192 



• KNOWLEDGE ♦ 



[Dec. 30, 1881. 



Honco, oqnating tho co-officiont« of x", wc have — 



2 n (3 71-1) (2 n-2) . . ■ ■ (n-fl) _ j, ^ ^^, 



—Ed.] 



1 . 2 . 3 . . . . n 

 ("j!Lr})y + ...« + '+! 



f 13] — Dividing an Ellipse. — I wish to know how to divide an 

 ellipse (1) thftt the radius vector may cut off pqunl parts of tlio 

 pcriphorv, and (2) thnt it may divide tho ellipse into equal areas. — 

 J. A. Ij. R. [The latter problem is solved in my " Geometry of 

 Cycloids," soction vii. The construction for o given oUipeo is suiB- 

 ciently simple, and can bo supplied if " J. A. L. R." particularly 

 requires it. The former problem cannot. W solved by any geo- 

 metrical mithod of construction. — Ed.] "^ 



anstofrsf to Correwittitntsf* 



O/ffr. 



mmunieations /or the Editor requir 

 b^orf the Siiturdajf preceding the 



irfulatioii o/trhick compel* u» to po to 

 nirrr3''TO CoBTtRSPONDKirTS.— 1. No qtie^tioiu 

 can be answered through the pott. 3. Letter* ten^ 

 cannot be forvarded ; nor can the namet '^ 



answer to private inqniriea. 3. A'o qtter 

 adcertUemenl' ran be inserted. 4. Letteri _ 

 contrary to Rule 3, free of charge. 5. Correepc 

 onlv of the paper, and put dravingn on a nepa 

 reply thouU have a title, and in replying to , 

 made to the number of letter or query, the page 



'.ifflr/y attention thould reach the 

 * %t i*$iie of Knowlbdgb, the 



I early in the ireelc. 



^^wj for ncientijic informalion 



t the Editor for corrr»pondent» 



qf correnpondenta be given in 



savouring of the nature of 



replies are inserted, unless 



I should write on one side 



f. 6. 'Eash letter^ query, or 



• queries, r^ercnee should be 



jticA it appears, a7id its title. 



Newtow Cbosland. That would be your beAr course. It would plcaso you, 

 and everyone would understand why youJTBtters could not appear here.— 

 J. Bblchbb. Whewell's *' Plurality of WorlBs" is now vcr^ much out of dite. 

 It is full of sugtjeslive matter, but even when yrhewell wrote it the work was not 

 re(jarded as of mut-h scientific weight.— >'. Kailway noise next week ; thanks.— 

 M. E. Pendbed. Having made no "vutsdn statement against a certain 

 bodv," nobody, certain or uncertain, %as a right to space here in reply. 

 Yoii simply wont out of your way to drag in the very, subjects we had 

 decided not to admit. the article you think we should not have pub- 

 lished was practically a part of our programme. You go on to Bay that 

 you would like to send U3 '& letter auent the article on suicide, anent 

 which, you ask U3 "this plain, straightforward, question : Is it or is it not 

 our intention to publish correspondence anent any social question?" We 

 an.^wcr, Not about any social.'questions, but about some such questions we should 

 admit correspondence. Suicide is not an inviting subject by any means— though 

 a review of a work recently published, on the statistics of suicide, suited our 

 pages well enough. Whether any letter you mi°htsend on that subject appeared 

 or not would depend on what you said in it.— J. M. Brown, Thanks for your 

 kindly expressions about our' chess. We were absolutely obliged to omit' the 

 column the week before last.— Young Staqee. If phrenology bus no absurdities, 

 then " none have we offended," for we objected only to its absurdities. Thanks for 

 the illusion . which has been submitted to Mr. Foster. Wo do not know who wrote 

 the elegant lines you quote.— G. F. J. Thanks.yourlettershall appear before long. 

 — E. C. R. asks where an explanation ha-s been offered of his auery, 13, p. 60. Jle 

 has searched in vain through Knowi-kdge, he says, for any such eiplanavion. If he 

 will tuni to querv- 13, p. 60, ho will see, over the initials E. C. R., the explana- 

 tion referred to. — M arias. *' Oh, no ; we never mention him " (inthe.se columns). 

 A. B. ^-Phrenology has been fairly tested, and the discrepancies between theory 

 and observation arc found to be far too numerous to be overlooked. There have 

 been marked cases of agreement, of course, or the theory would never have had 

 any adherents. Our readers would not care, we believe, for the article you suggest. 

