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