Experiments to Ascertain the Ratio of the Magnetic Forces Acting on a Needle Suspended Horizontally, in Paris and in London

I. Experiments to ascertain the ratio of the magnetic forces acting on a needle suspended horizontally, in Paris and in London. By Captain Edward Sabine, of the Royal Artillery, Secretary of the Royal Society. Read June 21, 1827. The magnetic needles employed in these experiments were cylinders of 0.16 inch diameter, and 2.4 inches in length, pointed at the ends: they were suspended by a single silk fibre of rather more than five inches in length. The box in which they were inclosed, as a protection from the weather, was of wood, having at the bottom a graduated circle in ivory, rather exceeding in diameter the length of the needles, and over the centre of which the silk fibre was suspended. The bottom of the box being rendered horizontal by means of foot screws, and shown to be so by an unattached spirit level, the zeros of the circle were placed in the direction of the magnetic meridian, and a needle was suspended in a horizontal position. Another needle was then employed to draw it 50 or 60 degrees from its natural direction; on the removal of which, the suspended needle resumed its direction in the ordinary process of vibration. The registry of the vibrations was commenced when the arc had diminished to 30°, and continued until it was reduced to below 5°: the method of registering the vibration will be best understood by a reference to the Tables at the close, and is too simple to require further explanation. The number of vibrations made by each needle between the arcs of 30° and 5° was usually from 300 to 400; and the time in which these were performed varied, in the different needles, from 12 to 16 minutes: the mean time of performing 100 vibrations between the specified arcs is the result deduced for each experiment. MDCCCXXVIII. Four of the needles, Nos. IV, VIII, X, and XI, with an apparatus in duplicate, were sent to me in the summer of 1826 by Professor Hansteen of Christiania, to be employed in obtaining the comparative magnetic intensity in different parts of Great Britain. Shortly after their arrival, an opportunity occurred of sending two of the needles, Nos. IV and XI, with an apparatus, to Captain Basil Hall, in Edinburgh; by whom, assisted by Lieut. Robert Craigie, of the Royal Navy, the experiments numbered 12 to 16 in the subjoined tables were made, in February 1827; and the needles returned, so as to be included in the comparative experiments between Paris and London. The two remaining needles, marked A and B, making six in all, were made, at my request, by Mr. Dollond, in the autumn of 1826, of the same size and form as those sent me by Professor Hansteen. On the 3rd of December 1826, being about seven weeks before I expected to leave England for Paris, I made the experiments 1 to 4, with needles A and B, VIII and X, in the garden of the Horticultural Society at Chiswick; and after an interval of six weeks, repeated, with the same needles, at Shernfold Park near Tunbridge Wells, on the 15th of January, the experiments 5 to 8, to ascertain that their magnetism had sustained no change. On the 30th of January, fifteen days only after this second trial, three of the needles, No. VIII, A, and B, (No. X having been accidentally mislaid on that day,) were employed in the garden of the Royal Observatory at Paris, in the experiments numbered 9 to 11; and on the 14th of March, Nos. X and XI (which last had been returned by Captain Hall from Edinburgh), and the needles A and B repeated, were employed in the experiments numbered 17 to 20; in which observations I had the pleasure of being assisted by Mr. William Ritchie, rector of Tain Academy in Scotland. An opportunity occurring, Nos. VIII, X, and XI, were sent to England early in April, and the experiments numbered 21 to 24 made with those three needles and, with No. IV (sent by Captain Hall to London, but which had not been forwarded to me in Paris), in the garden of the Horticultural Society at Chiswick, on the 23rd of April, by Captain Chapman of the Royal Artillery, who kindly undertook this trouble at my request; and having done so, returned them again to me at Paris. By Professor Hansteen's recommendation, the four needles which he had sent me were kept at all times separate from each other; the two which Mr. Dollond made had been on the contrary