March 14, 1895] 



NA 1 URE 



479 



determined all the simple groups whose orders do not exceed 

 660. The only other kniwn results in connection with the 

 question as to whether there is a simple group corresponding to 

 a given onler are as follows. There is no simple group who se 

 order is the power of a prime, or whose order contains two or 

 three pri ue facto's ; and the only simple group who^e order 

 contains four prime factor-^ is a group nf order 60. The lai ter 

 result was established in a paper pablishei in vol. xxv. of the 

 Proceedings ai Wis Mathematical Society. The present paper 

 aims at an exti-nsion of these results. If /j, /.,. . . . /,. are 

 distinct primes in ascending order, it is shown that in a group 

 ijf order 



the number of operations whose orders are divisible by /, and 

 by no lower prime is 



(/.-i)/, + i • ■ ./..-lA.'", 



from which it follows at once that a group whose order is of this 

 form can nei her be simple nor contain a simple subgroup.' It 

 is also shown that a group whose order is of the form 



A'A ■ • • A -]/""■ 



cannot be simple, and cannot contain a simple sub-group, with 

 the exception of the ca>e in which it con'ains a tetrahe.ir,al sub- 

 group ; in which cas- /j = 2,f„- 3. Thirdly, it is shown, with 

 certain limitations, that if no prime entering in the order of a 

 group, except the greatest, appears to a higher power than the 

 second, the group cannot be simple. Fourthly, it is proved 

 that no groups whose orders are of the forms. 



can be simple. A deduction from these results of general form , 

 aided by the con-ilerati )n of certain more pariicu'ar cases, is 

 that the only simple groups whose order is the product of fiv e 

 I primes are the kno«vn simple groups of orders 16S, 660, an d 

 1092. Finally, it is shown that if in a group of order 



/riA^s • • ■ A-i "« 1 ;*.."•» 



the subgroups of order 



Pi u Fi i' • ■ • F"-\ I'-i 



are all cyclical, the group cannot be simple, and cannot contain 

 a simple subgroup. 



Entomological Society, February 20. — Prof. Raphael 

 Meldola, F.k.S., President, in the chair. — Mr. W. M. Christy 

 exhibited specimens of Lyatna a«estis, caught in Sussex, last 

 summer, which had a white edgmg round the black discoidal 

 spot. lie said the specimens miijht, perhaps, be identical with 

 the northern form of the species known as the variety sa/maiis. 

 — Mr. H. Go^s exhibited a small collection of Lepidoptera fron 

 the South of France, male by Mr. Frank Hromilow. — Prof. 

 Meldola invited discussion upon the address delivered by Mr. 

 Elwes, as retiring president, on the " Geographical Distribution 

 of Butterflies," at the last annual meeting. lie remarked that 

 he had not himself had time to consider the paiter in an 

 adequate iiianner, but he thought that the discussion might lead 

 to a useful expression of opinion if ihespeakcrs would deal with 

 the question as to how far the scheme of distribution advocated 

 by Mr. Elwes w.as borne out by a comparis n with other orders 

 of insects. He was of opinion that in considering schemes of 

 geographical His ribution, the results arrived at were likely to 

 be of greater value the wirier the basis on which they rested, 

 and he therefore suggested that the ques ion might also be taken 

 into consideration as to how far it was justifiatile to draw con- 

 clusions from the consideration of one rlivision or one order 

 only. Dr. .Sharp, F R.S., remaiked that g-^ographical dis- 

 tribution consisted of two divi ions ; firstly, the facts ; secondly, 

 the generalisations and deductions that may be drawn from 

 them. He thought that as regards insects generally our know 

 ledge of the (acts was not yet sufficient to warrant many 

 generalisation*;. Siill the impressions of those who have paid 

 attention to particular groups of insects are even now of some 

 imporiance, though at present based on incomplete knowledge. 

 He thought the Khopalocera would prove to be a some*hat 



t It has been pointed out to the auihor since the paper was communi- 

 cated to the Society, thai this first result is contained in a paper by Herr 

 G. Frob:nius, Beriincr Sitzunssbeiicltte, r8()3. 



NO. 1324, VOL, 51 I 



exceptional group in their distribution. Notwithstanding that 

 Australia and New Zealand are so poor in them, this was by no 

 means the case with their Coleoptera, .\ustralia being very rich, 

 and its fauna of Coleoptera being very distinct. He thought 

 that if Lepidoptera generally were well collected in Australia 

 and New Zealand, it would be found that this order was not so 

 poor in species as was supposed. He instanced the case of the 

 Sandwich Islands, where it was supposed that there were very 

 few species of Lepidoptera, and yet some 500 species, or per- 

 haps more, had been recently found there by Mr. R. C. L. 

