August io, 1893J 



NA TURE 



!59 



writing, and informs us that 1441 copybooks were sent in (as 

 j^ainst 1 121 in 1892). An eighth competition is announced 

 for June 1894, when prizes to the amount of £(x> will be 

 awarded. 



The following is a complete list of the candidates to whom 

 the University of London has awarded the degree of Doctor of 

 Science this year : — Experimental Physics : Robert Wallace 

 Stewart ; Chemistry : Fredk. Daniel Chattaway and John Theo- 

 dore Hewitt ; Zoology : Henry Bargman Pollard ; Animal 

 Physiology : John William Pickering ; Geology and Physical 

 Geography : John Walter Gregory, William Fraser Hume, 

 Maria Matilda Ogilvie. 



3* 



2a„ sin 



SCIENTIFIC SERIALS. 



Bulletin of the New York Mathematical Society^ Vol. ii. No. 

 10. July 1893 (New York: Macmillan). — This young mathe- 

 matical society crowns the previous good work of its Bulletin, 

 in this, the concluding number of its second volume, by the 

 translation and publication of Dr. Felix Klein's "programme on 

 entering the philosophical faculty, and the senateof the University 

 of Erlangen in 1 872. " It is entitled " A comparative review of re- 

 cent researches in geometry " (pp. 215-249). The author prefixes 

 a note in which he states that the programme had a limited cir- 

 culation at first, with which he was then fairly well satisfied, 

 but now that Lie's "Theorie der Transformations gruppen " 

 has appeared, and that an Italian translation has been published 

 in the Annali di Matematica, it seems proper that a wider cir- • 

 culation should be given to his expositions. The translation, 1 

 which is a literal one, has been admirably done by Dr. M. W. 

 Haskell, and we feel sure that its publication will greatly extend 

 Dr. Klein's clientele. A few additional footnotes are supplied 

 here and there. Dr. F. N. Cole continues his previous work 

 with an article on " the transitive substitution-groups of nine 

 letters " (pp. 250-258). He points out that Mr. Askwith (Quar. 

 Jour, of Mathematics, vol. xxvi. ) gives only 22 of the 34 actually 

 existing types, and discusses the complete list of the transitive 

 groups of this degree, with brief explanations of the processes 

 by which he has obtained them. Prof. Ziwet gives a brief 

 analysis (pp. 258, 9) of the "Index du repertoire bibiiogra- 

 phique du Sciences Malhematiques, public par la Commission 

 permanente du repertoire " (Paris, 1893). Notes, lists of new 

 publications, and the index complete the number. 



In the Botanical Gazette for July, Mr. D. M. Mottier has a 

 paper on the embryo-sac and embryo of Senecio aureus ; his re- 

 sults agree closely with those of Strasburger on .5'. vulgaris ; Mr. 

 P. Dietel describes a number of new specimens of Uredineeeand 

 Ustilaginese ; Mr. G. F. Atkinson completes his account of the 

 biology of the organism which causes tubercles in the roots of 

 Leguminosas ; and Mr. C. Robertson contributes another to his 

 series of articles on flowers and insects. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, June 15. — "On the Annual and Semi- 

 annual Seismic Periods." By Charles Davison, M.A., Mathe- 

 matical Master at King Edward's High School, Birmingham. 

 Communicated by Prof. J. H. Poyniing, F. R. S. 



Metliod of Investigation. — -The method adopted is similar to 

 that employed by Dr. C. G. Knott in his paper on "Earth- 

 quake Frequency." 



If/ (9) be a periodic function of 9, then 



/(fl) = Oj -(- Oi cos (9 -f oj) + Oj cos (29 -1- o^) 



+ ... an cos («9 -I- a„) + ..., 

 from which it follows that 



, rH;'1^^^^^^^ ^ ^^^ ^ 2ai ^^g ^g ^ ^^j _ 2a, ^^^^^g ^ ^^j _!_ 

 irj t-wl-i IT "— 



cos («9 + a„) + 



This latter expression gives the mean value of /(9) through an 

 I interval Tr/2 on eiiher side of 9. From it, all terms involving 

 I even multiples of 9 are eliminated, and the coefficients of all 

 ' terms after the second are diminished to a greater extent than 



that of the second. 



