218 
Pacific tides meet along a line of comparatively still water, on which 
the ice accumulates so as to form an impassable barrier. This line 
passes through the following points:—North of Rensler Harbour; 
North of Wellington Channel; Banks’s Strait; North of Prince of Wales’s 
Strait. 
A general sketch of this theory was published, in April, 1858, in 
the ‘‘ Natural History Review,” and communicated by Mr. Haughton 
to Captain M‘Clintock in the summer of 1857. The practical conclu- 
sion deduced from this theory was, that no ship could pass from the 
Atlantic to the Pacific, or vice versd. Mr. Haughton stated that the 
discoveries of Captain M‘Clintock respecting the ‘‘ Erebus’ and ‘Terror’ 
confirmed this theory. 
The Rev. Roszrr Canmicuazt read the first part of a paper— 
ON CERTAIN METHODS IN THE CALCULUS OF FINITE DIFFERENCES. 
Secr. L.—On the Solution of Systems of Simultaneous Equations in the 
Calculus of Finite Differences. 
TueEre are many questions in physics, more especially in the departments 
of magnetism, heat, meteorology, and astronomy, in which the condi- 
tions for solution are given by observations made at periods separated 
by finite intervals, and the unknown quantities enter in certain linear 
combinations. It would seem to be obvious that, in some of these cases, 
the phenomena would admit, as their possible analytical expression, and 
in some cases would require as their only suitable expression, systems 
of simultaneous equations in finite differences. 
For instance, it seems evident that there are certain classes of phy- 
sical problems which are only susceptible of exposition by such a system 
as,—if %, V, Wz &c., are unknown functions of ¢ to be determined, 
mH, b,, q, &c., constants, and f, fo, fs, &c., functions of known form,— 
A.U;, = OU, + dy, + +.» » + fi) 7) 
A. 0; = Anil, + bv; + Cx0,+. . « +h,(4) 
A. W= Ash, + b30; + C3, +... +f(8) (’ 
&e. 
or, 
Urpin = AU, + by, + 0,4... +f(2) 
Vien = Ag, + br, + C7, +... +f,(t) 
Wein= Ag + 30, + C70, 4+... +f3() (’ 
&e. J 
So far as I am aware, no general method has been given for the solution 
of such systems of equations. In the following pages an attempt is 
made to supply the desideratum. 
