3d, For the arc of vibration.
4th, For any change in the magnetic condition of the cylinder.
In extensive voyages, the last-named correction, or that for the change in the cylinder itself, is the one which requires principal consideration. The corrections for temperature, and for the arc, on the first of which particularly much stress has sometimes been
laid, are important when extreme accuracy is sought; as for example, in comparing the force at stations which have served as the unities of different observers: their effect is, however, of little moment in observations which include great differences of the terrestrial intensity. But when the magnetic condition of the needle has varied, and interpolation becomes necessary, the instances are rare in which it can be done with entire satisfaction.
The time of vibration of this cylinder at Plymouth, with corrections applied for the chronometer's rate, the temperature, and the arc, was, in December 1831, 770,8 seconds, with a dip of 69° 27′,6, and in October 1836, 777,3 seconds with a dip of 69° 17′,5. The difference in its magnetic state, at the two periods, is shown by the squares of the times of vibration multiplied by the cosine of the dip observed at the respective periods. This makes known what the time of vibration of the same cylinder would have been, had it been free to move in the direction of the dipping-needle, instead of being suspended horizontally; and, consequently, if it had been acted upon by the total magnetic intensity, instead of by the horizontal component only. It is here assumed that the total terrestrial intensity is constant at the same place. This is doubtless not strictly true; but the amount of the change must be too small to require consideration in the period occupied by Captain Fitz-Roy's observations. The horizontal component must, however, necessarily vary with the changes in the dip: and it is, therefore, from the time of vibration in the direction of the dipping-needle, and not from the time of horizontal vibration, that the change, or otherwise, in the magnetism of the needle is to be inferred. We find, then, the equivalent time of vibration of this cylinder in the direction of the dipping-needle to have been 456,4 seconds in December 1831, and 462,2 seconds in October 1836; showing a difference of 5,8 seconds in fifty-eight months. If we compare this amount with the far greater loss of intensity sustained by this cylinder in the preceding voyage, it seems a probable supposition that, at the commencement of Captain Fitz-Roy's voyage, the cylinder had nearly attained its permanent magnetic state; and that its further loss of magnetism, occasioning an increase of 5,8 seconds in the time of vibration, took place in the early part of the voyage: supposing the loss to have been progressive, and not sudden, as from accidents, of which the observations give no indications.
Consistently with this supposition, the loss has been distributed through the first half, or twenty-nine months, of this voyage, in the proportion of three-tenths of a second per month in the first ten months, commencing December 1st 1831; two-tenths per month in the next nine months; and one-tenth per month in the remaining nine months. In the last twenty-nine months of the voyage, the intensity of the cylinder is supposed to have been uniform, and the same which it was found to possess on the return to England in 1836.
It is satisfactory that, with this compensation, the observations at Port Praya, in January 1832, and in September 1836, assign almost identically the same relative magnetic intensity to that station.
The correction for temperature for this cylinder not having been previously examined, I received it from Captain Fitz-Roy for that purpose, and made with it the following observations. The cylinder, in its own apparatus, was placed in a large earthen jar, glazed at the top, and standing in a larger earthen vessel, into which warm water could be poured at pleasure, and the cylinder was then vibrated alternately in heated air and in air of the natural temperature. These experiments were made at Tortington, in Sussex.
| Day. | Hour. | Thermom. (Reaumur.) | Time of Vibration | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| h. m. | ° | s | |||||||||||||||||||||||||
| Exp. 1 |  | June 12 | 11 50 A.M. | 12,00 | 774,91 |  | h. m. | ° | s | ||||||||||||||||||
| — | 0 12 P.M. | 12,00 | 775,37 | Mean, 0 12 P.M. | 12,0 | 775,33 Natural Temperature. | |||||||||||||||||||||
| — | 0 34 P.M. | 12,00 | 775,71 | ||||||||||||||||||||||||
| — | 1 58 P.M. | 31,65 | 777,31 | | |||||||||||||||||||||||
| — | 2 21 P.M. | 32,20 | 777,09 | Mean, 2 20 P.M. | 31,72 | 777,09 Heated Air. | |||||||||||||||||||||
| — | 2 42 P.M. | 31,30 | 776,86 | ||||||||||||||||||||||||
| — | 4 00 P.M. | 15,45 | 774,00 | | |||||||||||||||||||||||
| — | 4 22 P.M. | 15,80 | 774,25 | Mean, 4 22 P.M. | 15,65 | 774,16 Natural Temperature. | |||||||||||||||||||||
| — | 4 44 P.M. | 15,70 | 774,23 | ||||||||||||||||||||||||
| Exp. 2 | | June 13 | 10 49 A.M. | 14,90 | 773,77 | | Mean, 11 02 A.M. | 15,0 | 773,57 Natural Temperature. | ||||||||||||||||||
| — | 11 16 A.M. | 15,10 | 773,37 | ||||||||||||||||||||||||
| — | 0 20 P.M. | 34,80 | 775,94 | | Mean, 0 31 P.M. | 35,7 | 775,92 Heated Air. | ||||||||||||||||||||
| — | 0 42 P.M. | 36,55 | 775,89 | ||||||||||||||||||||||||
| — | 1 30 P.M. | 17,70 | 774,06 | | Mean, 1 41 P.M. | 16,8 | 774,08 Natural Temperature. | ||||||||||||||||||||
| — | 1 52 P.M. | 15,90 | 774,11 | ||||||||||||||||||||||||
| In the first Experiment,T=777,09; T′ 774.74; t=103°,4 Faht.; and t′=63°,1 Faht. In the second Experiment, T=775,92; T′ 773,83; t=112°,3 Faht.; and t′=67°,8 Faht.
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