341 



rockets 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, 2 S# , = 2. S(r . A x A; (1) 



* g,h &g \ g g, h)' \ J 



in which h is any integer number from 1 to n inclusive ; 

 x is independent of t, but Bx is a function of t and of 



x ,, . . . a? , the form of which function it is the object of the 



gj * g> n 



problem to discover ; 



*=»*.*.<**$*.'*?)• (2) 



<p being any real function of the semi-sum which follows it, 

 and m being any other real function of the index g -\- A g ; 

 while g-andg + Ag- represent any integer numbers from 

 negative to positive infinity. The equations to be integrated 

 may also be thus written : 



i\ -S A (rA I ,,+R'A x .S "A x ,A % ,\{\)' 



^g,h,t Ag\ g g,h,t l g g,h (h)l g g,h g g,h,tj K J 



in which 



the functions to be found by integration are now those of 



