170 Mansfield Merrhnan — List of Writings relating 



r= 0.6744897 



n 



2x^ being the sum of the squares of the errors and n the number of 

 observations, and that it is an even wager that the true value of r 

 lies between 



0.6744897 1^ 0.6744897 I—' 



\^ 0.6744897 [ 



and 



0.4769363 0.4769363 

 1 y^— 1 + ^ — 



In the second method the most probable value of the sum 2x"' is 

 discussed and formulae for jDrobable error found when m has the 

 values 1, 2, 3, 4, 5 and 6. The second of these, which agrees with 

 the one given above, is shown to be the best. The third method 

 leads to a diffei'ent and less accurate formula. 



Nothing in the investigation shows whether ^x^ is the sum of the 

 squares of the true or of the computed errors. By later writers it has 

 been generally taken as referring to the former. See 1816 Bessel, 

 1819 Young, 1823 Gauss, 1856 Peters, 1866 Borsch. 



1818 AuRAiN. 'Investigation of the Figure of the Earth and of 

 the Gravity in different Latitudes.' Trans. Anier. Phil. Soc, Vol. I, 

 pp. 119-135. 



A formula for the Jength of the seconds pendulum is determined 

 by the Method of Least Squares. Adrain alludes to the process as 

 liaving been discovered by himself in 1808. See Amer. Jour. jSci., 

 1871, Vol. I, p. 415, and Mem. Astron. 8oc. Lond., 1872, Vol. 

 XXXIX, p. 78. 



1818 Bessel. '• Fundamenta astronomim pro anno MDiJCLV 

 deducta ex observation ibiis viri incom^KirahiUs James Bradley in 

 specida astronomia Grenovicensi per annos 1750-1762 institutis.'' 

 Regiomonti, folio, pp. 325. 



In pages 18-21 results of the computations of the mean and proba- 

 ble errors of the declination and right ascension of certain stars as 

 deduced from the observations are given. Three sets of measure- 

 ments, two of 300 and one of 470, are investigated as a test of the expo- 

 nential law (p{x)-=z—j^e * , the theoretical number of errors be- 



tween given limits being computed from Kramp's tables and com- 

 pared with the actual number of residuals. A close agreement was 

 found, and this may perhaps be called a practical proof of the j^riu- 

 ciple of Least Squares. 



Tables of logarithms of e^^ I e~^ dt are given ; regula minimo- 



rmn quadratormn is several times applied; and in pages 116-123 