NO. 1241, VOL. 48] 



A definition of the unit earthquake having been adopted, the 

 earthquakes of different districts are classified in half-monthly 

 groups, the first half of February containing fourteen days, ai d 

 of all the other months fifteen days ; and the numbers so obtained 

 are reduced to intervals of equal length (fifteen days). The num- 

 bers for the two halves of each month are added together. The 

 mean of the numbers for the six months from November to April 

 gives the six-monthly mean corresponding to the end of January. 

 Six-monthly means are calculated in this way for the end of each 

 month ; each mean is divided by the average of all twelve, and 

 the difference between each quotient and unity is multiplied by 

 the augmenting factor I "589, in order to obtain the correct value 

 of the ratio a^ : «„. The curve obtained by plotting these reduced 

 means thus gives special prominence to the annual period, by 

 eliminating the semi-annual period and all those which are 

 fractions of six months, and by diminishing the amplitudes of all 

 other periods with respect to that of the annual period. 



In investigating the semi-annual period, the numbers corre- 

 sponding to the first halves of January and July are added together, 

 and so on ; the rest of the method being the same as for the 

 annual period. The result gives special prominence to the semi- 

 annual period by eliminating the annual period, and by eliminat- 

 ing or diminishing the amplitudes of all periods less than six 

 months. 



Seismic Periodicity in relation to Intensity. — This discussion 

 is founded on : (l) lists compiled from Mallet's great catalogue, 

 first, of shocks which were so slight as to be just perceptible, 

 and, secondly, of those which were strong enough to damage 

 buildings ; (2) Prof. Milne's classification of the Japanese 

 earthquakes of 1885 to 1889 according to the areas disturbed by 

 them ; and (3) different catalogues relating to the same district, it 

 being obvious that two such catalogues for the same time can 

 only differ by the omission or inclusion of slight shocks. 



"The following results are obtained : — (l) In both periods, the 

 amplitude is greater for slight than for strong shocks ; (2) there 

 appear to be two classes of slight shocks with an annual period, 

 the stronger having their maximum in winter, the weaker in 

 summer ; and (3) in the case of the semi-annual period, both 

 strong and slight shocks, as a rule, have nearly the same maxi- 

 mum epochs. 



Seismic Periodicity in relation to Geographical Position. — 

 The number of records examined is 62, 45 belonging to the 

 northern hemisphere, 14 to the southern, and 3 to equatorial 

 countries. 



1. Annual Period. — In every district, and in all but five re- 

 cords (which are obviously incomplete), there is a fairly well- 

 marked annual period. As a rule, different records for the same 

 district agree in giving the same, or nearly the same, maximun 

 epoch. Excluding, however, those which disagree in this respect, 

 we have left 34 records for the northern hemisphere, 9 for 

 the southern, and 2 for equatorial countries. In the northern 

 hemisphere, 4 records give the maximum in November, 16 in 

 December, and 5 in January ; in the southern hemisphere, 2 in 

 April, 2 in May, 3 In July, and 2 in August ; the end of the 

 month being supposed in each case. As a rule, then, the maxi- 

 mum epoch occurs in winter in both hemispheres. The ampli- 

 tude of the annual period ranges from 0'05 (New Zealand) 

 to 067 (Sicily and Algeria), the average of 57 records being 



0-33- 



2. Semi- Annual Period. — Of the 62 records examined, only 3 

 fail to show a seuii-annual period, the cause of the failure in these 

 cases being no doubt the imperfection of the seismic record. In 

 New Zealand and South-east Australia, the maximum epoch 

 generally fallseitherin February or March and August or Septem- 

 ber; in North America, as a rule, in March or April and Septem- 

 ber or October. But for other regions it does not seem possible as 

 yet to deduce any law. The amplitudes of the semi-annual period 

 ranges from 006 (southern hemisphere) to 079 (Mexico), the 

 average value being o 24. 



3. ill filteen cases, the amplitude of the semi-annual period ex- 

 ceeds that of the annual period. Eleven of these records include 

 the following insular districts, which are among the most well- 

 marked seismic regions in the world, namely, the Grecian Archi- 

 pelago, Japan, the Malay Archipelago, New Zealand, and the 

 West Indie.-. The average amplitude of the annual period in 

 these eleven cases is o i6, and that of the semi-annual period 

 o'24 ; i.e. the average amplitude of the annual period is just 

 hall that for all the distiicts examined, while in the case of 

 the semiannual period the average amplitudes are the same. 



Origin of the Annual Period. — In this, the concluding, section 



