But used in observations made at other places. In our observations, the time was obtained accurately from the transit instrument and astronomical clock; and the scale which was reflected from the mirror at the southern extremity of the bar, and read off by the variation transit, easily allowed of being marked to of a minute. The experience of the observers has satisfied them that dependence may be placed upon each separate reading within that limit of error. But other considerations make it necessary to determine the position of the magnetometer, for any assigned time, by more than a single reading. As the bar, in passing from one angle of declination to another, is maintained always in a vibratory state, it is necessary to eliminate what is due to the oscillation from what belongs to an absolute change of declination. If the arc of vibration were constant, it would be eliminated by observing the limits of excursion of the magnetised bar, and taking the mean between them. the natural tendency of the arc of vibration is to become shorter for every new excursion, and if the arc be of considerable length, this circumstance must be taken into account. As the decrease of arc must be nearly uniform for a few vibrations, this is done by noting the limits of three successive excursions, and the mean of two means thus obtained is the true position of the bar for the middle time. Thus, if a, b, c, are the readings, ((a+b)+(b+c) or (a+2b+c) gives the place of the magnetic meridian for the time when b was observed. If the arc of vibration is very small, this correction will be inappreciable, and the mean of two observations will suffice. But the declination itself, meanwhile, may vary by sudden and irregular movements, and then the process of observation and reduction becomes more intricate. Facts assure us that the magnetic meridian is subject to abrupt and lawless fluctuations, as well as uniform and progressive variations. The practical mischief of these disturbed motions is diminished, by the fact that they will most probably occur during periods of unusual perturbation; and although they must be kept in view when studying the laws of remarkable derangements of magnetic influence, their effect will be insensible in the regular and periodic changes. A greater difficulty that affects particularly simultaneous observations is this. The precise moment of time to which the mean result corresponds may not be that for which the declination is sought; and the interpolation of the required times between the observed times is a matter of troublesome and uncertain calculation. This labour is prevented by an ingenious device of Gauss, in the way of observing. If two observations of a bar are made at an interval equal to the time of one vibration, the mean is the place for the intermediate moment. This is a proposition mathematically exact, if the change of declination can be regarded as uniform and the arc of vibration constant. It will, therefore, be practically true whenever no remarkable disturbances are apprehended, and the arc of vibration is small; or within the same limitations as the other methods. If, now, the position of the magnetic meridian is desired for any definite moment, the first observation is made to precede this period by half the time of the bar's vibration, and the second to follow the period at the same distance. Thus, if t be the time of vibration, and T the time of mean observation, the actual observation must be made at T-t and T+t. For greater accuracy, the final result is made to depend on several partial results, as will be seen by an illustration. The time of vibration of the Gauss Magnetometer used at Cambridge is about 54. This is divided into as many parts as separate observations can be conveniently taken during that time. It has, therefore, been divided into 6 intervals of 9 each, and a separate observation is made at each interval. This is done during two vibrations of the needle, or 1'48. By taking the mean of every two observations which have an interval of 54'', we have a partial result for the middle time, and these partial results are combined so as to give a final result for any time when the declination is required. If this time is 2 5 the first observation is made at 2 4′ 6', and repeated at intervals of 9 till 2h 5' 54. An example is given from from the observations made June 26, at 0" of Gottingen mean time. Thus it appears that each position of the needle is determined from 13 separate observations; and as each reading is to of a minute, the mean of all may be considered as within a smaller error of observation, and only subject to the exception, that the law of reduction is not rigorously exact when the change of declination, during 1' 48', is not uniform. If the arc of vibration be so large as to have a sensible decrease, the effect is cancelled when the readings extend through twice the time of vibration. On term days this process is repeated every 5 during the 24 hours, so that 3,744 observations are made, which give 288 mean positions. This was the rule of the Observatory till June 26th, 1840, when a slight modification was introduced, which diminished the labour of observation and reduction, without