 Perkins, who had been sent to investigate the islarids by a 

 committee appointed by the Royal Society and British As- 

 sociation. — Mr. McLachlan, F.R.S.,said he was of opinion 

 that no definite demarcation of regions existed, but that all the 

 regions over-lapped ; in any case the retention of Pal.earctic 

 and Naearctic as separate provinces was not warranted on Ento- 

 mological data. He believed that atthe closeof theGlacial period 

 some insects instead of going north were dispersed southwards, 

 and that the present geographical distribution of some forms 

 might thus be accounted for. The discussion was continued by 

 Mr. Osbert Salvin, F.R.S., Mr. J. J. Walker, Herr Jacoby, 

 Mr. Champion, Mr. Elwes, and Prof. Meldola. — The Rev. 

 T. A. Marshall contributed a paper entitled "A Monograph of 

 British Braconidie, Part vi."— Mr. J. W. Tutt read a paper 

 entitled "An attempt to correlate the various systems of 

 Classification of the Lepidoptera recently proposed by various 

 authors." In this paper he criticised the opinions recently 

 expressed by Mr. G. F. Hampson.and Dr. T. A. Chapman, in 

 certain papers published by them. .\ discussion ensued, in 

 which Mr. Elwes, Prof. Meldola, and Mr. Tutt took part. 



Zoological Society, February 19.— Sir W. H. Flower, 

 K.C.B., F.R.S., President in the chair.— Mr. F. E Beddard, 

 F.R.S., read a paper in which he gave a description of the 

 brain of the Glutton {Gulo lusais). — .\ second paper by Mr. 

 Beddard contained a description of the brain of different 

 species of Lemurs that have died in the Society's Gardens, 

 pointing out the range of variation to be observed in the 

 cerebral convolutions of this order. —A communication was 

 read from Mr. C. Davies Sherborn and Dr. F. A. Jentink, in 

 which was given the dates of the publication of the parts of 

 Siebold's "Fauna Japonica" and Giebel's "Allgemeine 

 Zoologie " (first edition). — A communication was read from 

 Dr. J. de Bedriaga, "On the Pyrenean Newt, ^fJlge as f era, 

 Duges," dealing with the external, osteological, and larval 

 characters of this imperfectly-known Batrachian, and giving an 

 account of its habits. 



Linnean Society, February 21. — Mr. C. B. Clarke, F.R.S., 

 President, in the chair.— Mr. J. H. Vanstone exhibited 

 specimens of some nearly allied Hydrozoa, namely, Bcugain- 

 vellca r.imosa and B. musca, and after demonstrating their 

 structure, gave reasons for conclu'iing that although the latter 

 had been described as distinct by Prof, .\llman, the characters 

 relied upon were not of specific value but simply varieial. — 

 Mr. George Brebner exhiiiited some lantern slides of Glct-osi- 

 phoma capillaris aT\A oyhej Algae, viith accompanying descrip- 

 tions, anil gave an intereting account of his method of pre- 

 paring slides in colours.— On bthalf of Mr. J. Boerlage, the 

 President demonstrated the chief points in a paper communi- 

 cated by him on the identification of Chiovanlhiis Glusri, an 

 (ib-cure speces figured by Gieriner at the end of the last 

 century in his famous work " De (ructibus et seminibus Plan- 

 tarum," but hiiherto undetermined. From the researches of 

 Mr. B 'erlage it now appeared that it was evidently referable to 

 Seh podcndron costatiim, Kurz. This was made clear by the 

 excellent drawings which accompanied the paper, as well as by 

 ihe specimens which were exhibited. — .K paper was then read 

 by Mr. E. M. Hulmi s, on new marine Alga; from Japan. The 

 author pointed out that up to the pestnt time the known 

 sprcies of Algje from th.at country did not excee 1 300, or about 

 half ihe number found in Great Britain; but that the districts 

 around ihree centres only had been explored, namely Hakodadi, 

 Tokio, and Nagasaki, not« ithstanding the fact that seaweeds 

 are largely used as food by the Japanese, and form an iuipoitanl 

 article of commerce. The paper included descriptions of 

 twenty-three new species (the structure of which was shown by 

 means of the oxyhydrogen lantern) belonging to the genera 

 Ctadophora, Coaium, Diclyota, Diclyopleris, Polyzonias, 

 Chondrus, Gracitaria, Gratcloupia, Gymnogongrus, Halymeria, 

 Lethetshedtia, and Padina, 



