172 



NATURE 



[J line 28, 1877 



in short, one cycle is in this respect almost as good or as bad as 

 another. 



Now, if in any series of quantities, such as the rainfall obser- 

 vations at Madras, there be a law of periodicity, each observed 

 quantity may be supposed to be compounded of a periodical and 

 a non-periodical element. If we take the sum of a large number 

 of cycles, each of which coincides with the cycle of periodicity, 

 the non-periodical elements will tend to be eliminated, and the 

 means for the successive years of the cycle will indicate the 

 periodical elements for the successive intervals. At the same 

 time the differences of these means from the several original 

 quantities from which they were obtained will be the several non- 

 periodical elements. 



In proportion as the periodical elements are small or large in 

 relation to the corresponding non-periodical elements, so the 

 differences (obtained as above) wdl be inversely less or more 

 different from the differences between the individual observations 

 and the mean of the whole of them ; and if there be no periodi- 

 city, the two sets of differences would, in a sufficiently long series, 

 be identical. 



Hence it may be inferred that when the differences (taken as 

 before) closely approximate in magnitude to the mean difference 

 of the original observations from the arithmelical mean of all of 

 them, the periodical elements in those observations must be cor- 

 respondingly small ; and this applies manifestly to the eleven 

 year-cycle and to the whole of the arbitrary cycles for which 

 the differences were calculated. 



Further to test the reality of the periodicity, the author re- 

 arranged the series of sixty-four years' obst- rvatio ns, in a purely 

 arbitrary manner, in cycles of eleven years, by drawing the actual 

 observations at random one after another, and setting ihem down 

 in succession lill the whole were exhausted. From three 

 arbitrary cycles thus prepared, the differences averaged lO'g, 

 ii'2, and ii'6 — lesults which again indicate that the actual 

 sequence of the observed quantities of rain has no material effect 

 on the mean differences, or any such tendency to a diminution in 

 their numerical value, which is the necessary accompaniment of 

 a true periodical element. 



Moreover, the mere circumstance of any series of cyclical 

 means showing a single maximum and sint;le minimum gives no 

 real indication of such a result being a truly periodical feature. 

 It is obviijusly to argue in a circle, first to assume a cycle on 

 which to work, which shall give a sin^jle maximum and minimum, 

 and then to infer that there is true periodicity because of the single 

 maximum and minimum. The test of the periodicity is in truth 

 to be sought altogether outside of the particular values of the 

 successive elements of the cyclical means. 



It is manifest that a complication of periodical elements may 

 so mask one another as to prevent positive results being obtained 

 by the examination of the means and differences in the case before 

 us. But the whole scope of the present argument is negative, 

 and it leads to the conclusion that there is no proof of greater 

 tendency to periodicity in the eleven-year means than in the 

 original isolated observations. 



As the sun-spot period is not exactly a cycle of eleven years, 

 the author examined the results obtained by a comparison of the 

 observations corresponding to the known periods of maximum 

 and minimum sun-spots, without reference to any special length 

 of cycle. These results he also considered to be negative. 



A further test of the character of the conclusions was sought 

 from the rainfall observations at Bombay and Calcutta, which 

 have been made for the greater part of the peri' d over which 

 those at Madras extend. It is haidly conceivable that there 

 should be a coincidence with the sun-spot period, such as is 

 supposed to have been found at Madras, based on any physical 

 cause, which should not in some way be discernible in the rain- 

 fall at Bombay and Calcutta. 



The results thus got are also held to be entirely negative, and 

 to indicate no concordance among the means of the several years 

 of the cycle at the different places. The Bombay and Calcutta 

 observations, treated as those of Madras were, to ascertain the 

 deviations of individual observations from the successive means 

 of the cycle, give quite similar results. 



Although the special object of the communication was to deal 

 with the alleged correspondence between the Madras rainfall 

 and the sun-spot periods, the author had also turned his 

 attention to Mr. Meldrum's speculations of a similar character, 

 and had tested some of them in the manner explained. 



Among these were the Greenwich observations for fifty-five 

 years, which will be found at p. 307 of vol. xxi. of the Proceed- 

 ings of the Royal Society, and the results got from them 



were quite analogous to that obtained from the Indian obser- 

 vations. 



