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^ ^> \^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 it lU 122 £f Lfi 12.0 1.1 U& CIHM/ICMH CIHM/ICMH Microfiche Collection de Series. microfiches. Canadian Institute for Historical Microreproductions /Institut Canadian de microreproductions historiques Tschnical and Bibliographic Notas/Notaslachniquas at bibliographiquaa Thi tot Tha inttituta hasattamptad to obtain tha baat L'Institut a microfilmi la meilleurexemplaira original copyavailabiaforfilming. Faaturas ofthis qu'il lui a At* possible de se procurer. Les details copywhich may ba bibliographically uniqua. da cet exemplaira qui sont paut-Atre uniques du which mayaJtarany oftha imagaa in tha point devue bibliographique, qui peuvent modifier Thi raproduction. orwhich may significantly changa une image reproduite. ou qui peuvent exiger une pos tha usual mathod of filming, ara chackod balow. modification dans la mAthode normaia da filmoge of sont indiquAs ci-dessous. filnl D Colourrd covars/ Coloured pages/ Couvartura da coulaur Pages de couleur Ori( bog D Covars damagad/ Pages damaged/ the CouvarturaandommagAa PagesendommagAes sior othi D first Covars rastorad and/orlaminatad/ Pages restored and/or laminated/ sior Couvartura restaurAa at/ou pallicul6a I I Pages restaurAes at/ou pelliculAes ori D Covartitia missing/ ryj PPaaggeess ddiissccoolloouurreedd,, ssttaaiinneedd oorr ffooxxeetd/ Latitra da couvartura manqua Pages dAcolorAes. tachetAes ou piquAes D Colourad maps/ PPaaggeess ddeettaacchheedd// Tha Cartas gtegraphiquas en coulaur I I Pages dAtachAas shal TIN D Colour^ ink (i.a. otharthan blueor black)/ r^ SShhoowwtthhrroouugghh// whi Encra da coulaur (i.a. autra qua biaua ou noira) Transparence Mai D Colourad platas and/or illustrations/ QQuuaalliittyyooff pprriirnt varies/ diffi Pianchasat/ou illustrations an coulaur I I QualitAinA'jale de I'impression enti begi D Bound Mdth ctharmatarial/ r~~| IInncclluuddeess ssuupppplleemmeennttaarryy mmaatteerriiial/ righi requ RaliA avac d'«utras documents Comprend du matAriel supplAmentaire metl n Tight binding may cause shadows or distortion Onlyedition available/ along interior margin/ I I SauleAdition disponible LareliureserrAe peutcauserde I'ombre ou de la distortion la long de la marge intirieure D Pages wholly or partially obscur J by errata slips, tissues, etc., have been refilmed to Blank leaves added during restoration may ensurethe best possible image/ appearwithin the text. Whenever possible, these Les pages totalamentou partiallement have been omitted from filming/ obscurcies par un feuillet d'errata. une paiure. II se peutquecortaines pages blanches ajouttes etc.. ont AtAfilmAes A nouveau de lagon A lorsd'une restauration apparaissent dans lataxte. obtenir la meilleure image poscible. mais. lorsque cela Atait possible, ces pages n'ont pas AtA filmAes. D Additional comments:/ Commentaires supplAmentaires: This item is filmed at the reduction ratio checked below/ Ce document est filmA au taux de rAduction indiquA ci-dessous. 10X 14X 18X 22X 2ex aox y 12X 16X 20X 24X 28X 32X Th« copy filmad h«r« hat b—n raproducad thanks L'axampiaira film* fut raproduit grflca k la to tha ganaroaityof: ginirositi da: Library, Biblioth4qua, DtpartnwntofNationalDafanoa MinistiradalaDMamaNationala M Tha Imagaa appaaring haraaratha bast quality Las imagas suivantes ont raproduites avac ie posslbia considaring tha condition and lagibility plus grand soin. compte tenu do la condition et oftha original copy and in icaaping with tha da la nattatA da l'axampiaira iWrmi. et en filming contractspacificationa. conformiti avac las conditions du contrat de filmagb. 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Tha laat recorded frame on each microfiche Un des symboles suivants apparaltra sur ia shall contain tha symbol •^»»>(meaning "CON- derniire image d—e^cheque microfiche, selon Ie TINUED"), orthesymbol (meaning "END"), cas: la syVmbols signifie 'A SUIVRE ', Ie whicheverapplies. symbols signifie "FIN". Maps, plates, charts, etc., may befilmed at Les cartes, planches, tableaux, etc., peuvent Atre different reduction ratioa. Thoaatoo largeto be filmteA des taux de reduction diffirents. entirely included in one exposure ara filmed Lorsque Ie document est trop grand pour Atre beginning in the upper left hand corner, leftto reproduiten un scul ciichA. il estfilm6 A partir rightand top to bottom, as many frames aa de I'angia supArieurgauche, de gauche A droite, required. The following diagrams illustratethe et da hautan bas. en prenant ie iiombre method: d'images nAcessaire. Les diagrammes suivants illustrant la mAthode. 1 *^*-^^i^/-^^ r •eXc^j^ V// L A TKEATISE ON ANALYTICAL STATICS. EonDon- C. J. CLAY and SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, AVE MARIA LANE. GLASGOW: 263, ARGYLE STREET. LEIPZIG: F. A. BROCKHAUS. NEW YORK: MACMILLAN AND CO. BOMBAY: GEORGE BELL AND SONS. ^g \ A TEEATISE ON ANALYTICAL STATICS WITH NUMEROUS EXAMPLES BT EDWARD JOHX ROUTH, Sc.D., LL.D. M.A., F.R.S., &c., HON. FELLOW OF PETEKHOUSE, CAMBniDOE FELLOW OF THE UNIVERSITY OF LONDON. ;' VOLUME I. SECOND EDITION CAMBRIDGE AT THE UNIVERSITY PRESS 1896 [All Rights reserved.] Fir$t Edition IWDI "'Wid Edition 1896 CAMBRIDGE: PKINTI liy j. AND C. K. CLAY, AT THE CNIVKnSITY PRESS. PREFACE. 1~\URING many years it has been my duty and pleasure to "^"^ give courses of lectures on various Mathematical subjects to successive generations of students. The course on Statics has been made the groundwork of the present treatise. It has however been necessary to make many additions; for in a treatise all pirts of the subject must be discussed in a connected form, while in a series of lectures a suitable choice has to be made. A portion only of the science of Statics has been included in this volume. It is felt that such subjects as Attractions, Astatics, and the Bending of rods could not bo adequately treated at the end of a treatise without either making the volume too bulky or requiring the other parts to be unduly curtailed. These re- maining portions appear in the second volume. In order to learn Statics it is essential to the student to work numerous examples. Besides some of my own construction, I have collected a large number from the University and College Examination papers. Some of these are so good as to deserve to rank among the theorems of the science rather than among the examples. Solutions have been given to many of the examples, sometimes at length and in other cases in the form of hints when these appeared sufficient. I have endeavoured to refer each result to its original author. I have however found that it is a very difficult task to effect this R. s. I. 6