542 Proceedings of Roycd Society of Edinhurgh. 
The Third Section, extending only to 4 pp., deals with another 
special form, whose elements are finite differences of a set of 
functions. 
The Fourth Section, consisting of four chapters, and extending 
to 27 pp., has for its subject a third special form, foreshadowed by 
Wronski, the characteristic of which is that one of the indices 
denotes repetition of an operation involving differentiation. 
When these Sections come to be considered in their proper 
places, it will be seen that very great credit is due to Schweins for 
his labours, and that he has been most undeservedly neglected. 
The fact that he had ever written on determinants was only brought 
to light in 1884 : * and, so far as can be gathered, his treatise had 
no influence whatever either on the work of succeeding investigators, 
or in diffusing a knowledge of the subject. 
JACOBI (1827). 
[Ueber die Hauptaxen der Flachen der zweiten Ordnung. 
Crellds Journal, ii. pp. 227-233.] 
[De singulari quadam duplicis Integralis transformatione. Crelle’s 
Journal, ii. pp. 234-242.] 
[Ueber die Pfaffsche Methode, eine gewohnliche lineare Dififerential- 
gleichung zwischen 2?z Variabeln durch ein System von n 
Gleichungen zu integriren. Crelle's Journal, ii. pp. 347-357.] 
We come here simultaneously on the names of a great mathema- 
tician and a great mathematical journal. Crelle’s Journal filr die 
reine und angewandte Mathematik, which began to appear at the 
end of the year 1825, and which without any of the symptoms of 
old age still survives, has rendered on more than one occasion 
important service towards the advancement of the theory of deter- 
minants. Its first contributor on the subject and one of its greatest 
was Jacobi. At a later date he published in the Journal an 
excellent monograph on Determinants; but even his earliest papers 
show that he had begun to find it a useful weapon of research. 
In the first of the memoirs above noted, dealing with the subject 
* v. Phil. Mag. for November : An overlooked Discoverer in the Theory of 
Determinants. 