 — BbxTbovato. We understand : correspondents are to be wholly neglected, or 

 they are to be left onl^ a page or two of the smallest print, and we are to fill 

 Kkowledok with articles by "able individuals," preferably perhaps enlarging 

 each number to twice the present size. We should displease correspondents, and 

 each number would involve a heavy loss. But those are mere details. Bkx 

 TaoyATO "prefers such articles to tho uncertain lucubrations of unknown 

 individual-^." — Jas. Obbex. Thanks. The illusion you illustrate had 

 already been sent by Mr. Ilodd, and before that Mr. Foster had had 

 it in his collection.' It shall appear soon, but not, as you suggest, 

 at the back of a star map.— Chtef Librabian. Thanks; but we are too modest 

 to nre.'^ent Knowledge as published. We wait retiringly till sought for.- 

 .1. E. OoBR. Wo will trv to find room for your note on the star in Cassiopeia. 

 Thanks.— .1. A. L. R. Wo know beforehand that no one can tell you the 

 number of known languages; still we insert your query.— Jas. Grke'n. Do 

 not you think it would be better to study the theory of evolution a little before 

 attacking it ? If you had, you would know that the theory, as now understood, 

 involves, as an absolute necessity, the "survival of the fittest" o»/v. You ask 

 why there are not, at the present moment, examples of every gradation from one 

 extreme to the other (from monads to monkeys, and thence to men), this being 

 precisely the question which you would refrain from asking if you hod studied 

 even Buperficially the views of Darwin, Wallace, IlaMkel, Spencer, and the 

 re^«(. They show that the fittest survive, and you ask. Where are the others? 

 Understand, wo are not saying that they of necessity are right, and believers in 

 the doctrine of multiplied special creations of necessity wrong. We are not 

 urging our own or any man's opinion against yours. AVe are simply saj-ing that 

 A you do not as yet know what the doctrine. is which you are attacking. If you 

 *• did, you would' not find the points you mention militating against it.— R. C. 

 Thanits ; but thnt particular solulion of the magic square problem has !»een 

 suflicientlv di.touHsed in lotters recoived during the last four weeks,— Mrs. Dr. 

 KiNGPORD. The reviewer of the *' Perfect Way in Diet" nhoutd have wrillen 

 Mr<. rather than Miss; but s» long as our present manner of Kueaking English 

 remains unchanged. " Dr. Anna Kingsford" will not be regarded as a k-gitimate 

 expression. A gentleman may recognise to tho full a lady's professional skill, and 

 her title to a diploma, but he' can no more address her ad *' Doctor " or " Pro- 

 fo"jior," without smiling, than he could gravely atldre-'^s her as "sir." Even in 

 Amorica, where ladv professors, doctors, Ac. are more numerous than here, ihis 

 is found to bo tho case. Miss Mitchell, for instance, at Vassar College, knows 

 ' than many professors of the science in her own country and this 



nore astronomy than many professors of the science in her own country and this ; 



hr is also distinctly entitled (o be called Profasnor, and she prefers to be so called. 



man has ever yet been abl^ so to address bor in a perrectly natural manner. 



Bui 



and tb« younit ladie* who att/<nd her cUammi, though th«j try hard to do •», moil 

 certainly fail. — H.FiTz Hart. Ask youmelf lbnujnialqumtioni*hieb»ci««ee putsia 

 such coiiei ; li there any noniiblp relation of tmD"f* and eff»yrt in tLiiir we ' .\ri.] too 

 will at onee mc« (hat the hazel twig mu^t harft hA^n h«<UI by < « 



whoro water-springs were. 1'ho trick tit b« old oa th(« hill* htj . 



come. — W. A. We agree with you that there it, a rlear diitr I 



.an but think " and "I cannot but think. "—Bkii. S'^m" part- ..- 



been injured without any notireoblo cbang'>, but certainly it i' n ■: " -'r; tly 

 true," as a general itatciDent, that injury to the bnin i^ not followed br aoj 

 "noticeable injur)-." — CLbDAFAU. Thanks for interesting story, nn-i for 

 poolry ; but we could not well offer a prize of £100 for a poem on knosfI.'d|;*».— 

 v.. JuKR*». Propose to havo some papers on the Arabic nam^a of the iitan 

 Mhortly in Ksowlbdob.— J. W. Chestkb. It i!i, we believe, out of print.- W. 

 KiDD. Your solution is not ot'rrect. Will give the solution in the next number. 

 The problem is not m simple as you scorn to think. As an exercise try thii. A 

 l>ody projected vertically upwards will not fall to the east, but to the west of the 

 point whence it was projected ; moreover, it will bo traveUiog weetwardi not only 

 when ascending, but when descending also. 