kept together in a small ivory case; the needles being placed parallel, but not touching, the north pole of the one being opposed to the south pole of the other, but not connected. Being desirous of ascertaining the effect which separation might have on the magnetism of these needles (A and B), they were removed from each other after the experiments of the 14th of March, and kept apart until the 30th of April; when they were again tried in the garden of the Observatory at Paris, in experiments 25 and 26, and their time of vibration was found the same as before. Nos. VIII and XI, which had arrived from Captain Chapman, were tried on the same day, Experiments 27 and 28, and Nos. IV and X, which arrived a few days after, on the 10th of May, in the experiments 29 and 30. Finally, on my return to England in June, the needles were again taken to the garden at Chiswick, and the experiments 31 to 34 made on the 11th of June. The place of observation in the garden at Chiswick was near the middle of the Arboretum; and in the garden of the Observatory at Paris, in the Cabinet of M. Arago, specially constructed for magnetic observations, which he kindly permitted me to occupy for the purpose. The Tables at the close contain the full details of the temperatures and the hours of the day at which the several experiments were made. It will be seen that the variations of temperature included at each station were very considerable; but care was taken that the mean temperature of the several experiments with each needle should, in most cases at least, approach the same amount at London and at Paris: | Needle | Temperature at London | Temperature at Paris | |----------|-----------------------|----------------------| | Needle IV| 54.5 | 62 | | Needle VIII| 50 | 52.5 | | Needle X | 40.5 | 59 | | Needle XI| 54.5 | 66.5 | | Needle A | 55 | 54 | | Needle B | 54.5 | 53 | Still the preponderance of high temperatures was at Paris; and it is expedient therefore to reduce the several results to a nearer accord with what they would have been, had they been all made at the same temperature. I avail myself for this purpose of a formula for the reduction of different tem- peratures, which Professor Hansteen has derived from experiments made with a cylinder precisely similar in all respects to those which he sent to me. Supposing the time of $n$ vibrations in the temperature $t$ to be $T$ seconds, and in the temperature $t'$ to be $T'$ seconds, $T = T' \left[1 - 0.000165 (t' - t)\right]$, the temperature being expressed in degrees of Fahrenheit. It is possible that this reduction may not be strictly correct for all cylinders of the same shape and make as that from whence it was originally derived; but it may at least be confidently presumed, that the results obtained by such cylinders being corrected by it, will more nearly approach a strict relation to each other, than when no attempt is made to counteract the effect of differences of temperature: and that, viewing the small ultimate amount to be compensated in the present case, this formula may be considered as being quite sufficient for the purpose. The following Table presents in one view the results obtained with each needle at the different stations at which they were tried. | Needle | Date | Therm. | Time of Vibration | Reduction to 40° | Corrected Time of Vibration | |--------|-----------------------|--------|-------------------|------------------|----------------------------| | IV | Apr. 23, 1827, 1 p.m. | 40 | 341.69 | 0.00 | 341.69 | | | June 11, 1827, 2½ p.m.| 69 | 343.21 | -1.64 | 341.57 | | | Mean | | | | 341.63 | | | May 10, 1827, 5½ p.m. | 62 | 331.12 | -1.20 | 329.92 | | VIII | Dec. 3, 1826, 2½ p.m. | 41 | 275.85 | -0.05 | 275.80 | | | Apr. 23, 1827, 2 p.m. | 40 | 276.44 | 0.00 | 276.44 | | | June 4, 1827, 1½ p.m. | 69 | 278.02 | -1.33 | 276.69 | | | Mean | | | | 276.31 | | | Jan. 30, 1827, 11½ a.m.| 28 | 267.22 | +0.53 | 267.75 | | | Apr. 30, 1827, 5½ p.m.| 77 | 268.76 | -1.64 | 267.12 | | | Mean | | | | 267.435 | | X | Dec. 3, 1826, 2 p.m. | 41 | 329.63 | -0.05 | 329.58 | | | Apr. 23, 1827, 2½ p.m.| 40 | 330.86 | 0.00 | 330.86 | | | Mean | | | | 330.22 | | | Mar. 14, 1827, 1½ p.m.| 56 | 319.17 | -0.84 | 318.33 | | | May 10, 1827, 5 p.m. | 62 | 320.38 | -1.16 | 319.22 | | | Mean | | | | 318.775 | | XI | Apr. 23, 1827, 3 p.m. | 40 | 313.98 | 0.00 | 313.98 | | | June 11, 1827, 3½ p.m.