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16° 9' 4. If now we wish to know the declination at any instant in this particular month all we have to do is to measure the corresponding ordinate and add its value, at the rate of IO' per cm., to the base value 16° 9'-4 just found. Matters are a little more complicated in the case of the horizontal and vertical force magneto graphs. Both instruments usually possess a sensible temperature coefficient, 'i.e. the position of the magnet is dependent to some extent on the temperature it happens to possess, and allowance has thus to be made for the difference from a standard temperature. In the case of the vertical force an “ observed " value is derived by combining the observed value of the inclination with the simultaneous value of the horizontal force derived from the horizontal force magneto graph after the base value of the latter has been determined. In themselves the results of the absolute observations are of minor interest. Their main importance is that they provide the means of fixing the value of the base line in the curves. Unless they are made carefully and sufficiently often the information derivable from the curves suffers in accuracy, especially that relating to the secular change. It is from the curves that information is derived as to the regular diurnal variation and irregular changes. In some Observatories it is customary to publish a complete record of the values of the magnetic elements at every hour for each day of the year. A useful and not unusual addition to this is a statement of the absolutely largest and smallest values of each element recorded during each day, with the precise times of their occurrence. On days of large disturbance even hourly readings give but a very imperfect idea of the phenomena, and it is customary at some observatories, e.g. Greenwich, to reproduce the n10re disturbed curves in the annual volume. In calculating the regular diurnal variation it is usual to consider each month separately. So far as is known at present, it is entirely or almost entirely a matter of accident at what precise hours specially high or low values of an element may present themselves during an individual highly disturbed day; whilst the range of the element on such a day may be 5, IO or even 20 times as large as on the average undisturbed day of the month. It is thus customary when calculating diurnal inequalities to omit the days of largest disturbance, as their inclusion would introduce too large an element of uncertainty. Highly disturbed days are more than usually common in some years, and in some months of the year, thus their omission may produce effects other than that intended. Even on days of lesser disturbance difficulties present themselves. There may be to and fro move merits of considerable amplitude occupying under an hour, and the hour may come exactly at the crest or at the very lowest part of the trough. Thus, if the reading represents in every case the ordinate at the precise hour a considerable element of chance may be introduced. If one is dealing with a mean from several hundred days such “ accidents ” can be trusted to practically neutralize one another, but this is much less fully the case when the period IS as short as a month. To meet this difficulty it is customary at some observatories to derive hourly values from a freehand curve of continuous curvature, drawn so as to smooth out the apparently irregular movements. Instead of drawing a freehand curve it has been proposed to use a planimeter, and to accept as the hourlly value of the ordinate the mean derived from a consideration of the area included between the curve, the base line and ordinates at the thirty minutes before and after each hour.

§ 4. Partly on account of the uncertainties due to disturbances, and partly with a view to economy of labour, it has been the practice at some observatories to derive diurnal inequalities from a comparatively small number of undisturbed or quiet days. Beginning with x890, five days a month were selected at Greenwich by the astronomer royal as conspicuously quiet. In the selection regard was paid to the desirability that the arithmetic mean of the five dates should answer to near the middle of the month. In some of the other English observatories the routine measurement of the curves was limited to these selected quiet days. At Greenwich itself diurnal inequalities were derived regularly from the quiet days alone and also from all the days of the month, excluding those of large disturbance. If a quiet day differed from an ordinary day only in that the diurnal variation in the latter was partly obscured by irregular disturbances, then supposing enough days taken to smooth out irregularities, one would get the same diurnal inequality from ordinary and from quiet days. It was found, however, that this was hardly ever the case (see §§ 29 and 30). The quiet day scheme thus failed to secure exactly what was originally aimed at; on the other hand, it led to the discovery of a number of interesting resultscalculatcd to throw valuable sidelights on the phenomena of terrestrial magnetism. The idea of selecting quiet days seems due originally to H. Wild. His selected quiet days for St Petersburg and Pavlovsk were very few in number, in some months not even a single day reaching his standard of freedom from disturbance. In later years the International Magnetic Committee requested the authorities of each observatory to arrange the days of each month in three groups representing the quiet, the moderately disturbed and the highly disturbed. The statistics are collected and published on behalf of the committee, the first to undertake the duty being M. Snellen. The days are in all cases counted from Greenwich midnight, so that the results are strictly synchronous. The results promise to be of much interest.

