202 Mansfield Merrirnan — List of Writings relating 



1857 Bei.lavitis. Considernzioiii sulla theoria della proLabilita. 

 Atti Istit. Venezia for 1856-7, pp. 299-321. 



1857 Bond. 'On the use of Equivalent Factors in the Method of 

 Least Squares.' Mem. Araer. ^4 cac?., Vol. VI, pp. 179-212. — Also 

 privately printed, Cambridge, 1858, 4to, pp. Sfi. 



It is shown that it is unnecessary to adhere in numerical computa- 

 tions to the strict letter of the Method of Least Squares, and that its 



application " requires the use of such numbers only, in the 



arithmetical processes peculiar to it and characteristic of the Method, 

 as may be designated by one of the numerals 0, 1, 2,. . . .9, or of the 

 fractions i, i, • • - .^, or by a product of one of these numbers by an 

 integral power of 10.'' 



1857 Boole. On the Application of the Theory of Probabilities to 

 the question of the Combination of Testimonies or Judgments. 

 Trans. Soc. Edinb., Vol. XX I, pp. 597-652. 



In the tii'st part of this memoir the rule of the arithmetical mean is 

 discussed. "The result of Boolic's investigation is that if n oh^ovxn.- 

 tions7^>i, ^^2,. ■ . .^/„ be made upon the same quantity, then the most 

 probaV)le value of that quantity is a certain linear function of jOj, jj'z^ 

 .. . .p„\ this Boole demonstrates by his Calculus of Logic, and the 

 analysis is of so peculiar a character that. . . .1 feel scarcely qualified 



to express a decided opinion on its merits the [final j result 



takes the for^n of the arithmetic mean." — Glaisher, Mem. Astron. 

 Soc. Lond., 1872, Vol. XXXIX, p. 124. 



In the latter part of the paper Heksciiel's demonstration is repro- 

 duced and defended against the arguments of Ellis; see 1850. See 

 Glaishkk's paper, just quoted, pp. 115. 



1857 DiENGER, '• AusgleicJuing der Beohachtangsfehler nach der 

 Methode der Meinsten Quadratssummen. Mit zahlreichen Anwen- 

 dung, namentlich anf geodatische Messtmge/i.'' Braunschweig, 8vo, 

 pp. viii, 168. 



.\n excellent elementary text-book. Gauss's proof of 1809 is 

 followed, with the improvement that the probability of a definite 

 error is an infinitesimal. See 1852 Diunger. Among the practical 

 questions treated is the theory of repetitions in angle measurements. 



1857 DoNKiN. 'On an Analogy relating to the Theory of Proba- 

 bilities, and on the Principle of the Method of Least Squares.' Quart. 

 Jour. 3Iath., Vol. I, pp. 152-162. 



Donkin observes that if two observations of an unknown quantity 

 give x=:a and x=ib, then the most probable value oi x is ^(a-j-b), but 

 that we cannot regard the arithmetical mean of more than two obser- 

 vations as most probable. Taking ./• to re]>resent the tiue value of 

 the unknown quantity Donkin says : " .... it appears a natural and 