| 69 | 315.37 | -1.53 | 313.84 | | | Mean | | | | 313.91 | | | Mar. 14, 1827, 2½ p.m.| 56 | 304.13 | -0.80 | 303.33 | | | Apr. 30, 1827, 5 p.m. | 77 | 304.73 | -1.86 | 302.87 | | | Mean | | | | 303.10 | | A | Dec. 3, 1826, 3½ p.m. | 41 | 247.03 | -0.05 | 246.98 | | | June 11, 1827, 4 p.m. | 69 | 250.07 | -1.20 | 248.87 | | | Mean | | | | 247.925 | | | Jan. 30, 1827, Noon. | 28 | 238.95 | +0.48 | 239.43 | | | Mar. 14, 1827, 2½ p.m.| 56 | 240.73 | -0.63 | 240.10 | | | Apr. 30, 1827, 3½ p.m.| 77 | 241.20 | -1.47 | 239.73 | | | Mean | | | | 239.573 | | B | Dec. 3, 1826, 3 p.m. | 41 | 345.94 | -0.05 | 345.89 | | | June 15, 1827, 3½ p.m.| 68 | 349.16 | -1.59 | 347.57 | | | Mean | | | | 346.73 | | | Jan. 30, 1827, 1 p.m. | 28 | 331.85 | +0.66 | 332.51 | | | Mar. 14, 1827, 3 p.m. | 56 | 337.21 | -0.88 | 336.33 | | | Apr. 30, 1827, 3 p.m. | 77 | 338.01 | -2.06 | 335.95 | | | Mean | | | | 334.93 | From the results in the preceding Table it appears that when the horizontal intensity in London is taken as unity, the same intensity in Paris is shown by the several cylinders to be as follows: By Needle IV = 1,0732 By Needle VIII = 1,0675 By Needle X = 1,0726 By Needle XI = 1,0723 By Needle A = 1,0709 By Needle B = 1,0717 Mean . . . . 1,07137 or 1,0714. From the very careful observations which are regularly made on the dip of the needle at the Royal Observatory at Paris, the mean dip corresponding to the period when these experiments were made is known to have been 67° 58'. In assuming the dip at the same period at London to have been 69° 45', which is allowing a diminution of 3' per annum since it was observed in 1821 to be 70° 04', (Phil. Trans. for 1822, Art. I.) we cannot fail to be sufficiently near the truth for the present purpose. The horizontal intensity at Paris being then as 1,0714, to unity at London, it results that the absolute intensity of terrestrial magnetism was greater at London than at Paris at the period of these experiments by about eleven parts in a thousand. The experiments of Captain Hall and Lieut. Craigie at Edinburgh with Nos. IV and XI give the following results: | Needle | Date | Temp. | Time of Vibration | Reduction to 40° | Corrected Time of Vib. | |--------|------------|-------|-------------------|------------------|------------------------| | No. IV | Feb. 15, 1827 | 32 | 350.47 | +0.46 | 350.93 | | No. XI | Feb. 15, 1827 | 32 | 321.07 | +0.43 | 321.50 | Vibrations in London at 40° page 4. Corrected Time of Vib. 341.63 Vibrations in London at 40° page 4. Corrected Time of Vib. 313.91 Whence the horizontal intensity at Edinburgh, when the same intensity at London is taken as unity, is by No. IV = 0.9477 No. XI = 0.9534 And by a mean of the two Needles, 0.9505. In the Horticultural Society's Garden at Chiswick, near London: December 3d, 1826. Observer, Captain Sabine. Therm. 41°. Chron. Molyneux 407. Rate, nearly Mean Time. | Exp. 1. Needle VIII. Hour 2½ P.M. | Exp. 2. Needle X. Hour 2 P.M. | |----------------------------------|--------------------------------| | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | | 0 | 40 29,6 | 260 | 52 27,6 | 11 58 | 0 | 8 56 | 200 | 19 56,4 | 11 00,4 | | 10 | 40 57,6 | 270 | 52 55,2 | 11 57,6 | 10 | 9 29,2 | 210 | 20 29,2 | 11 00 | | 20 | 41 25,2 | 280 | 53 22,8 | 11 57,6 | 20 | 10 02,8| 220 | 21 02 | 10 59,2 | | 30 | 41 53,2 | 290 | 53 50,4 | 11 57,2 | 30 | 10 35,6| 230 | 21 34,8 | 10 59,2 | | 40 | 42 20,8 | 300 | 54 17,6 | 11 56,8 | 40 | 11 08,8| 240 | 22 08 | 10 59,2 | | 50 | 42 48,8 | 310 | 54 45,6 | 11 56,8 | 50 | 11 42,4| 250 | 22 40,8 | 10 58,4 | | 60 | 43 16,4 | 320 | 55 12,8 | 11 56,4 | 60 | 12 15,2| 260 | 23 13,6 | 10 58,4 | | 80 | 44 12 | | | | 80 | 13 21,2| | | | | 100 | 45 07,2 | | | | 100 | 14 27,2| | | | | 120 | 46 02,8 | | | | 120 | 15 32,8| | | | | 140 | 46 57,6 | | | | 140 | 16 38,8| | | | | 160 | 47 52,8 | | | | 160 | 17 44,8| | | | | 180 | 48 47,6 | | | | 180 | 18 50,4| | | | | 200 | 49 42,8 | | | | | | | | | | 220 | 50 38 | | | | | | | | | | 240 | 51 32,4 | | | | | | | | | Mean . . . 