Further, to illustrate the argument on which the paper was based, 

 the case was considered, in which a well-ascer'ained periodicity 

 exists, as that of the diurnal barometric oscillation. The figures 

 used were taken at random from an old Madras register, the 

 intervals being made two-hourly, and the entries and the differ- 

 ences of the observed barometric heights from the daily means in 

 thousandths of an inch, so as to reduce the calculations. 



The figures being merely illustrative, the circumstance of their 

 not exactly representing any physical phenomenon_|Was a matter 

 of no significance. 



The treatment of these figures led to results very different from 

 those t;ot from the rainfall observations. The mean difference 

 of all the supposed observations from the mean ot all of them 

 being thirty, the mean of the differences between the two-hourly 

 means and the original figures was reduced to seven, indicating the 

 distinct |iresence of a periodicity. 



Re-arranging the figures in an arbitrary cycle of ten periods 

 instead of twclve,the mean of the differences which before was seven 

 was increased to thirty, showing that with the total destruction of 

 the periodicity the mean difference of the two-hourly means and 

 the original figures was the same as the rnean difference with the 

 arithmetical mean of all of them. 



In conclusion, the author specially explained that he did not 

 call in question the possible or actual occurrence of terrestrial 

 phenomena corresponding to the sun-spot period, but only desired 

 to point out that in the case of the rainfall obscrvali jus under 

 review the evidence was not sufficient to establish either any 

 periodicity or such a correspondence. 



In some remarks made subsequently the author pointed out 

 how the comparison of the successive combination of the obser- 

 vations, beginning with one cycle and then combining two, and 

 so on, till the whole were united, supplied another way of treating 

 the fig ires which showed that the successive means of the differ- 

 ences between the mean rainfall for the combined cycles and the 

 mean for the several years of the cycle when combined, followed 

 the law that would hold good if there were no appreciable 

 periodicity, that is to say, that this mean should gradually dimi- 

 nish in a ratio inverse to the square root ot the number of cycles 

 combined. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE 



Cambridge. — Prof. Humphry has been appointed to repre- 

 sent the University at the 400th anniversary ot the University of 

 Upsala in September next. 



Prof. Adams' report to the observatory syndicate for the year 

 from May, 1S76, to May, 1S77, does not contain anything of un- 

 usual interest. The year has been exceptionally favourable for 

 astronomical observations, and 3,618 observations were made 

 with the Transit circle. AU the publications of the observatory 

 are well forward, and the general work has been carried on 

 smoothly and efficiently. 



The following awards have been made for proficiency in 

 natural science at St. John's College : — To F. T. S. Houghton, 

 a foundation scholarship, the Wri^dit's Prize, and augmentation 

 of exhibition to 100/. ior the past year. To Marr, Slater, F. J. 

 Allen, Stewart, augmentations of e.\hibitions. 



London. — A public meeting in support of the London School 

 of Medicine for Women was held the other day at St. George's 

 Hall, the especial object being to raise 5,000/., with a view of 

 enabling the Executive Council to carry out an arrangement with 

 the authorities of the Royal Free Hospital, under which students 

 from the school were to receive clinical instruction. Mr. Cowper- 

 Temple, M.P. , Mrs. Garrett- Anderson, and Mrs. Westlake were 

 amongst the speakers. 2,600/. have already been subscribed. 



The Senate of the London University have decided by a 

 majority of five not to postpone giving medical degrees to 

 women till all the other faculties were open to them. 



Manchester. — On Friday last the scholarships and prizes 

 gained during the session by students in the Faculties of Arts, 

 Science, and Law were distributed at the Owens College. The 

 Daton Senior Mathemitical Scholarship was gamed by J- ?• 

 Whitney ; the Ualion Junior Mathematical Scholarship by J. D. 

 Pennington ; the Dalton Chemical Scholarship by J. K. Crow ; 

 the Piatt Physiological Scholarship by L. Larmuth. Mr. Crow 

 presented a research upon the " Hypovanadoijs Compounds," 



