170 METEOROLOGY [TERRESTRIAL MAGNETISM. data sufficiently accurate for a discussion, in a complete manner, of questions relating to solar periodicity before the time when Schwabe had finally matured his system of solar observations, which was not until the year 1832. We have, however, a much longer series of the diurnal ranges of magnetic declination, which we have seen to follow very closely all the variations of sun-spot frequency, so it is conceivable that they may give us a better estimate of true solar activity than that which can be derived from the direct measure ment of spotted areas. These considerations have induced Messrs Stewart and Dodgson to attempt an analysis of the diurnal ranges of magnetic declination, their method being that which has been pursued by Baxendell and probably other astronomers with observations of variable stars. 1 The observations at their disposal for this research were those which had been used by Professor Elias Loomis in his comparison of the mean daily range of the magnetic declination with the extent of the black spots on the sun (American Journal of Science and Arts, vol. 1. No. cxlix.). These observations are recorded as monthly means of diurnal declination range, and it was found necessary to multiply each by a certain factor, first on account of the change of declination range from one month to another, and secondly to bring them all to the standard of the Prague observa tions, Prague being the place where the longest series of such obser vations has been made. For this latter purpose precisely the same corrections were applied as those made by Professor Loomis. The result of this analysis has been to indicate the existence of three inequalities, two dominant ones with periods of about ten and a half and twelve years, and a subsidiary one with a period of about sixteen and a quarter years. By these means the observed annual values of declination range have been reproduced with an average error of 39". The amount of agreement between the observed and calculated values will be seen from the following diagram (fig. 36). 50. Notwithstanding the considerable amount of agreement h I 7800 1 1870 cH /V /v/ J
A V 7870 7880 I8SO Fig. 36. between the results of observation and calculation which appears in the diagram, it would secrn that the series of observed values at present obtainable is too short to render the analysis a very accurate one. It will certainly not bear carrying back forty or fifty years beyond its starting point, which was in 1784, and it would be very hazardous to carry it forward any consider- i Proc. Lit. and Phil. Society of Manchester, March 8, 1881. able length into the future. It will be seen that calculation indicates a maximum of declination range about 1884, but not so pronounced a maximum as that of 1871. Here then we have a prevision which observation will either fulfil or contradict, giving us a practical test of the value of this analysis. 51. The remarks now made would seem at first sight to imply that we are not yet furnished with sufficient yearly records either of declination ranges or of accurate sun-spot observations to enable us to analyse the long-period solar inequality with such completeness as to carry our calculations more than a very short distance into the future with any chance of success, and that we may have to wait for another hundred years observations before we are able to do so. On reflection, however, it would seem that long-period inequalities may be caused by the superposition of those of short period, and thus that an analysis of the latter may lead to that of the former. It would relieve us if this were found to be the case ; for the observations at our disposal may be sufficient to enable us completely to analyse short-period inequalities, assuming that we have in such the elements of a true periodicity. A remark made by the authors of the above analysis would seem to indicate that a connexion of this nature between long and short periods does in all probability exist. It is a well-known fact that the so-called eleven-yearly oscillations of declination range are at certain times large and at other times small. Thus, for instance they have been large for the last forty years, but they were small about the earlier part of the present century. Now it is clear from an inspection of the observations (see fig. 36) that a series of large oscillations is accompanied with an exaltation of the base line, or line denoting average efficiency, while a series of small oscillations is accompanied with a depression of the same. The result is a long-period curve of the base line, the beat period, so to speak, of the eleven-yearly inequality. Now a phenomenon precisely similar occurs in connexion with shorter periods. If we take inequalities having a period of three or four months, we find that such are alternately well-developed or of large range and badly-developed or of small range, and that a large range of such is accompanied with an exaltation of the base line or line of average efficiency, while a small range is accompanied with a depression of the same. The result is a curve of the base line of which the period is roughly speaking eleven years. May we not therefore imagine that the so-called eleven-yearly period, or, to speak more correctly, the ten and a half and twelve-yearly periods into which the eleven-yearly period may perhaps be analysed, may be in reality beat periods for shorter disturbances ? Is it not there fore possible that a study of these shorter periods may give us information regarding the nature of the eleven-yearly period, whether for sun-spots or declination ranges, which the small series of actual observations is incompetent to afford ? 52. Declination- Range Weather. Allusion has already been made to magnetical weather as perhaps having laws similar in some respects to those which regulate meteorological weather. Now the diurnal ranges of magnetic declination and those of atmospheric temperature present us with elements of the two weathers that can easily be discussed. Again there is strong evidence for supposing that an element of meteorological weather, such, for instance, as temperature-range, travels as a rule from west to east, so that a peculiar style of temperature-range might be expected to appeal- first in America and some days afterwards in Great Britain. It becomes therefore a question for inquiry whether this travelling from west to east applies also to magnetical weather as evidenced by the diurnal declination-range. Stewart is of opinion that this law of travelling applies to both, but that magnetical weather, travels faster than meteorological (see Proc. Roy. Soc., January 10, October 23, 1879, and June 9, 1881 ). From the preliminary discussion made by him it would appear that Kew lags behind Toronto as regards phase of magnetical weather by 1 6 days, that Prague lags behind Kew 07 days, and that Trevandrum lags behind Kew by 97 days. This conclusion cannot, however, be regarded as established until it is confirmed by a more complete discussion of observations. 53. Disturbance- Diurnal Variation of Declination. Magnetic storms ( 38) were so named by Baron Humboldt, one of the first observers of such phenomena. From observations at Paris, Berlin, and Freiburg he found that very frequently, though not universally, these three stations were simultaneously affected by such storms. The observation of magnetic disturbances was afterwards pursued in a systematic manner by Gauss and Weber of Gottingen. Term days were instituted for this purpose by these observers, that is to say, periods each of twenty -four hours length during which observa tions were simultaneously made at intervals of five minutes at Gottingen and about twenty other stations distributed generally over the continent of Europe. Finally, the establishment by the British Government of the colonial magnetic observatories, and the energy and sagacity of their director, Sir E. Sabine, have very greatly increased our knowledge of these remarkable phenomena._ Sabine has not merely separated the disturbed from the undis turbed observations as explained in 38, but he has divided the
former into two categories (1) those tending to increase westerly