February 15, 1906] 



NA TURE 



\79 



parison of the two intervals of 75 years were exceedingly 

 puzzling. While the observations beginning with about 

 1826 showed a nearly homogeneous variation of 11125 

 years, this period seemed almost entirely absent between 

 1749 and 1S26. Its place was during that interval taken 

 by two important groups of periodicities, one of which 

 had a periodic time of about 925 years, while the second 

 had an average period of 1375 years. The latter period 

 was represented more nearly by what in spectroscopy is 

 called a "band," extending from 1325 to 1425 years, but 

 some of this want of definiteness may be due to the de- 

 ficiencv in observational data. For some time I was 

 inclined to draw the conclusion that such periodii ities as 

 we observe are comparatively short lived, and replaced by 

 a number of others which in their turn die out. A more 

 detailed investigation, however, convinced me that the 

 periodicities are, as regards the interval of time elapsing 

 between successive maxima, extremely regular, occurring 

 with what may prove to be astronomical accuracy. The 

 key of the solution is, I believe, to be found in the over- 

 lapping of a number of periods, all of which are regular 

 as regards time, but vary considerably as regards intensity, 

 so that one or other may for a certain number of years 

 become inactive. Their real existence is proved by the fact 

 that whenever they reappear after a period of inactivity, 

 the phase of the renewed periodic action fits in exactly 

 with the continuation of the old period. 



A periodicity of about 4-78 years runs through the whole 

 of the observations. Its amplitude being about one-sixth 

 of that of the eleven-year period is too great to be 

 accounted for by accident. It appears separately in the 

 series of Wolf's numbers, ranging from 1749-1826 and 

 from 1826—1900. It also appears in the series depending 

 on the measurement of areas. The phases of the period 

 as determined from these series are in good agreement, and 

 even while I was inclined to question the permanency of 

 the eleven-year period ' never felt any doubt that during 

 the whole length of 150 years this period has been acting. 

 Its time, determined as accurately as possible from the 

 combined records, was 4-81 years, but I believe that if 

 greater weight were given to the more recent and more 

 complete observations the number would be slightly re- 

 duced. As regards the main period, which has certainly 

 given its character to the sun-spot statistics during the 

 greater part of the last century, I find the time as deter- 

 mined from the observations since 1826 alone to be 11 125 

 years. This agrees well with Wolfer's estimate of 11-124, 

 and Newcomb's investigation, which led to 11-13 as tne 

 most probable number. 



If to the most accurate series of measurements of sun- 

 spot areas which begin in 1832 we apply a process the 

 result of which is the elimination of the chief period, and 

 draw a curve representing what is left, we find decided 

 maxima during the years 1836, 1845, 1853, 1862, and 

 1870, the intervals being alternately 9 and 8 years, or 

 8-5 years on the average. The periodogram based on 

 Wolf's numbers for the complete interval 1749-1900 shows 

 a decided maximum of intensity for a periodicity of 825 

 years. Adopting this period provisionally, and disregard- 

 ing all observations since 1826, we may use Wolf's series 

 previous to that date for the determination of the phase 

 of the period in question, and thus forecast the maxima 

 for the subsequent interval. We thus obtain 18363, 

 18447, 1852-9, 1861-2, 18694, ' r almost exact agreement 

 with the above. The slight disagreement of phase would 

 be corrected by assuming the time to have been 832 years. 



A periodicity of about 13-5 years shows as a maximum 

 of intensity in the periodogram for the complete interval. 

 In connection with it the following facts seem remarkable. 

 There are in Wolf's records three cases of successive 

 maxima having an interval of between 13 and 14 years. 

 They are : — 1626-0— 1639-5, '1816.4— 1829-9, 1870 6-1883-9. 

 Also the interval between 1639-5 and 1816-4 ' s thirteen 

 times 13-61, and the interval between 1829-9 ar| d 18706 is 

 three times 1357. Thus the maxima all fit in with a 

 period of about 13-6 years, which with varying intensity 

 seems to have run through the whole record of observ- 

 ations. 



Not wishing to lay too great a stress on what may 

 prove to be merely a numerical coincidence, I return to the 

 three periods which have been determined with some 



NO. 1894, VOL. 73] 



accuracy. It was only after the periodic times had been 

 independently determined that the following remarkable 

 relationship between the numbers was discovered. Taking 

 frequencies into consideration, we are led to form the 

 reciprocals of the periodic times, and thus find 



Adding up we find 



'11.125 = 0-08989 

 1/8-32 =o- 12019. 



1 4-76 = 0-21008. 



Hence the sum of the frequencies of two of the periods 

 agrees within the possible errors with the frequency of the 

 third period. But it is also found that the two first 

 numbers are very nearly in the ratio of three to four, so 

 that we may also express the three periodic times as sub- 

 periods of 33 375 years. Thus 



3 X33-37S = II - I2 5 

 1X33-375= 8-344 

 T* 33375= 4-7°8. 



How far this connection is accurate or approximate it is 

 impossible to say at present, but the fact that the three 

 periods which have been traced with a considerable degree 

 of certainty should also bear a remarkablv simple relation- 

 ship to each other is worthy of note. 



If we accept a period twice as long as that given above, 

 we might account for other periodicities of which at 

 present the times are only approximately determined ; thus 

 Ax 66-75 would lead us to 1334, in fair agreement with 

 the period of 13-57 years which has been mentioned above. 

 But the difference is greater than it should be, and at the 

 present I do not wish to put forward the longer. 



Arthur Schuster. 



NATURAL HISTORY AND ARCHEOLOGY OF 



THE WATERLILIES. 1 

 AIR. CONARD has embodied the result of several years' 

 1 work on the waterlilies in the sumptuous volume 



before us. The monograph opens with an historical 

 account of the plants as they were known to the ancients, 

 and then deals with the group from a modern botanical 

 point of view. 



An interesting part of the memoir deals with the 

 morphology and development of the plants, and the reader 

 will find much that is worth reading therein. It must be 

 confessed, however, that, taken as a whole, this portion 

 occupies a somewhat large number of pages in proportion 

 to the amount of valuable information it contains. the 

 structure of the root is given at some length, but one 

 would have liked to see a comparative treatment given 

 that embraced not only the roots of different species, but 

 also those of an individual plant at various stages of the 

 life-history. Possibly such an investigation might throw 

 light on the nature or origin of the " Liorrhizic " 

 character of the roots in the waterlilies. Mr. Conard 

 gives a good account of the formation of the intercellular 

 spaces and the diaphragms so characteristic of the order, 

 and he mentions an interesting occurrence of stomata on 

 the under surface of the aerial leaves that rise above the 

 level of the water in Nymphaea odorala var. minor. 



The occurrence of stipules is a point of some note, and 

 it may be remarked that their absence from the early 

 leaves of the seedlings detracts from their phylogenetic 

 significance in the group. 



A short sketch of the development of the flower is in- 

 cluded in the monograph, and we think it might have 

 been considerably extended with no small advantage. The 

 flowers, as is well known, occupy a remarkable position 

 in waterlilies, where they apparently replace a leaf. The 

 author was led to adopt a suggestion made by Caspary 

 as to the morphology of the flower which explains the 

 anomaly and at the same time appears to fit the facts of 

 development. The anterior sepal, which appears first, and 

 often well below the others, is regarded as morphologically- 

 representing the bract, whilst the two lateral sepals are 



1 "The Waterlilies. A Monograph of the Genus Njrrpha-a.'' By 

 Henry S. Conard. Pp. xiii + 279. (Published by the Carnegie Institution 

 of Washington, 1905.) 



