to the Method of Least Squares. 211 



1867 Hagen, '■Grundzuge der Wahrschemlichkeits-Meclinung.'' 

 Second edition, Berlin, large 8vo, pp. x, 187. 



This is rewritten from the edition of 1837. The proof of the law 

 of facility is given snbstantially the same as before. The distinction 

 between trne and com}»uted errors is not however clearly drawn. 



The book is an excellent one for stndents and engineers, the greater 

 part being of a practical cliaracter. 



1867 Hansen. 'Von der Methode der kleinsten Quadrate im 

 Allgemeinen and in ihrer Anwendnng anf die Geodasie.' Ahhandl. 

 Sdchslsch. (resell.., Vol. XIII, pp. 571-806. — Also separately, Leipzig, 



8vo, pp. 2:36. 



- i . , . 

 In the opening pages the law of facility (p{x)z=^h7T "e-/i'^a-' is deduced 



by Gauss's method of 1809, x being regarded as the residual or com- 

 puted error. The remarks on page 797 concerning probable errors 

 seem to be true and valualVie. The book is particularly full in the treat- 

 ment of conditioned observations, and is a valuable one for geodetic 

 engineers. See 1868 and 1869 for supplements to the work. 



1867 ScHOTT. 'Results of the primary triangulation of the coast 



of New England, from the northeastern boundary to the vicinity of 



New York.' Report Coast Survey U. S. for 1865, pp. 187-20:5, 



A continuation of Schott's articles of 1855 and 1866, devoted 

 mainly to the discussion of the probable errors of the linear and 

 angular measurements of the triangulation. A comparison is also 

 given of the measured lengths of three base lines with the lengths as 

 computed through the triangulation. The paper is a very valuable one. 



1867 Thompson and Tait. 'Experience.' Chap. Ill, of their 

 Treatise on Natural Philosophy, (Oxford, 8vo), Vol. I, pp. 30:3-320. 



Herschel's proof (1850) is given and spoken of as " simple and 

 apparently satisfactory." See below 1872 Schlomilch. 



1867 TcHEBYCHEFF. ' Dcs valcurs moyens.' Rec. Sci. Math.., Vol, 

 II. — Liouville's Jour. Math., Vol. XII, pp. 177-184. 



On " Esperances mathematiques," their arithmetical means, etc. 



1868 Fbisiani. ' Sulle piil vantaggiosa combinazione delle osser- 



vazioni.' Mem. Istit. Lombardo, Vol. II, pp. 1-21. 



The principle of Least Squares is proved, assuming that the arith- 

 metical mean gives the most probable result. 



1868 Hansen. ' Fortgesetzte geodatische Untersuchungen, beste- 

 hend in zehn Supplementen zur Abhandlung von der Methode der 



