172 Mansfield Merrhnan — TJst of Writings relating 



26 triangles. Laplace shows that the probable error of the computed 

 distance is 8.194 metres. The investigation is reproduced in the Third 

 Supplement (1820), pp. 3-7. 



1819 Laplace. 'JMemoii'e sur I'application ducalciil des probabil- 

 ites aux observations, et specialement aux opi'rations du nivellement.' 

 Annal. (Jhem. et Phys., Vol. XII, pp. 337-341. 



On the results of a discussion of the probability of errors in the 

 computed elevation of Paris. The discussion itself is given in the 

 Third Supplement (1820), pp. 16-28. 



1819 Paucker. '•JJeber die Anvjendung der Methode der kleinsten 

 Quadratssmnnie auf phgsikalischeu Heobachtw/ geti.'' Mitau, 4to, 

 pp. 32. 



Published as a Gymnasium "Programm." It contains an applica- 

 tion of the Method of Least Squares to the determination of empiri- 

 cal formulae for the expansion of fluids, the specific gravity of water, 

 and the elasticity of steam. See 1825 Muncke. 



1819 Walbeck. Dissertatio de forma et magydtudine tellvris, ex 

 diniensis arcuhus meridiani definiendis. Abo, Svo. 



The first discussion of measurements of several arcs of meridians by 

 the Method of Least Squares. 



1819 Young. Remarks on the probabilities of eri*or in physical 



observations, and on the density of the earth, considered, especially 



with regard to the reduction of experiments on the pendulum.' Phil. 



Trans. Land, for 1819, pp. 70-95. 



Pages 70-83 are devoted to the Tlieory of Errors. Besides many 

 interesting remarks it contains a method for finding probable errors, 

 sup])Osing that the probabilities of the several errors are proportional 

 to the terms of the series (l-j-l)'", m being an even number. His re- 

 sult for the probable error of the mean of n observations is 



R = 0.85 — j^ 

 nWn 



2x 

 in which — denotes "the mean of all the actual errors." Young 

 n 



refers to Bessel, Gauss, tfec, as having used only the sum of the 



squares of the errors in determining the probable error, and regards 



his method as more accurate. See 1816. 



1820 Bessel. ' Bestimmung der geraden Aufsteigungen der 36 

 MASKELYNESchen Fundamental-Sterne fiir 1815, auf Konigsberger 

 Beobachtungen gegrundet.' Ahhandl. Alad. Berlin for 1818-19, 

 pp. 19-36 of the mathematical part. — Ahhandl. von Bessel (Leipzig, 

 1875, 4to), Vol. II, pp. 238-245. 



