242 Imperial Institute of France. 



M. Legendre next proves that the rule by which a mean 

 may be obtained from the result of different observations, 

 arises from a very siinple principle of the smaller squares. 



This information is of much importance, as far as it au- 

 thorizes the astronomers to take the value of several hun- 

 dred observations to form a final equation from them, 

 which will present the means of thus uniting several groups 

 of particular equations, to form as many final equations as 

 may be judged proper, and applying the method of the 

 small squares without engaging in endless calculations. 



This remark might of itself be considered as a sort of 

 demonstration ; but afterwards, by a happy reconciliation, 

 M. Legendre refers his formulae to those by which we find 

 the centre of gravity of several equal masses placed around 

 sevei'al given points. He concludes that his principle in 

 some measure makes known the centre, around which are 

 ranged all the results furnished by experience in the neatest 

 manner possible. 



To explain the method still further, after having applied 

 it to perfect the elements of his comet, he applies it to the 

 last measurement of the meridian. He had to determine 

 the most probable flattening which resulted from the four 

 arcs measured, and the correction of the 45th degree pretty 

 nearly ascertained by the members of the commission. 



These two unknown quantities must be found by keeping 

 as close as possible to the five observed latitudes. 



He expresses the errors of five latitudes en fondion of 

 the two unknown quantities, and his method conducts 

 him to a flattening {applatissement) of -rr^, and to a 45th 

 degree weaker than had been supposed by twelve toises and 

 a half. This flattening appeared to him to be too strong, 

 and its degree too small ; but the errors of the latitudes 

 scarcely exceed the errors which we may fairly suppose to 

 exist : he afterwards supposes the flattening as at -^^^ ; but 

 then the errors of latitude found by his method go the 

 length of 3, 4, and frequently nearly 6"; which is scarcely 

 credible. 



Such are the principles of M. Legendre : we take the 

 opportunity of mentioning him here, because his memoir 

 having been printed in another shape, they have not named 

 him in the volume of the Institute. 



In his Precedents, written upon the arc of the meridian, 

 M. Legendre had not in any way mentioned the method 

 which he has denominated that of small squares, {moindres 

 carries,) which appears to decide that in 1799 he was not 

 i\i j'ossession of them. 



Bosco- 



