1888 - 89 .] Dr T. Muir on the Theory of Determinants. 
769 
HESSE (1843). 
[Ueber die Bildung der Endgleicbung, welche durch Elimination 
einer Yariabeln aus zwei algebraischen Gleichungen hervorgeht, 
und die Bestimmung ihres Grades. Crelle’s Journal , xxvii. 
pp. 1-5.] 
Hesse, at this time, must have been unaware of Richelot’s paper 
(dated from the same University), and Grunert’s paper, not to speak 
of writings published outside Germany, for the method which he 
gives of finding the final equation is nothing more nor less than 
Sylvester’s dialytic method. His exposition, to say the least, is 
not preferable to Grunert’s, and the determinant of the (m + n) tli 
order which he prints is misleading in points of detail. 
GRASSMAHH (June 1844). 
[Die Wissenschaft der extensiven Grosse, oder die Ausdehnungs- 
lehre, eine neue mathematische Disciplin dargestellt und 
durch Anwendungen erlautert. Erster Theil, die lineale Aus- 
dehnungslehre enthaltend. xxxii + 279 pp. Leipzig, 1844.] 
A quite peculiar form of the law of formation of a determinant 
had its origin with Grassmann. Grassmann, it will be remembered, 
was one of the most distinguished of the mathematicians who 
occupied themselves with the search for an Algebra of directed 
quantities , or with the allied problem of the geometrical interpreta- 
tion of the so-called imaginary expressions of ordinary algebra. By 
the beginning of the third decade of the century, the way had 
been gradually, though intermittingly, prepared for important dis- 
coveries on the subject by the writings of Wallis (1685), Buee(1805), 
Argand (1806), Servois (1813), Mourey (1828), Warren (1828), and 
Gauss (1831).* With Hamilton and Grassmann important dis- 
coveries came. Hamilton, whose writings of 1833 and 1835 show 
that even then he had meditated to some purpose on the matter, 
announced in 1843 his great invention of Quaternions. In 1844 
Grassmann followed with the first part of the Ausdehnungslehre. 
* See art. “Quaternions,” by Professor Tait, in Encyclopaedia Britannica ; 
or Hamilton’s Lectures on Quaternions. 
