{ 292 ) 
Art. XVII. — On the Method of Minminm Squares^, employed in 
the Reduction of Experiments^ being a Translation qf the 
Appendix to an Essay of Legendre'' s^ entitled^ “ No Livelies 
Methodes pour la Determination des Orbites des Cometes,’” 
with Remarhs. By George Harvey, Esq. Member of the 
London Astronomical Society. 
A Translation of an Essay by Legendre, on the subject of 
Minimum Squares^ may not be unacceptable to such of the 
readers of the Edinburgh Journal, as may not have had an op- 
portunity of consulting the able memoirs which have ap- 
peared on this very important subject, in the writings of some 
of the Continental mathematicians. I have selected the paper 
of Legendre ; because that distinguished geometer was the first 
who added to the equations of condition employed by Euler, in 
his paper on the inequalities of Jupiter and Saturn, and by 
Mayer, in his Essay on the Moon’s Libration^^ — an equation 
which should involve the additional condition of making the 
sums of the squares of the errors of observation a minimum. In 
another paper, I shall give the very able demonstration which 
Laplace has alforded, in his Theorie Andlytique des Probabili- 
ty^ that the result which Legendre’s principle alFords, is the 
best which the conditions of any problem can require ; since the 
result of the investigation leaves the least possible error, and, at 
the same time, points out the limits within which its aberrations 
are confined. 
To the experimental philosopher, the method of minimum 
squares will be frequently found of singular utility and value. 
In the varied departments of natural philosophy, in practical astro- 
nomy, and, indeed, in every inquiry where the conditions to be 
determined are exhibited under the form of algebraical coeffi- 
cients, it will fix the mean position or value of the object of re- 
search, with a degree of certainty and precision not to be attain-* 
ed by any other method. 
The essay of Legendre here alluded to, was published origi- 
nally as an appendix to the work which appeared in 1805 , and 
entitled Nouvelles Methodes pour la Determination des Orbites 
des CometeSi and which is distinguished for the same beautiful re- 
finement, that characterises the other productions of this celebrat- 
