of Edinburgh, Session 1885-86. 
547 
Monday, ls£ February 1886, 
JOHN MURRAY, Esq., Ph.D., Vice-President, in the Chair., 
The following Communications were read : — • 
1. The Theory of Determinants in the Historical Order of 
its Development. By Thomas Muir, M.A., LL.D. 
Part I . — Determinants in General (1693—1779). 
In October 1881 I published in the Quarterly Journal of Mathe- 
matics (xviii. pp. 110-149) a “ List of Writings on Determinants,” 
which contained the titles of all the hooks, pamphlets, memoirs, 
magazine articles, &c., which were then known to me to exist on 
the subject of the Theory of Determinants. The list consisted of 
489 entries arranged in chronological order, the first date being 
1693, and the last 1880. During the three years which have 
elapsed since it was published, I have been steadily making manu- 
script additions to it, not merely in the way of continuation for the 
purpose of keeping it up to date, hut also by the intercalation of 
omitted titles unearthed in the course of my own researches, or 
brought to my notice by obliging correspondents. 
The continuation of the list from 1880 forwards is comparatively 
an easy matter : it is not by any means easy to render equally com- 
plete that portion of the list which pertains to the eighteenth century. 
In the early history of a scientific subject, before the nomenclature 
has become fixed, the mere titles of writings are insufficient guides : 
the searcher’s work is, consequently, minute and laborious, and he 
never can be quite sure that his labours are at an end. As far, 
however, as Determinants are concerned, I am inclined now to think 
that the writings which are unknown cannot be of much import- 
ance, and that the time has come for using the collected material in 
the production of a detailed history of the subject. 
The plan proposed to be followed is not to give one connected 
history of determinants as a whole, but to give separately the 
history of each of the sections into which the subject has been 
divided, viz., to deal with determinants in general, and thereafter 
in order with the various special forms. This will not only tend to 