11 57,2 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 275,85 sec. | Exp. 3. Needle A. Hour 3½ P.M. | Exp. 4. Needle B. Hour 3 P.M. | |--------------------------------|--------------------------------| | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | | 0 | 40 43,2 | 300 | 53 05,2 | 12 22 | 0 | 14 33,6 | 200 | 26 06,8 | 11 33,2 | | 10 | 41 08,4 | 310 | 53 30 | 12 21,6 | 10 | 15 08,8 | 210 | 26 41,6 | 11 32,8 | | 20 | 41 33,2 | 320 | 53 54,8 | 12 21,6 | 20 | 15 43,6 | 220 | 27 16 | 11 32,4 | | 30 | 41 58,4 | 330 | 54 19,2 | 12 20,8 | 30 | 16 18,4 | 230 | 27 50 | 11 31,6 | | 40 | 42 23,2 | 340 | 54 44 | 12 20,8 | 40 | 16 53,2 | 240 | 28 24,4 | 11 31,2 | | 50 | 42 48 | 350 | 55 08,4 | 12 20,4 | 50 | 17 28 | 250 | 28 59,2 | 11 31,2 | | 60 | 43 12,8 | 360 | 55 33,2 | 12 20,4 | 60 | 18 02,8 | 260 | 29 33,6 | 11 30,8 | | 80 | 44 03,8 | | | | 80 | 19 12 | | | | | 100 | 44 52 | | | | 100 | 20 21,2 | | | | | 120 | 45 41,6 | | | | 120 | 21 30,4 | | | | | 140 | 46 31,2 | | | | 140 | 22 39,6 | | | | | 160 | 47 20,4 | | | | 160 | 23 48,8 | | | | | 180 | 48 09,6 | | | | 180 | 24 58,4 | | | | | 200 | 48 59,2 | | | | | | | | | | 220 | 49 48,4 | | | | | | | | | | 240 | 50 37,6 | | | | | | | | | | 260 | 51 26,8 | | | | | | | | | | 280 | 52 16 | | | | | | | | | Mean . . . 12 21,09 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 247,03 sec. Mean . . . 11 31,89 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 345,94 sec. In the grounds of Shernfold Park, Frant, Sussex: January 15th, 1827. Observer, Captain Sabine. Therm. 38°. Chron. Molyneux 407. Rate, Mean Time. **Exp. 5. Needle VIII. Hour 2½ P.M.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns. in | |--------|-------|--------|-------|---------------| | 0 | m s | 300 | 44 58 | 13 44,4 | | 10 | 31 41,6 | 310 | 45 25,2 | 13 43,6 | | 20 | 32 09,2 | 320 | 45 52,6 | 13 43,4 | | 30 | 32 37,2 | 330 | 46 20 | 13 42,8 | | 40 | 33 05,2 | 340 | 46 47,6 | 13 42,4 | | 50 | 33 32,2 | 350 | 47 14,2 | 13 42 | | 60 | 34 00,8 | 360 | 47 42,8 | 13 42 | | 80 | 34 55,2 | | | | | 100 | 35 50 | | | | | 120 | 36 45,2 | | | | | 140 | 37 40,4 | | | | | 160 | 38 35,2 | | | | | 180 | 39 29,6 | | | | | 200 | 40 24,4 | | | | | 220 | 41 19,6 | | | | | 240 | 42 14,4 | | | | | 260 | 43 09,2 | | | | | 280 | 44 04 | | | | Mean . . . 13 42,94 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 274,31 sec. **Exp. 6. Needle X. Hour 1½ P.M.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns. in | |--------|-------|--------|-------|---------------| | 0 | m s | 43 28,8 | 300 | 59 54 | | 10 | 44 02 | 310 | 00 26,4 | 16 24,4 | | 20 | 44 35,2 | 320 | 00 59,6 | 16 24,4 | | 30 | 45 08,4 | 330 | 01 32 | 16 23,6 | | 40 | 45 41,2 | 340 | 02 04,4 | 16 23,2 | | 50 | 46 14,4 | 350 | 02 37,2 | 16 23,8 | | 60 | 46 47,2 | 360 | 03 10 | 16 22,8 | | 80 | 47 53,2 | | | | | 100 | 48 58,8 | | | | | 120 | 50 04,4 | | | | | 140 | 51 10 | | | | | 160 | 52 15,2 | | | | | 180 | 53 21,2 | | | | | 200 | 54 26,8 | | | | | 220 | 55 32 | | | | | 240 | 56 37,2 | | | | | 260 | 57 42,8 | | | | | 280 | 58 48,4 | | | | Mean . . . 16 23,77 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 327,92 sec. **Exp. 7. Needle A. Hour 3½ P.M.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns. in | |--------|-------|--------|-------|---------------| | 0 | m s | 300 | 42 24 | 12 18 | | 10 | 30 31,6 | 310 | 42 48,8 | 12 17,2 | | 20 | 30 56 | 320 | 43 12,8 | 12 16,8 | | 30 | 31 20,8 | 330 | 43 37,6 | 12 16,8 | | 40 | 31 45,6 | 340 | 44 02 | 12 16,4 | | 50 | 32 10,4 | 350 | 44 26,4 | 12 16 | | 60 | 32 35,2 | 360 | 44 50,8 | 12 15,6 | | 80 | 33 24,8 | | | | | 100 | 34 14 | | | | | 120 | 35 03,2 | | | | | 140 | 35 52 | | | | | 160 | 36 41,2 | | | | | 180 | 37 30 | | | | | 200 | 38 19,2 | | | | | 220 | 39 08 | | | | | 240 | 39 57,2 | | | | | 260 | 40 46 | | | | | 280 | 41 35,2 | | | | Mean . . . 12 16,69 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 245,56 sec. **Exp. 8. Needle B. Hour 4 P.M.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns. in | |--------|-------|--------|-------|---------------| | 0 | m s | 2 32,8 | 300 | 19 47,6 | | 10 | 3 07,6 | 310 | 20 21,6 | 17 14 | | 20 | 3 42,4 | 320 | 20 56 | 17 13,6 | | 30 | 4 17,2 | 330 | 21 30,4 | 17 13,2 | | 40 | 4 52 | 340 | 22 05,2 | 17 13,2 | | 50 | 5 26,8 | 350 | 22 39,2 | 17 12,4 | | 60 | 6 01,2 | 360 | 23 13,2 | 17 12 | | 80 | 7 10,4 | | | | | 100 | 8 19,2 | | | | | 120 | 9 28,4 | | | | | 140 | 10 37,2 | | | | | 160 | 11 46,4 | | | | | 180 | 12 55,2 | | | | | 200 | 14 04,4 | | | | | 220 | 15 12,8 | | | | | 240 | 16 21,2 | | | | | 260 | 17 30 | | | | | 280 | 18 39,2 | | | | Mean . . . 17 13,31 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 344,44 sec. In the Garden of the Observatory at Paris: January 30th, 1827. Observer, Captain Sabine. Therm. 28°. Chron. Molyneux, No. 407. Rate, Mean Time. **Exp. 9. Needle VIII. Hour 11½.