May 24, 1877] 



NA TURE 



63 



the second. This increase Gauss did not think could 

 go on long, and he predicted that by continuing the 

 observations for several years, an oscillation in the mean 

 value would present itself. It is not a little curious that 

 in discussing the Gottingen observations for the ne.xt 

 three years. Dr. Goldschmidt should have failed to remark 

 that the maximum was attained in 1S37, and that there- 

 after the mean diurnal oscillation was diminishing. This 

 was reserved for Dr. Lamont, the distinguished astronomer 

 of Munich, who, in the end of 1S45, by adding the mean 

 oscillations obtained from his own observations in 1842- 

 1845, to those already found for the preceding years at 

 Gottingen, was able to state that the minimum was then 

 attained, but that a longer series of observations was re- 

 quired, in order to determine the law of the oscillation. 



It was only in the end of 1851, when the maximum 

 oscillation (which occurred in 1S48-49) was decidedly 

 past, and the mean oscillation had again begun to dimi- 

 nish in value, that Dr. Lamont published his conclusion 

 that the diurnal oscillation of magnetic declination (as 

 well as of magnetic force) obe\ed a law whose mean 

 duration was nearly lol years. For the determination of 

 this mean he employed the epoch of maximum oscilla- 

 tions shown by Cassini's observations in 1787 (already 

 noticed by Kaemtz), and he assumed that there were six 

 periods from that date till 1849. 



Schwabe had previously, from his persevering observa- 

 tions of the number of spots on the sun's surface, arrived 

 at the conclusion that these obeyed a decennial law, so 

 that the number was a maximum in 1S28, 1837, and 1848, 

 while it was a minimum in 1833 and 1S43. The agree- 

 ment of the epochs, 1843 and 1848, with those of mini- 

 mum and maximum magnetic disturbance deduced by 

 Sir E. Sabine froui the observations made in the colonial 

 observatories, was at once remarked by him, as well as 

 that of Lamont's epochs with those of Schwabe. 



This coincidence was also immediately afterwards, and 

 quite independently, brought to public notice by Dr. 

 Wolf, of Bern (now of Zurich), and M. Gautier, of 

 Geneva. It is, however, with the important labours of 

 the former of these philosophers that we are most con- 

 cerned. Dr. Wolf began at once a systematic search for 

 observations of sun-spots, and examined hundreds of 

 volumes printed and in manuscript, dating from the first 

 discovery of the existence of spots on the sun's surface. 

 All the observations thus accumulated he has endeavoured 

 to connect and to reduce to a common unit; and from the 

 numbers thus obtained he has concluded that the sun- 

 spot period, as well as that of the magnetic variations, 

 occupies on the average ii\ years. 



One great cause of the difference between the results 

 of the Munich and Zurich astronomers is to be found in 

 the interval 1787 to 1818. According to the former, 

 three periods oiig/ii to have occurred in this interval ; 

 according to the latter, only one maximum happened, i?i 

 fact, between the two of 1787 and 18 iS. Dr. Wolf has 

 concluded, from the magnetic observations of Gilpin 

 (1786-1806), that a minimum of the diurnal oscillation of 

 the magnetic needle occurred in 1796, and a maximum 

 in 1803, and these epochs he bas supported by the 

 observations of the numbers of sun-spots, as well as of 

 those of the aurora borealis, a phenomenon known to be 

 associated with magnetic disturbance, and to have the 

 same epochs of frequency. On the other hand. Dr. 

 Lamont has maintained that Gilpin's observations are 

 without value, as his needle was supported on a steel 

 pivot, and sometimes did not move freely ; he has also 

 objected to the observations of sun-spot frequency made 

 during the time in question, that they were made rarely, 

 without any common system, and by few observers, some 

 having at times seen no spots when others saw many. 



If we could assume with the astronomer of Munich 

 that Gilpin's observations and those of sun-spot and 

 auroral frequency made at the same time are worthless, 



all our knowledge of the epochs of magnetic oscillations 

 since 18 18, and of sun-spot frequency since 1836, would 

 induce us to conclude that there were really three periods 

 during the thirty-one years 1787-181S. If, however, any 

 value can be given to the observations during that inter- 

 val, it is not allowable to assume that the durations of the 

 periods have always been the same, the more especially 

 that we know the period has varied in length from eight 

 to twelve years within the last half century. That some 

 value is due to observations of three different phenomena 

 has been allowed by most writers, and Dr. Wolf's period 

 of II J years has, in consequence, been accepted by many 

 of the most eminent men of science who have had occa- 

 sion to allude to the subject. 



Having had to study this question in connection with 

 the results of observations made during twenty-three 

 years at Trevandrum, I have examined with care the 

 magnetic observations of the last and the present cen- 

 tury, determined the exact times for which the yearly 

 mean diurnal oscillation of the magnetic needle was a 

 maximum or minimum, and have arrived at the following 

 conclusions : — ' 



ist. That there are not sufficient grounds for rejecting 

 the observations of Gilpin, which appear to be in general 

 trustworthy as regards the change of mean position of the 

 needle from year to year, and of the diurnal range from 

 winter to summer. 



2nd. That these observations should, according to the 

 mean law, show a maximum near 1797, and another 

 should have occurred near 1S07. I have found that they 

 do indicate a maximum in the former year ; and though 

 another maximum appears in 1803, that there are grounds 

 for believing the maximum may really have occurred after 

 1S06, when Gilpin's series terminated. 



It has to be stated, however, that the maximum shown 

 by Gilpin's observations in 1797 is very small ; that the 

 whole interval between the preceding and following mini- 

 mum is not six years ; and that no such short period and 

 small maximum have been observed during the last half 

 century. Since, however, the shortness of the period and 

 the smallness of the maximum are both confirmed by the 

 observations known to us of the frequency of sun-spots 

 and of the aurora borealis, I can only conclude, in con- 

 formity with the facts, that both these were real pheno- 

 mena, which may yet be repeated and aid in the deter- 

 mination of the cause of the decennial period. The mean 

 duration of the period at which I arrive is therefore 

 almost exactly that which Dr. Lamont had previously 

 obtained, or io'45 years. 



For this result the facts have been taken as they present 

 themselves ; since it would be difficult to conclude that 

 the observers of all the three phenomena could have erred 

 in the same way during nearly twenty years. In addition 

 t J this, after a careful study of Dr. Wolf's sun-spot numbers, 

 I find it impossible to accept his period of 11 J years. 

 How ill the facts satisfy this result may be shown by two 

 comparisons in which the epochs accepted by the Zurich 

 astronomer are employed. 



Thus a maximum of the magnetic oscillation occurred 

 in 1787 by the observations of Cassini and Gilpin ; this 

 epoch has been confirmed nearly by Dr. Wolf's sun-spot 

 numbers, and by Prof. Loomis for the auroral frequency. 

 We have then the last observed maximum 18709, about 

 which there can be no doubt. In the interval between 

 these two maxima there were, according to Dr. Wolf, only 

 seven periods, consequently we have — 



1870-9— 1787-3 ^ ?,yG 

 7 7 



-- 1 1 -y4 years, 



a period which differs as much from his mean period as 

 that does from Dr. Lamont's. If on the other hand we 

 take one of Dr. Wolf's sun-spot epochs about eighty years 



' See "On the De 

 pp. 563-594- 



.\1 Period," &c., rnv:s. Roy. Sot. Etf//r., xwil, 