§ 5. The intensity and direction of the resultant magnetic force at a spot-i.e. the force experienced by a unit magnetic pole-are known if we know the three components of force parallel to any set of orthogonal axes. It is usual to take for these axes the vertical at the spot and two perpendicular axes in the horizontal plane; the latter are usually taken in and perpendicular to the geographical meridian. The usual notation in mathematical work is X to the north, Y to the west or east, and Z vertically downwards. The international magnetic committee have recommended that Y be taken positive to the east, but the fact that the declination is westerly over most of Europe has often led to the opposite procedure, and writers are not always as careful as they should be in stating their choice. Apart from mathematical calculations, the more usual course is to define the force by its horizontal and vertical components -usually termed Hand V-and by the declination or angle which the horizontal component makes with the astronomical meridian. The declination is sometimes counted from 0° to 360°, 0° answering to the case when the so-called north pole (or north seeking pole) is directed towards geographical north, 90° to the case when it is directed to the east, and so on. It is more usual, however, to reckon declination only from 0° to 180°, characterizing it as easterly or westerly according as the north pole points to the east or to the west of the geographical meridian. The force is also completely defined by H or V, together with D the declination, and I the inclination to the horizon of the dipping needle. Instead of H and D some writers make use of N the northerly component, and W the westerly (or E the easterly). The resultant force itself is denoted sometimes by R, sometimes by T (total force). The following relationships exist between the symbols


HE / (X”-I-YQ). REV (X'+Y2+Z').

tan D=Y/X, tan I=V/H.-The

term magnetic element is applied to R or any of the components, and even to the angles D and I.

§ 6. Declination is the element concerning which our knowledge is most complete. and most reliable. With a good uniiilar magnetometer, at a fixed observatory distant Cham from the magnetic poles, having a fixed mark of known azimuth, the observational uncertainty in a single observation should not exceed o'- 5 or at most 1'-o. It cannot be taken for granted that different unifilars, even by the best makers, will give absolutely identical values for the declination, but as a matter of fact the differences observed are usually very trifling. The chief source of uncertainty in the observation lies in the torsion of the suspension fibre, usually of silk or more rarely of phosphor bronze or other metal. A very stout suspension must be avoided at all cost, but the fibre must not be so thin as to have a considerable risk of breaking even in skilled hands. Near a magnetic pole the directive force on the declination magnet is reduced, and the effects of-torsion are correspondingly increased. On the other hand, the regular and irregular changes of declination are much enhanced. If an observation consisting of four readings of declination occupies twelve minutes, the chances are that in this time the range at an English station will not exceed 1', whereas at an arctic or antarctic station it will frequently exceed 1o'. Much greater uncertainty thus attaches to declination results in the Arctic and Antarctic than to those in temperate latitudes. In the case of secular change data one important consideration is that the observations should be taken at an absolutely fixed spot, free from any artificial source of disturbance. In the case of many of the older observations of which records exist, the precise spot cannot be very exactly fixed, and not infrequently the site has become unsuitable through the erection of buildings not free from iron. Apart from buildings, much depends on whether the neighbourhood is free from basaltic and other magnetic rocks. If there are no local disturbances of this sort, a few yards difference is usually »without appreciable influence, and even a few miles difference is of minor importance when one is calculating the mean secular change for a long period of years. When, however, local disturbances exist, even a few feet difference in the site may be important, and in the absence of positive knowledge to the contrary it is only prudent to act as if the site were disturbed. Near a magnetic pole the declination naturally changes very rapidly when one travels in the direction perpendicular to the lines of equal declination, so that the exact position of the site of observation is there of special importance.