XCviii THEORY OF ERRORS. 



In case the weights are equal, or in case p =i g = r, >^ = ^, and there 

 result, — 



Square of mean error of observed angle = \ c^, 



" " correction to observed angle = \ c\ 

 " adjusted angle = § r^, 



u (( a 



where c is the error of closure of the triangle ; so that in this case of equal weights 

 the three mean errors are to one another as IsJt,, i, and l\j2. 



References. 



The literature of the theory of errors, especially as exemplified by the method 

 of least squares, is very extensive. Amongst the best treatises the following are 

 worthy of special mention : Method of Least Squares, Appendix to vol. ii. of 

 Chauvenet's " Spherical and Practical Astronomy," Philadelphia : J. B. Lippin- 

 cott & Co., 8vo, 5th ed., 1887. " A Treatise on the Adjustment of Observations, 

 with Applications to Geodetic Work and Other Measures of Precision," by T. W. 

 Wright. New York : D. Van Nostrand, 8vo, 1884. "On the Algebraical and 

 Numerical Theory of Errors of Observation and on the Combination of Observa- 

 tions," by Sir George Biddle Airy. London : Macmillan & Co., i2mo, 2d ed., 

 1875. " Die Ausgleichungsrechnung nach der Methode der Kleinsten Quadrate, 

 mit Anwendungen auf die Geodasie und die Theorie der Messinstrumente," von 

 F. R. Helmert. Leipzig : B. G. Teubner, 8vo, 1872. 



