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this process is repeated every 51 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 401, 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.





Times corresof Partial Re-ponding to Parthe Scale. sults. tial Results.

3 39 10

19 28 37 46 55

4 13 22 31 40

49 Means.


The Final Mean 105.2 106.

39' 3711 gives 105.854 105.1 105.937

46 as the number 105.2 105.812

55 on the scale 105.5 105.875 40 4 corresponding 106.0 105.750 13 to the magne106.2 105.750

tic meridian at 106.4

3h39' 59'1.5. 106.3 106.2 105.854 105.854 39' 5911.5


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 purpose, and embracing every case that can occur. Look in the 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.

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1 083 094 | 104 115 125 135 146 156


2 167 177 | 187 | 198 208 209 229 240



250 260 271 281 292 302 312 323


4 333 344 354 | 365 375 385 396 406


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8 667 | 677 | 687 698 708 719 729 740


9 750 760 771781792 802 812 823


10 833 | 844 | 854 865 875 885 896 906 10

11 917 927 837 948 758 969 979 990 11

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It must be observed, that the mean result obtained above corresponds to 36 39" 591.5, 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

ment occurs whose cause is not looked for and generally found in the uniform operation of the simple law of gravity in its direct or reflected action upon the various members of the solar system. The singular fact of Encke's comet, which experiences a delay which has been attributed to a resisting medium, may be regarded as a solitary exception to the general truth. The laws of motion among the heavenly bodies are so few and clear, that the character of the disturbance will generally indicate something in regard to the cause which produces it. But the elements of the earth's magnetism are exposed to abrupt and violent fluctuations, which, so far as the circumstances are known, acknowledge no periods, and, although perhaps capable of being explained by many conceivable causes, which are in constant operation, and, therefore, at the disposal of the philosopher, they cannot be distinctly brought home to any single one, and are at present regarded as inexplicable. These magnetic hurricanes, as they have been fancifully called, are often exhibited during auroral appearances, but many of them, so far as has been observed, are not coincident in time with this or any other class of natural phenomena. Now, every observed position of the needle, for a given moment, is beset with all these regular and irregular variations ; which must be carefully eliminated, by multiplying the number, and shifting the exposure of the observations, before we can be assured what is the exact and absolute value of the element for that time. And when we are seeking the amount of any particular order of perturbations, we must proceed as in the astronomical case, by selecting, as far as may be, times for observation, when the disturbance in question is a maximum, and all others are of minimum value. The practice of the observer will supply many artifices of this sort, for eluding or grappling with difficulties, which appear, at first sight, insurmountable. It is obvious, that when the object is to ascertain the steady and periodical variations of the meridian, we should exclude from the comparison those days whose serenity is affected by what Humboldt has denominated magnetic storms, just as we should pass over days of violent winds and tempests, in deducing the gradual rise and fall of temperature during the 24 hours. No attempt should be made to frame an hypothesis, or even to hazard a conjecture in regard even to the variations of the shortest period from one year's observations, however unremitted they may have been ; but these observations may be of use in confirming a theory long entertained and well established by facts noticed in other places.

The observations of Graham, in 1772, which resulted in the detection of the diurnal variation of the magnetic meridian at London, have been repeated since in various parts of the world with increased delicacy and skill, and with the same general result which is briefly described. The magnetized bar, free to place itself in the magnetic meridian, does not remain in one fixed position during the day; but sometime in the morning, between six and eight o'clock, as

the average statement, it starts in a westerly direction, and moves that way

till between one and three in the afternoon; then it begins to retrace its steps back to the east again. These points of maximum and minimum declination are formed in every diurnal curve, and at nearly the same hour. We shall hereafter see what the limits of the time are. There are two ways in which the bar regains its first position. In some places, as Paris for example, it arrives at its greatest eastern elongation again between eight and eleven o'clock in the evening, and then remains stationary till the time of morning excursion has come round once more. In other places, as at Cambridge, it travels eastward till evening, and then goes back to form a secondary point of maximum westerly deviation about three o'clock, A. M.; after which it passes eastward, and recovers at eight o'clock the place it occupied 24 hours before. In certain cases, especially in northern latitudes, even when the secondary maximum and minimum are not formed, the bar does not remain stationary during the night, but occupies nearly all the time from three P.m. to eight A.m. in returning through the space it has just passed over in seven hours. Again, the arc traversed by the bar in its daily excursions, varies perceptibly from one day to another ; but the approximate law is, that in the six months from the vernal to the autumnal equinox, its value is between 13' and 15'; and, in the remaining six months, the mean of the daily arc is between 8! and 10'. But there may be single days when it amounts to 25', and others when it is as small as 6'.

Gauss thinks that eight A. M. and 1 P. M., of mean solar time, are never far from the periods of daily minimum and maximum declination in Gottingen, and that part of the globe. It appears, from a report in regard to the magnetic state of the Russian empire, for 1837, that, at St. Petersburg, the greatest westerly position of the north end of the magnetic meridian is near two o'clock P. M., and the opposite position is at eight in the morning, with the exception of November, December, and January, when it occurs later. This is easily explained, by the high latitude of the place, when we come to consider the dependence of this daily motion on

Since the declination is easterly in some parts of Russia, it follows that the maximum declination there is in the morning, and the minimum in the afternoon. As the report in question has been published with great care, we extract a table of the monthly

the sun.

• Annuaire Magnetique et Météorologique du Corps de Ingénieurs des Mines de Russie. Année 1837. St. Petersburg, 1839.

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