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | m s | 15 47,2 | 300 | 29 09,6 | 13 22,4 | | 10 | 16 14 | 310 | 29 36,4 | 13 22,4 | | 20 | 16 41,2 | 320 | 30 03,2 | 13 22 | | 30 | 17 08 | 330 | 30 29,6 | 13 21,6 | | 40 | 17 35,2 | 340 | 30 56 | 13 20,8 | | 50 | 18 01,6 | 350 | 31 23,2 | 13 21,6 | | 60 | 18 28,8 | 360 | 31 49,6 | 13 20,8 | | 80 | 19 22,4 | | | | | 100 | 20 16 | | | | | 120 | 21 09,6 | | | | | 140 | 22 03,2 | | | | | 160 | 22 56,8 | | | | | 180 | 23 50 | | | | | 200 | 24 43,6 | | | | | 220 | 25 37,2 | | | | | 240 | 26 30,4 | | | | | 260 | 27 23,2 | | | | | 280 | 28 16,8 | | | | Mean . . . 13 21,66 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 267,22 sec. **Exp. 10. Needle A. Hour Noon.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | m s | 14 15,6 | 300 | 26 13,2 | 11 57,6 | | 10 | 14 39,6 | 310 | 26 37,2 | 11 57,6 | | 20 | 15 04 | 320 | 27 00,8 | 11 56,8 | | 30 | 15 28 | 330 | 27 24,8 | 11 56,8 | | 40 | 15 52 | 340 | 27 48,8 | 11 56,8 | | 50 | 16 16 | 350 | 28 12,4 | 11 56,4 | | 60 | 16 40,4 | 360 | 28 36,4 | 11 56 | | 80 | 17 28,8 | | | | | 100 | 18 16 | | | | | 120 | 19 03,6 | | | | | 140 | 19 51,6 | | | | | 160 | 20 39,6 | | | | | 180 | 21 27,6 | | | | | 200 | 22 15,2 | | | | | 220 | 23 02,8 | | | | | 240 | 23 50,4 | | | | | 260 | 24 38,4 | | | | | 280 | 25 26 | | | | Mean . . . 11 56,86 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 238,95 sec. **Exp. 11. Needle B. Hour 12 to 1 P.M.** | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | m s | 43 49,6 | 300 | 00 26,8 | 16 37,2 | | 10 | 44 23,6 | 310 | 01 00 | 16 36,4 | | 20 | 44 56,8 | 320 | 01 32,8 | 16 36 | | 30 | 45 30,4 | 330 | 02 05,6 | 16 35,2 | | 40 | 46 04 | 340 | 02 39,2 | 16 35,2 | | 50 | 46 37,2 | 350 | 03 12 | 16 34,8 | | 60 | 47 10,8 | 360 | 03 44,8 | 16 34 | | 80 | 48 17,6 | | | | | 100 | 49 24 | | | | | 120 | 50 30,4 | | | | | 140 | 51 36,8 | | | | | 160 | 52 43,2 | | | | | 180 | 53 49 | | | | | 200 | 54 55,6 | | | | | 220 | 56 02 | | | | | 240 | 57 08 | | | | | 260 | 58 14,4 | | | | | 280 | 59 20,4 | | | | Mean . . . 16 35,54 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 331,85 sec. Edinburgh: February 15th, 1827. Observers, Captain Basil Hall and Lieut. Robert Craigie, R.N. Therm. 32°. Barom. 30,00. Chron. gaining 1°,5 per diem. | Exp. 12. Needle IV. | Exp. 13. Needle IV. | Exp. 14. Needle IV. | |--------------------|--------------------|--------------------| | Vib°s. | Time. | Vib°s. | Time. | Vib°s. | Time. | | 0 | 8 47,5 | 0 | 33 59,5 | 0 | 4 24 | | 10 | 9 23,5 | 10 | 34 35,5 | 20 | 5 35 | | 20 | 9 58,5 | 20 | 35 11,0 | 40 | 6 45,5 | | 30 | 10 34 | 30 | 35 45,5 | 60 | 7 55,8 | | 40 | 11 09,5 | 40 | 36 20,7 | 80 | 9 06,5 | | 50 | 11 45,5 | 50 | 36 56,0 | 100 | 10 16,5 | | 60 | 12 19,5 | 70 | 38 06,5 | 120 | 11 26,5 | | 80 | 13 29,8 | 90 | 39 16,5 | 140 | 12 36,8 | | 100 | 14 59,7 | 110 | 40 26,5 | 160 | 13 46,8 | | 120 | 15 50,0 | 130 | 41 37,0 | 180 | 14 56,5 | | 140 | 16 59,5 | 150 | 42 46,5 | 200 | 16 06,5 | | 160 | 18 09,5 | 170 | 43 57,0 | 220 | 17 16,5 | | 180 | 19 19,5 | 190 | 45 06,5 | 240 | 18 26,5 | | 200 | 20 29,5 | 210 | 46 16,5 | 260 | 19 35,9 | | 220 | 21 39,5 | 230 | 47 26,0 | 280 | 20 46,0 | | 240 | 22 49,8 | 250 | 48 36,5 | | | | 260 | 23 59,2 | 270 | 49 46,0 | | | | 280 | 25 09,0 | | | | | Exp. 15. Needle XI. | Vib°s. | Time. | Vib°s. | Time. | 300 Vib°s in | |--------|-------|--------|-------|--------------| | 0 | 47 31,0 | 0 | 16 52,5 | 300 | | 10 | 48 03,5 | 10 | 17 25,0 | 310 | | 20 | 48 36,0 | 20 | 17 57,5 | 320 | | 30 | 49 08,5 | 30 | 18 30,0 | 330 | | 40 | 49 41,0 | 40 | 19 02,5 | 340 | | 50 | 50 13,5 | 50 | 19 35,0 | 350 | | 60 | 50 45,5 | 60 | 20 07,3 | 360 | | 80 | 51 50,2 | 80 | 21 11,7 | | | 100 | 52 54,8 | 100 | 22 16 | | | 120 | 53 58,8 | 120 | 23 20 | | | 140 | 55 03,5 | 140 | 24 24,5 | | | 160 | 56 07,5 | 160 | 25 29 | | | 180 | 57 12,0 | 180 | 26 33 | | | 200 | 58 16,2 | 200 | 27 37 | | | 220 | 59 20,0 | 220 | 28 41,2 | | | 240 | 60 24,0 | 240 | 29 45 | | | 260 | 61 28,0 | 260 | 30 49 | | | 280 | 61 32,0 | 280 | 31 53,2 | | Mean . . . 