 This week being the Christmas holidays necessitates some slight changes of 

 arrangement. We take the opportunity to publish matter which has been lyiDf 

 over for seyeral weeks. More recent correspondents will understand the delay. 



Later.- Christn 



s holidays, and in particular Bank Monday. catLne someiinet 

 lient delays, increased br postal delay.s due to multitndiwiai 

 ChriHtmos greetings. We are prevented this w<M>k from giving our paper on Iht 

 Pyramid, and a paper on the Telescope, by a Fellow of the Royal Astronomioal 

 Society, because the illustrations for both these papers were not in hand in good 

 time. However, so far as the latter paper is concerned, it is fitting that it sboidA 

 appear in tho first number of the New Year, in which also will be the first of oar 

 monthly Star Maps, in which &ome features have been introduced whicfa^ wv 

 believe, our readers will regard as decided improvements. 



The Protective Effect of Vaccination.— Dr. Henry Tomkinaj 

 medical superintendent of the fever hospital belonging to the Man- 

 chester Koyal Infirmary at Jlonsall, in a paper which he read 

 recently at Owens College, said : — " The most strikinj* of all evidence 

 is, perliiips, tliat derived from tho small-pox hospitals themselves. 

 Here tho protective influence of vaccination is seen and proved in a 

 manner beyond all cavil. At Highf^te, during an experience of 

 forty years, no nurse or servant, having been re- vaccinated, has ever 

 contracted the disease, and evidence of the same character I can 

 myself bring forward, for during the whole time that I have had 

 charge of the fever hospital, more than a thousand cases of small- 

 pox have passed under my care, yet no servant, nurse, porter or 

 other person engaged there has, after re-vaccination, ever taken it, 

 though exposed daily to infection in its most concentrated form. 

 One woman, a laundress, who escaped vaccination, took the disease 

 and died ; one nurse, who some years before had suffered from 

 small-pox, and was then considered protected, had a very mild 

 attack; and this summer a workman, who did not live on the 

 j)remises, but came in to work as a painter, was not vaccinated, 

 and liad rather a sevoro attack; and still more recently a 

 servant, who by an oversight was allowed to go about her 

 work three days before being vaccinated, had, before the latter 

 had run its course, a slight abortive attack. Again, among all the 

 students who during the past two years have attended the hospital 

 for clinical instruction, not one has suffered, all having been re- 

 vaccinated before being permitted to enter tho small-pox wards. 

 And in their case the false argument which opponents of vaccination 

 have brought forward to explain the immunity enjoyed by nurses 

 and others in attendance on the sick, — viz., that constant interconrae 

 and exposure to infection renders them proof against it by the 

 system becoming inured to the poison, cannot be applied, as these 

 gentlemen attend tho hospital only a few hours once a week. I 

 defy the most enthusiastic or conscientious of anti-vaccinators to 

 I)roduce evidence liko this on his side of the (piestion, or to brin^ 

 for^vard even half-a-dozen persons, choose them whence he may, 

 who have not been protected against small-pox, and expose them i 

 the students are exposed, without more or less of the number taking 

 the disease. Facts such as these should convert the most ardei^ 

 anti-vaccinator from his folly, and convince him that a weapon of 

 defence so powerful ns vaccination should not be left to the pleaeore 

 of the individual, but that the State has the right and duty to look 

 after its most thorough performance. — Times. 



Contents of Ki^owledge No. 8. 



PAGB 



The So-called Elements. By Prof. 



C. A. Y'oung 161 



What is a Grape ? By Grant Allen 153 

 Studies of Volcanic Action. Part II. 



Bv G. F. RodweU IM 



Our" I'nbidden Guests. Part IT. 



Bv Dr. Andrew WiUon, F.R.S.E. 155 

 Solids. Liquids, and Gases. Port V. 



Bv W. Mattieu Williams 156 



The Evolution of Man 15" 



Mallet's SeLimometors (Illustrated) 157 

 The Faure Accumulator. By W. 



Lvnd 158 



The Wyandotte Indians. Bj Miss 



A. W. Buokland 168 



Xotc on the Spheoridal State. By 

 W. F. Barrett. F.R.S.K. ] 



An Instrument for Drawing the 

 Conic Sections. By Thomas Thorp . , 

 (IllHstrateJ) 10 



CORHBSPOXDKXCK UO f 



The Northern Skiea in Decembar— 



(Illustrated) 



Queri^s 



HepUes toQuerios «. 



Notes on Art and Science 



Our Mathematical Column Ifj 



Our ChR*n Column 



Onr Whist Column 



Answers (o Corrcspondeots 



