Se ee. 
341 
tockets rose 800 yards; if fired at Plinlimmon, they will be 
visible at Dublin, and probably even at Oxford; on the 
other hand, from Knocklaid, near Ballycastle, county Antrim, 
they could be seen at points on the west coast of Scotland, 
which see Ben Lomond, and can be joined by powder signals 
on it with Edinburgh. This however would require a transit 
instrument to be established, but the object to be effected is 
so important that Dr. Robinson hopes to accomplish it. 
The President concluded his account of his First Series 
of Researches respecting Vibration, connected with the 
Theory of Light. The following is an outline of one of the 
investigations which are contained in the Series referred to. 
It is proposed to integrate the system of equations in 
mixed differences, 
D, 84, , =a, 2° R.A, ,)3 (1) 
in which % is any integer number from 1 to » inclusive; 
oh is independent of ¢, but on, , 18 a function of ¢ and of 
Eyre, 4? the form of which function it is the object of the 
problem to discover ; 
rig mag b(S ZayilA, a an)? (2) 
_ @ being any real function of the semi-sum which follows it, 
and m being any other real function of the index g+Ag; 
while g and g+ Ag represent any integer numbers from 
negative to positive infinity. The equations to be integrated 
may also be thus written : 
la 
Seen =2,,(8 By Ee, hyt +R e, Tp Zay dg? pat g E wat)? (ly 
~ in which 
v= ms ag % (33a (4 g ©») )s (2) 
the functions to be found by integration are now those of 
