156 Mansjield Merriman — List of Writings relating 



able that the error of a single observation may be any one of the 

 quantities, — v, ... —3, —2, — 1, 0, 1, 2, 3,. .. .v. The second gives 

 a method of determining that probability, provided the probabilities 

 of the single errors — u, — v-\-\,. ...—], 0, 1,. . . v — 1, v are propor- 

 tional to the tei-ms 1, 2,. . . .v, v + 1, ij, . . . .2, 1. This is illustrated by 

 a numerical example. Simpson remarks that the advantage of the 

 mean can be shown, whatever series be used to express the chances 

 of tlie errors. 



IVSV Simpson. 'An Attempt to show the Advantage arising by 

 Taking the Mean of a Number of Observations, in practical Astron- 

 omy.' Miscellaneous Tracts. . . .(London, 4to), pp. 64-75. 



A reprint of the preceding, the opening and closing paragraplis 

 being omitted and nearly four pages of new matter added. We find 

 here the following axioms stated for the first time; 1. that positive 

 and negative errors are equally probable, 2. that there are certain 

 assignable limits within which all errors may be supposed to fall. 



In the added matter the case of contimtous errors is discussed, and 

 the probability that the error of the mean is less than an assigned 

 value found for the case of the second proposition by making ti and 

 other quantities in the formuUe infinite. Simpson represents the law 

 of facility of error geometrically by the sides of an isosceles triangle 

 and draws a curve to show the increased precision of the mean as 

 compared with single observations. He closes by finding under the 

 same supposition as to the law of facility, the probability that the 

 mean is nearer to the truth than a single observation taken at ran- 

 dom. The whole memoir must have been extremely valuable at the 

 time of its publication. 



1760 BoscoviCH. De recentissimis graduum dimensionibus, et 

 figura, ac magnitudine terrae inde derivanda. Philosophia. receutior 

 d Benedicto StxVY. . . . (Romae, 3 vols., 8vo), Vol. 11, pp. 406-426. 



A method of combining discordant observations upon the lengths 

 of degrees of the earth's meridian is here given. The adjustment is 

 effected u.nder the two conditions that the sum of the negative errors 

 shall be equal to the sum of the positive errors, and that each sum 

 shall have the least possible value. The problem was solved by a 

 geometric construction depending upon the properties of the centre 

 of gravity of figures. 



The method is also given in the French translation of Boscovich's 

 work of 1755. See Lindenau in ZacJi's Monatliche Correspondent^ 

 1806, Vol. XIV, p. 132; Todhunter, ^/s^. of Tlieories of Attrac- 

 tion , Vol. I, pp. 321-332; and below, 1785 Bernoulli, 1792 



Laplace. 



1760 Lambert. Photometria sive de mensura et gradibus lum- 

 inis Augustas Vindelicorum, 8vo, pp. [xxx], 547. 



Contains many remarks on the arithmetical mean and also proposes 

 a method for judging of the precision of the measurements, which 



