A Text-Book on the Method of Least Squares (Classic Reprint)

PREFACE TO THE FIRST EDITION. The fI Elements of the Mlethod of Least Squares," published in (Si7, was written with two objects in view: first, to present the fundamental princilJles and processes of the subject in so plain a manner, and to i11ustrate their application by such simple and practical examples, as to render it accessible to ch-i} engineers who have not had the benefit of extended mathematical training; and. secondly. to give an elementary exposition of the theory which would be adapted to the needs oi a large and constantly increasing class of students_ In preparing the foHowing pages the author has likewise kept these two objects continually in mind. Vhile the former work has been used as a basis, the alterations and additions have been so numerous and radical as to render this a new and distinct book rather than a second edition. lne arrangement of the theoretical and practical parts is cr:tirely different. In Chapters I to IV is presented the mathe

Table of Contents

CLSSIFlC"TIO~ OF ODSERYATIO:'S; EkRORS OF OBS£RVATlO S •; PRoI :-:CIPLES OF PRORAIULITY; PROBLEMS; CHAPTER 11; LA IV OF PROBA BIl/TY OP ERROR,; AXIO)IS DERIVED FRO!>! EX:PERIE~CE; THE PROU,IHLlTY CURVE ,; FIRST DEDUCTIO" OF THE L w OF' ERROR,; SECO:-i"O DEOVCTIO:-; Ot' THE LAW OF ERROR; DISCUSSTO:-: OF THE PI:ODABILITY Cl'R'F; THE PRODAIJILITV I ;-;TEGIlAL; Cm4PARIsO::-: OF" THEORY A1'O EXPFRIE~CE; RDIRKS O~ THE FUXOA!>{E~TAL FOR:lIUL •• S; PROBt,E~S AND Qt;ERIES •; CHAPTER III; THE AD7UST:tENT OP OBSERVATIO_VS; )VEIGHTS OF OfiSERVATlONS; 'l'HE PRIXCIPLE OF LEAST SQiARES; DIRECT OnSER'ATW:-i"$ Ox A SII'CLE Qt;:Xl'ITV; [XDEPEXDENT OIlSERYAnONS OF EQUAl "'EIGHT; I~OEPF~DENT O~SERVATJOXS OF l:XI::Ql'AL WEIGHT; SOLln'lOX OF ~OR)I-L EQUAT!O~S; CO:iOI"rIOXED OllSI::R,A"'IO~S; PI