compromising the accuracy of the result. Thus, the observation of June 26th, 3h 40/, P. M.,* which was the first one made in this way, stands thus: it should be remembered, that the column of figures to the right of the point are not tenths but eighths. By this method, which is the same in principle as the other, only 12 observations are made, and the mean of them is the same as the mean of the partial results, so that the latter column in the table is unnecessary, and a great part of the labour of reduction is saved. The number 12 is a convenient divisor, and after the whole minutes are found the decimals are taken out of a table calculated for this Look in the purpose, and embracing every case that can occur. vertical column at the right or left for the whole numbers of the Gottingen mean time is to be understood wherever it is not otherwise stated. remainder, after dividing by 12, and in the top or bottom line for the eights, and in the corresponding square is the decimal value of the remainder. 5 417 427 437 448 458 469 479 490 5 6 500 510 521 531 542 552 562 573 6 7 583 594 604 615 625 635 646 656 ས 7 8 667 677 687 698 708 719 729 740 8 9 750 760 771 781 792 802 812 823 9 10 833 844 854 865 875 885 896 906 10 It must be observed, that the mean result obtained above corresponds to 3 39" 59".5, and not 3h 40'. But the difference of half a second comes within the limits of unavoidable errors of observation, and is of no weight in deciding on the comparative merits of the two methods, each of which depends on a knowledge of the time of vibration of the bar. But this time changes slightly from one period to another, and although always assumed to be 54", it is strictly 53'.4, on the average, and oscillates about this mean value.* Whenever observations have been made with the Gauss Magnetometer, since June 26th, 1840, it has been the rule of the Observatory, recommended by its superior simplicity, and freedom from all practical objections, to take 12 readings at The mean of 28 vibrations in April was 53'.05; of 21 in July, 53.38; of 22 in September, 53".45; of 12 in October, 53.65. intervals of 9", commencing 50" before the real time, and to consider the mean of them as the final determination of position for that moment. Neither the Gauss method, nor that of Cambridge, which is based on it, is practicable when the bar is agitated by unusual magnetic influences, as in seasons of violent disturbance, in consequence of the great extent of its motion. In such emergencies, the extreme of every excursion is recorded, so long as this perturbation continues, and an approximate time is obtained as exact as circumstances allow. The reduction is then made by this formula, (a+2b+c,) which has been already explained. After the mean results for every five minutes, during the 24 hours of a day, are obtained by any of these processes, they are used as the data for projecting a diurnal curve of magnetic declination. Two lines are drawn upon a sheet of paper, at right angles to each other, and assumed as the axes of rectangular co-ordinates. One of them is divided into 24 equal intervals, each of which is subdivided into smaller parts, according to the scale of the chart. The other line is also divided in portions corresponding to degrees and minutes of arc. Any point that is most convenient may be selected as the origin of the co-ordinates, and, by considering the time as ordinate, and the result of observation annexed to it as abscissa, we obtain as many points of a daily curve as there are mean results of observation. In ordinary term-days the number is 288. When so many points are fixed upon the sheet, they are connected by straight lines or curves of the simplest curvature. From the details published in regard to the principle of observing, it may be inferred how closely these curves will represent the actual magnetic changes for the day. It cannot be denied that disturbances may happen, of less amount than the minimum quantity of observation, or at less periods than 5', which will elude the vigilance and refinements of the present state of magnetic science. It has been noticed on more than one occasion that the bar has been instantaneously checked in the midst of a vibration, and forced to retrace its steps by a long sweep in the opposite direction. The lines which are now drawn straight, or in the most natural curve from one fixed point to another on the sheet, might, if they were sensible of the shorter and more rapid magnetic impulses, change their curvature several times during the passage. Plates II. III. IV. and V. represent the diurnal curves of magnetic declination for the days given on the plates; and we are first to consider, from an attention to them, as well as to the figures which describe the other days at the end of the communication, whether the fact of a regular cycle of variations in the declination during the 24 hours is confirmed by these observations. The theory appears now to be well established, that the elements of terrestrial magnetism are subject to daily, monthly, yearly, and secular perturbations, similar to the periodical and secular variations which are known in astronomy. But in the astronomical problem, no derange |