193.1 | LAMBERT—MACLAURIN’S SERIES OF EQUATIONS. 5 
HistoricaL NOTE. 
Lagrange, in the memoir ‘‘ Nouvelle methode pour 
resoudre les Equations Litterales par le moyen des Series,” 
read before the Berlin Academy in 1770, found all the roots 
of an equation in infinite series. McClintock, in Volume 
xvii of the American Journal of Mathematics, obtained by his 
Calculus of Enlargement series better adapted to computa- 
tion. It was recognized that these series may be obtained 
by Lagrange’s series. McClintock calls the coefficients of 
the terms which have been underscored the dominants of the 
equation. The method of the present paper brings the com- 
putation of the roots of equations by means of series within 
the range of elementary instruction. 
Since completing this paper the author found in an extract 
of a letter from Cauchy to Coriolis, of January 29, 1837, 
published in the Comptes Rendus of the Paris Academy, an 
announcement of important results to be obtained by break- 
ing up an equation into two parts and introducing as a factor 
a parameter into one part, which parameter is ultimately to 
be made unity. Ina postscript Cauchy states he discovered 
the advantage of making one part a binomial. But the 
author has been unable to find the method sketched in this 
letter developed. It would indeed be surprising if a method 
so strikingly direct had escaped notice. 
LEHIGH UNIVERSITY, SOUTH BETHLEHEM, PA, 
