RESOLUTION OF ALGEBRAICAL EQUATIONS. 127 
But, Gentlemen, I trespass on the privileges of this chair. Let it 
be my apology to you that the event I mourn is—from accidental cir- 
cumstances,—peculiarly associated with this meeting and your choice 
of me as your President. Permit me, in closing an address already 
too protracted, in which I have aimed at indicating some of those lines 
of abstract thought whereby science is enlarging our views and widen- 
ing our sphere of knowledge, to invite you, as in a sense the self- 
constituted acolytes in this temple of Canadian science, to enter with 
renewed energy and devotion on the work of another year ; remember- 
ing, each one of us, that we know not how few our years of work nay 
be. We may indeed—in a far more absolute and literal sense than 
Newton could,—say, after all our work is accomplished, that we 
‘seem to have been only like a boy playing on the sea-shore, and 
diverting himself in now and then finding a smoother pebble or a 
prettier shell than ordinary, whilst the great ocean of truth lay all 
undiscovered before us.” But yet let us remember this at least, that 
that great ocean of truth does lie before us, and even those pebbles 
which our puerile labours gather on its shore, may include here and 
there a gem of purest ray; and meanwhile the search for truth, and 
even the play along the pleasant shores of its great unexplored ocean, 
will bring to each one of us his own exceeding great reward. 
RESOLUTION OF ALGEBRAICAL EQUATIONS, 
(Continued from the last Number of the Journal.) 
BY THE REV. GEORGE PAXTON YOUNG, M.A., 
PROFESSOR OF LOGIC AND METAPHYSICS IN KNOX’sS COLLEGE, TORONTO.. 
ProrositTion VI, 
If all the cognate functions (not necessarily unequal) of f (p), an 
integral function of a variable p, be, 
sa) iol) Neb IU iti aivd Saint ald ext) ian Ay 
and if 
X = (#—¢1) (w@—¢e) ...... (e—¢m) 
== 0 tA OP A OOP ail +A; dew) 
then the coefficients Aj, Ag, &c., may be exhibited as rational ex- 
pressions, that is, (see Def. 1), rational functions of p. 
