Whence the formula T′=T [1 × 0.000068 (60°-t)], in which T is the time of vibration at any station, t, the temperature of the cylinder in degrees of Fahrenheit, and T′ is the equivalent time at a standard temperature of 60°. The thermometer was noted at the beginning and ending of every set of vibrations, and was always placed in the box with the cylinder.
At all Captain Fitz-Roy's stations the apparatus was placed for observation on a stand, which raised it from two to three feet above the ground, thereby rendering the cylinder somewhat less liable to be disturbed by local influences: it was not furnished with a means of examining the strict horizontality of the cylinder, that improvement having been introduced into M. Hansteen's apparatus at a later period. On this point Captain Fitz-Roy remarks: "A small leaden tripod was used as a stand, whose upper surface was adjusted by a small spirit-level—or roughly by the trough of an artificial horizon, filled with mercury. Upon the leaden stand the box containing the needle was adjusted by its foot-screws, so that the suspending fibre of silk hung centrally in the wooden tube, the needle's centre being over that of the graduated circle, and the needle itself near, but not touching, the bottom of the box. The needle was not always strictly parallel to the bottom of the box, nor strictly horizontal, because I would not move the brass stirrup in which it was suspended, but its deviation from strict horizontality never exceeded two degrees, and was seldom nearly so much."
The time of completing every tenth vibration was recorded. The time of performing 300 vibrations is deduced from a mean generally of seven partial results: i.e. from the 0th to the 300th; 10th to the 310th; and so on, to the 60th and 360th vibrations; the commencing vibration being always at an arc of 20°. In a very few instances the number of vibrations observed, after the commencing arc of 20°, was less than 360; in such cases the first vibration after the arc had become 20° has still been taken as the commencing one, though previous ones may have been recorded; it being kept strictly in view, to obtain the relative time of vibration in arcs as nearly the same as possible, and not exceeding 20° as the initial. The arc was reduced to 10° generally about the 100th vibration; and one thousandth of the time of vibration has been taken throughout the series as the correction to infinitely small arcs.
The object of noting the time of every tenth vibration is to check errors in the counting, which will sometimes occur in the course of the 360, particularly with the very short and quick-moving needles of M. Hansteen's very portable apparatus, and at stations of low dip, where the horizontal force is greatest, and the needle consequently moves most quickly. Several such mistakes evidently occurred. When the time of completing every supposed tenth vibration is observed with tolerable exactness, and the duration of each pair of vibrations decidedly exceeds any irregularity of probable occurrence, apart from miscounting the number of vibrations, such mistakes can be discovered with ease, and rectified with certainty. This has been done in every case where no doubt could exist of a mistake of the kind having occurred; such as when all the intervals are of nearly equal duration, with one or two exceptions, which differ as much as three or four seconds from the general body. There are two stations, however, Callao and Keeling Islands, where the rectification is not so clear, or the true result so obvious. At Callao there are three series of horizontal intensities, each of forty observed intervals, which should be of ten vibrations each. Several of these intervals are between 17,5 and 18,5 seconds, and several others between 20,5 and 21,5 seconds. These can hardly represent an equal number of vibrations, because the difference between them is greater than can easily be supposed due to any uncertainty in seizing the particular beat of the chronometer at which the vibration was completed; it is, moreover, about the time that would be occupied by two vibrations more or less. The question then arises, do the longer intervals represent 12, and the shorter 10 vibrations, or do the longer represent 10, and the shorter 8? In the former supposition the intensity at Callao would be about 1.01 (Paris = 1.348): in the latter about 0.75. The difference shews how great an error would be risked by either assumption. If we take a mean of all the intervals as they stand, the amount of error risked would be certainly lessened; but we should assuredly not have the true time of three hundred vibrations, except on one supposition: namely, that the irregularities in question are not errors in estimating the number of vibrations, but that each interval really represented an equal number, and that some unusual and accidental cause occasioned the needle to differ so greatly in successive intervals. But this
supposition would imply a disturbing cause vitiating the series as a measure of the magnetic intensity at the station. I have not ventured, therefore, to draw any conclusion from these observations, farther than to notice, as above, the limits within which, in either of the two first suppositions, the intensity would fall.
A nearly similar reasoning applies to the observations at Keeling Islands; of three series, one is decidedly so irregular, that no inference could be drawn from it; in the two other series the irregularities are neither so frequent, nor so large: my general impression (in the uncertainty created by the irregularity of the first series), is, that the majority of the intervals are of twelve vibrations, and not of ten: if of twelve, the intensity would be about 1,21; if of ten, about 0,85.
The inconvenience of the rapid motion of the needle, occasioned, at one part of the voyage, the practice to be discontinued of observing every tenth vibration, and every twentieth was substituted. This no doubt relieved the perplexity in which the observer occasionally found himself, in having to observe, and record, and be prepared again to observe, at every twenty seconds or less, and so far the change enabled him to observe better. But still, the disadvantage remains, in so quick moving a needle, that if a mistake of two vibrations is made, the difference of time occasioned is not of so marked and decided a character as to be at all times at once distinguished. It is of much more importance that there should be no miscount of the vibrations, than that the times should be recorded correctly to the fraction of a second. It is only the earlier and later times that are finally influential; but every undetected error in the number of vibrations falls with its whole weight upon the result.