16 03,5 Whence the Mean Time of 100 Vibrations in Arcs between 30° and 5° 321,17 sec. Exp. 16. Needle XI. | Vib°s. | Time. | Vib°s. | Time. | 300 Vib°s in | |--------|-------|--------|-------|--------------| | 0 | 32 57 | 0 | 16 04,5 | 300 | | 10 | 33 29 | 10 | 16 04 | 310 | | 20 | 34 00,2 | 20 | 16 02,7 | 320 | | 30 | 34 33 | 30 | 16 03 | 330 | | 40 | 35 04,8 | 40 | 16 02,3 | 340 | | 50 | 35 37,0 | 50 | 16 02 | 350 | | 60 | 36 09,0 | 60 | 16 01,7 | 360 | | 80 | | 80 | | | | 100 | | 100 | | | | 120 | | 120 | | | | 140 | | 140 | | | | 160 | | 160 | | | | 180 | | 180 | | | | 200 | | 200 | | | | 220 | | 220 | | | | 240 | | 240 | | | | 260 | | 260 | | | | 280 | | 280 | | | Mean . . . 16 02,9 Whence the Mean Time of 100 Vibrations in Arcs between 30° and 5° 320,97 sec. MDCCCXXVIII. In the Garden of the Observatory at Paris: March 14th, 1827. Observers, Captain Sabine and Mr. Ritchie. Therm. 56°. Chron. Molyneux, No. 407. Rate, Mean Time. **Exp. 17. Needle X. Hour 1 to 2 P.M.** | Vibns | Time | Vibns | Time | 300 Vibns in | |-------|------|-------|------|--------------| | | | | | | | 0 | 31 | 13,6 | 300 | 47 | | 10 | 31 | 46 | 310 | 47 | | 20 | 32 | 18,4 | 320 | 48 | | 30 | 32 | 50,4 | 330 | 48 | | 40 | 33 | 22,4 | 340 | 49 | | 50 | 33 | 54,8 | 350 | 49 | | 60 | 34 | 26,8 | 360 | 50 | | 80 | 35 | 30,8 | | | | 100 | 36 | 34,8 | | | | 120 | 37 | 38,8 | | | | 140 | 38 | 42,8 | | | | 160 | 39 | 46,4 | | | | 180 | 40 | 50 | | | | 200 | 41 | 54 | | | | 220 | 42 | 58 | | | | 240 | 44 | 01,6 | | | | 260 | 45 | 05,2 | | | | 280 | 46 | 08,8 | | | Mean . . . . 15 57,5 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 319,17 sec. **Exp. 18. Needle XI. Hour 2 to 3 P.M.** | Vibns | Time | Vibns | Time | 300 Vibns in | |-------|------|-------|------|--------------| | | | | | | | 0 | 59 | 17,2 | 300 | 14 | | 10 | 59 | 48 | 310 | 15 | | 20 | 59 | 01,2 | 320 | 15 | | 30 | 00 | 49,6 | 330 | 16 | | 40 | 01 | 20,4 | 340 | 16 | | 50 | 01 | 50,8 | 350 | 17 | | 60 | 02 | 21,2 | 360 | 17 | | 80 | 03 | 22,4 | | | | 100 | 04 | 23,6 | | | | 120 | 05 | 24,8 | | | | 140 | 06 | 25,2 | | | | 160 | 07 | 26 | | | | 180 | 08 | 26,8 | | | | 200 | 09 | 27,6 | | | | 220 | 10 | 28,4 | | | | 240 | 11 | 28,8 | | | | 260 | 12 | 29,6 | | | | 280 | 13 | 30,4 | | | Mean . . . . 15 12,4 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 304,13 sec. **Exp. 19. Needle A. Hour 2 to 3 P.M.** | Vibns | Time | Vibns | Time | 300 Vibns in | |-------|------|-------|------|--------------| | | | | | | | 0 | 26 | 54 | 300 | 38 | | 10 | 27 | 18,2 | 310 | 39 | | 20 | 27 | 42,8 | 320 | 39 | | 30 | 28 | 07,2 | 330 | 40 | | 40 | 28 | 31,2 | 340 | 40 | | 50 | 28 | 55,6 | 350 | 40 | | 60 | 29 | 20 | 360 | 41 | | 80 | 30 | 08,4 | | | | 100 | 30 | 56,8 | | | | 120 | 31 | 44,8 | | | | 140 | 32 | 32,8 | | | | 160 | 33 | 21,2 | | | | 180 | 34 | 09,2 | | | | 200 | 34 | 57,2 | | | | 220 | 35 | 45,2 | | | | 240 | 36 | 33,2 | | | | 260 | 37 | 21,2 | | | | 280 | 38 | 09,2 | | | Mean . . . . 12 02,2 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 240,73 sec. **Exp. 20. Needle B. Hour 3 P.M.** | Vibns | Time | Vibns | Time | 300 Vibns in | |-------|------|-------|------|--------------| | | | | | | | 0 | 51 | 52 | 300 | 08 | | 10 | 52 | 26 | 310 | 09 | | 20 | 53 | 00,6 | 320 | 09 | | 30 | 53 | 34,4 | 330 | 10 | | 40 | 54 | 08,4 | 340 | 10 | | 50 | 54 | 42,8 | 350 | 11 | | 60 | 55 | 16,4 | 360 | 12 | | 80 | 56 | 24 | | | | 100 | 57 | 31,6 | | | | 120 | 58 | 39,6 | | | | 140 | 59 | 46,8 | | | | 160 | 00 | 54 | | | | 180 | 02 | 01,6 | | | | 200 | 03 | 08,8 | | | | 220 | 04 | 16 | | | | 240 | 05 | 23,2 | | | | 260 | 06 | 30,8 | | | | 280 | 07 | 37,6 | | | Mean . . . . 16 51,63 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 337,21 sec. In the Garden of the Horticultural Society, at Chiswick, near London: April 23d, 1827. Observer, Captain Chapman, R.A. Therm. 40°. | Exp. 21. Needle IV. Hour 1 P.M. | Exp. 22. Needle VIII. Hour 2 P.M. | |-------------------------------|---------------------------------| | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | | 0 | m s | 300 | m s | m s | 0 | m s | 300 | m s | m s | | 10 | 28 06 | 310 | 45 11 | 17 05 | 10 | 8 00 | 310 | 21 49 | 13 49 | | 20 | 28 40 | 320 | 45 45 | 17 05 | 20 | 8 27 | 320 | 22 16 | 13 49 | | 30 | 29 15 | 330 | 46 20 | 17 05 | 30 | 8 55 | 330 | 22 45 | 13 50 | | 40 | 29 49 | 340 | 46 54,5| 17 05,5 | 40 | 9 23 | 340 | 23 13 | 13 50 | | 50 | 30 23 | 350 | 47 28 | 17 05 | 50 | 9 51 | 350 | 23 40 | 13 49 | | 60 | 30 57 | 360 | 48 02 | 17 05 | 60 | 10 18 | | | | | 80 | 32 07 | | | | 80 | 11 14 | | | Mean ....13 49,33 | | 100 | 33 15 | | | | 100 | 12 09 | | | | | 120 | 34 23,5| | | | 120 | 13 04 | | | | | 140 | 35 31 | | | | 140 | 14 00 | | | | | 160 | 36 39 | | | | 160 | 14 56 | | | | | 180 | 37 49 | | | | 180 | 15 51 | | | | | 200 | 38 57 | | | | 200 | 16 46 | | | | | 220 | 40 05 | | | | 220 | 17 41,5| | | | | 240 | 41 13 | | | | 240 | 18 36 | | | | | 260 | 42 21 | | | | 260 | 19 32 | | | | | 280 | 43 29,5| | | | 280 | 20 27 | | | | Mean ....17 05,07 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 341,69 sec. Mean ....13 49,33 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 276,44 sec. | Exp. 23. Needle X. Hour 2 to 3 P.M. | Exp. 24. Needle XI. Hour 3 P.M. | |-----------------------------------|---------------------------------| | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | | 0 | m s | 300 | m s | m s | 0 | m s | 300 | m s | m s | | 10 | 38 26 | 310 | 54 59 | 16 33 | 10 | 4 09 | 310 | 20 22 | 15 42 | | 20 | 38 58 | 320 | 55 32 | 16 34 | 20 | 5 11,5| 320 | 20 54 | 15 42,5 | | 30 | 39 32,5| 330 | 56 05 | 16 32,5 | 30 | 5 44 | 330 | 21 26 | 15 42 | | 40 | 40 05 | 340 | 57 11 | 16 32 | 40 | 6 15 | 340 | 21 57 | 15 42 | | 50 | 41 11,5| 350 | 57 44 | 16 32,5 | 50 | 6 47 | 350 | 22 29 | 15 42 | | 60 | 41 46 | 360 | 58 17 | 16 31 | 60 | 7 18 | 360 | 22 59 | 15 41 | | 80 | 42 52,5| | | | 80 | 8 21 | | | | | 100 | 43 58 | | | | 100 | 9 24 | | | Mean ....15 41,93 | | 120 | 45 05 | | | | 120 | 10 27 | | | | | 140 | 46 10,5| | | | 140 | 11 30,5| | | | | 160 | 47 17 | | | | 160 | 12 33 | | | | | 180 | 48 23 | | | | 180 | 13 35 | | | | | 200 | 49 29,5| | | | 200 | 14 38 | | | | | 220 | 50 35,5| | | | 220 | 15 40,5| | | | | 240 | 51 42 | | | | 240 | 16 44 | | | | | 260 | 52 48 | | | | 260 | 17 46 | | | | | 280 | 53 53,5| | | | 280 | 18 49,5| | | | Mean ....16 32,57 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 330,86 sec. Mean ....15 41,93 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 313,98 sec. In the Garden of the Observatory at Paris: April 30th, 1827. Observer, Captain Sabine. Therm. 77°. Chron. Molyneux No. 407. Rate, Mean Time. | Exp. 25. Needle A. Hour 3½ P.M. | Exp. 26. Needle B. Hour 3 P.M. | |-------------------------------|-------------------------------| | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | | 0 | m s | 300 | m s | 0 | m s | 300 | m s | | 10 | 33 29,2 | 310 | 45 58 | 10 | 2 16 | 310 | 19 41,2 | | 20 | 34 18 | 320 | 46 22 | 20 | 3 24,8 | 320 | 19 45,2 | | 30 | 34 42,8 | 330 | 46 46 | 30 | 3 58,8 | 330 | 20 18,8 | | 40 | 35 07,2 | 340 | 47 10,4 | 40 | 3 58,8 | 340 | 20 52,4 | | 50 | 35 31,2 | 350 | 47 34,4 | 50 | 4 33,2 | 350 | 21 26,0 | | 60 | 35 55,6 | 360 | 47 58,4 | 60 | 5 07,2 | 360 | 22 00,4 | | 120 | 38 20,4 | | | 100 | 7 22,8 | | | | 180 | 40 44,8 | | | 140 | 9 37,6 | | | | 240 | 43 09,2 | | | 180 | 11 52,8| | | | | Mean ... 12 03,6 | | | 220 | 14 07,6 | | | | | | | | 280 | 17 30 | | | Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 241,2 sec. | Exp. 27. Needle XI. Hour 5 P.M. | Exp. 28. Needle VIII. Hour 5½ P.M. | |-------------------------------|-------------------------------| | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | Vibns. | Time. | | 0 | m s | 350 | m s | 0 | m s | 300 | m s | | 10 | 58 43,2 | 360 | 17 01,6 | 10 | 31 48 | 310 | 45 15,2 | | 20 | 59 14,4 | 370 | 17 32 | 20 | 32 15,6 | 320 | 45 42 | | 30 | 59 45,2 | 380 | 18 02,4 | 30 | 32 42,8 | 330 | 46 09,2 | | 40 | 00 16 | 390 | 18 32,8 | 40 | 33 10 | 340 | 46 35,6 | | 50 | 01 17,2 | 400 | 19 03,2 | 50 | 33 36,8 | 350 | 47 02,4 | | 60 | 01 48 | 410 | 19 33,6 | 60 | 34 04 | 360 | 47 29,6 | | 120 | 04 51,2 | | | 80 | 34 58 | | | | 180 | 07 54,4 | | | 100 | 35 51,6 | | | | 200 | 08 55,2 | | | 120 | 36 45,2 | | | | 220 | 09 56 | | | 140 | 37 39,3 | | | | 240 | 10 57,2 | | | 160 | 38 32,8 | | | | 260 | 11 58 | | | 180 | 39 26,4 | | | | 280 | 12 58,8 | | | 200 | — | | | | 300 | 14 00 | | | 220 | 41 13,6 | | | | 320 | 15 00,8 | | | 240 | 42 07 | | | | 340 | 16 01,2 | | | 260 | 43 01,2 | | | | | Mean ... 17 46,57 | | | 280 | 43 54,4 | | | Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 304,734 sec. Mean ... 13 26,286 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 268,76 sec. ### In the Garden of the Observatory at Paris: May 10th, 1827. **Observer, Captain Sabine.** Therm. 