in London, to be 67.15 per diem, instead of 67.12, the difference between Mr. Fallows's calculation and mine amounting only to three hundredths of a vibration per diem. The small amount of the difference, on the employment of the more correct elements of reduction, is an illustration of the remark, with which I concluded the paper on the reduction to a vacuum of an invariable pendulum (Phil. Trans. 1829, page 236.) ; that in relative experiments, computed before the true reduction to a vacuum was known, and in which a correction for expansion was employed, derived directly from the vibration of the pendulum at the same spot in different temperatures, (as is the case in Mr. Fallows's calculation,) a compensation takes place of the errors of the respective reductions for expansion and resistance, leaving the only uncompensated error in the final result, that arising from barometric differences, which in all cases of comparison between stations not far removed from the level of the sea, cannot be otherwise than extremely small. In Mr. Fallows's calculation he has taken the rate in London of the invariable pendulum which Captain Ronald took out to the Cape, solely from my observations with it: if, however, Captain Ronald's observations with the same pendulum in London be added to mine, and a true mean be taken corresponding to the number of observations of each observer, the retardation is precisely that stated by Mr. Fallows; namely, 67.12 vibrations per diem.