62°. Chron. Molyneux No. 407. Rate, Mean Time. #### Exp. 29. Needle X. Hour 5 P.M. | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | 10 52,4 | 300 | 26 55,2 | 16 02,8 | | 10 | 11 25,2 | 310 | 27 27,2 | 16 02 | | 20 | 11 57,6 | 320 | 27 59,2 | 16 01,6 | | 30 | 12 30 | 330 | 28 30,8 | 16 00,8 | | 40 | 13 02,4 | 340 | 29 02,8 | 16 00,4 | | 50 | 13 34,4 | 350 | 29 34,8 | 16 00,4 | | 60 | 14 06,8 | 360 | 30 06,8 | 16 00 | | 80 | 15 11,2 | | | | | 100 | 16 15,2 | | | | | 120 | 17 19,2 | | | | | 140 | 18 23,2 | | | | | 160 | 19 27,2 | | | | | 180 | 20 31,6 | | | | | 200 | 21 35,6 | | | | | 220 | 22 39,6 | | | | | 240 | 23 43,6 | | | | | 260 | 24 47,2 | | | | | 280 | 25 51,2 | | | | Mean . . . 16 01,14 --- #### Exp. 30. Needle IV. Hour 5½ P.M. | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | 39 57,2 | 300 | 56 32 | 16 34,8 | | 10 | 40 31,2 | 310 | 57 04,8 | 16 33,6 | | 20 | 41 04,4 | 320 | 57 38 | 16 33,6 | | 30 | 41 38 | 330 | 58 11,2 | 16 33,2 | | 40 | 42 11,2 | 340 | 58 44,4 | 16 33,2 | | 50 | 42 44,4 | 350 | 59 17,2 | 16 32,8 | | 60 | 43 18 | 360 | 59 50,4 | 16 32,4 | | 80 | 44 25,2 | | | | | 100 | 45 31,2 | | | | | 120 | 46 37,2 | | | | | 140 | 47 43,6 | | | | | 160 | 48 49,6 | | | | | 180 | 49 56 | | | | | 200 | 51 02,4 | | | | | 220 | 52 08 | | | | | 240 | 53 14 | | | | | 260 | 54 20 | | | | | 280 | 55 26 | | | | Mean . . . 16 33,37 --- ### In the Garden of the Horticultural Society at Chiswick: June 11th, 1827. **Observer, Captain Sabine.** Therm. 69°. Chron. Molyneux No. 407. Rate, Mean Time nearly. #### Exp. 31. Needle IV. Hour 3½ P.M. | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | 45 04,6 | 300 | 62 15,2 | 17 11,6 | | 10 | 45 39,6 | 310 | 62 49,6 | 17 10 | | 20 | 46 14 | 320 | 63 23,6 | 17 09,6 | | 30 | 46 48,4 | 330 | 63 57,6 | 17 09,2 | | 40 | 47 23,4 | 340 | 64 32 | 17 08,6 | | 50 | 47 57,6 | 350 | 65 06,8 | 17 09,2 | | 60 | 48 32 | 360 | 65 41,2 | 17 09,2 | | 80 | 49 41,2 | | | | | 100 | 50 50 | | | | | 120 | — | | | | | 140 | 53 07,6 | | | | | 160 | — | | | | | 180 | 55 24,8 | | | | | 200 | 56 33,2 | | | | | 220 | 57 41,6 | | | | | 240 | 58 50 | | | | | 260 | 59 58,4 | | | | | 280 | 61 05,6 | | | | Mean . . . 17 09,63 --- #### Exp. 32. Needle VIII. Hour 1½ P.M. | Vibns. | Time. | Vibns. | Time. | 300 Vibns in | |--------|-------|--------|-------|--------------| | 0 | 44 43,2 | 300 | 58 38 | 13 54,8 | | 10 | 45 11,6 | 310 | 59 06 | 13 54,4 | | 20 | 45 39,6 | 320 | 59 34,4 | 13 54,8 | | 30 | 46 07,6 | 330 | 60 01,6 | 13 54 | | 40 | 46 35,6 | 340 | 60 29,6 | 13 54 | | 50 | 47 03,6 | 350 | 60 56,8 | 13 53,2 | | 60 | 47 31,6 | 360 | 61 24,8 | 13 53,2 | | 80 | 48 27,6 | | | | | 100 | — | | | | | 120 | 50 18,8 | | | | | 140 | 51 14,4 | | | | | 160 | 52 10,4 | | | | | 180 | 53 05,6 | | | | | 200 | 54 01,2 | | | | | 220 | 54 56,8 | | | | | 240 | 55 52,4 | | | | | 260 | 56 48 | | | | | 280 | 57 43,2 | | | | Mean . . . 13 54,06 --- Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° --- 320,38 sec. --- 331,12 sec. --- 278,02 sec. In the Garden of the Horticultural Society at Chiswick, near London: June 11th, 1827. Observer, Captain Sabine. Therm. 69°. Chron. Molyneux No. 407. Rate, Mean Time nearly. | Exp. 33. Needle XI. Hour 3½ P.M. | Exp. 34. Needle A. Hour 4 P.M. | |---------------------------------|--------------------------------| | Vib# | Time. | Vib# | Time. | Vib# | Time. | Vib# | Time. | |------|-------|------|-------|------|-------|------|-------| | 0 | 21 00,4 | 300 | 36 48 | 15 47,6 | 0 | 48 57,2 | 300 | 01 28,8 | 12 31,6 | | 10 | 21 32,4 | 310 | 37 19,2 | 15 46,8 | 10 | 49 22,4 | 310 | 01 53,6 | 12 31,2 | | 20 | 22 04,4 | 320 | 37 50,8 | 15 46,4 | 20 | 49 48 | 320 | 02 18,4 | 12 30,4 | | 30 | 22 36 | 330 | 38 22,4 | 15 46,4 | 30 | 49 13,2 | 330 | 02 43,2 | 12 30 | | 40 | 23 08 | 340 | 38 53,6 | 15 45,6 | 40 | 50 38,8 | 340 | 03 08,4 | 12 29,6 | | 50 | 23 39,6 | 350 | 39 24,8 | 15 45,2 | 50 | 51 03,6 | 350 | 03 43,2 | 12 29,6 | | 60 | 24 11,2 | 360 | 39 56 | 15 44,8 | 60 | 51 29,2 | 360 | 03 58,4 | 12 29,2 | | 80 | 25 14,8 | | | | 80 | 52 19,2 | | | | | 100 | 26 18 | | | | 100 | 53 09,2 | | | | | 120 | 27 21 | | | | 120 | 53 59,2 | | | | | 140 | 28 24,4 | | | | 140 | 54 49,2 | | | | | 160 | 29 27,6 | | | | 160 | 55 39,2 | | | | | 180 | 30 30,4 | | | | 180 | 56 29,2 | | | | | 200 | 31 33,2 | | | | 200 | 57 18,8 | | | | | 220 | 32 36,4 | | | | 220 | 58 08,8 | | | | | 240 | 33 39,6 | | | | 240 | 58 58,8 | | | | | 260 | 34 42,4 | | | | 260 | 59 48,8 | | | | | 280 | 35 45,2 | | | | 280 | 00 38,8 | | | | Mean . . . . 15 46,11 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 315,97 sec. Mean . . . . 12 30,23 Whence the Mean Time of 100 Vibrations between the Arcs of 30° and 5° 250,07 sec.