246 
and the solution, in series, required is— 
Men (pe"-1- &,) (per-1- Ba) 
REGbnnie Awe oer Nemveen DE N'Y ES u £ 
> @ aise) Garlna | (ph =I=a,) (peda 
+ 
OC, (lt)? {1-4 (pl +m -1-8,) (pl +a,-1-6)) 
= ——— 74 &e. 
Me (panda) lve tee ae | 
a8 
FS 1+ «—1-,) (p1+e,-—1-) 
5. In the Differential Calculus, the following transformation of a 
theorem previously stated is occasionally useful, namely, 
aos Fi (xD) . au = F (aD +m) u. 
a” 
The theorem in the calculus of Finite Differences, corresponding in ex- 
pression, though not in power, to this, and possibly suggested before, may 
be thus enunciated. If 
(@)m= (a +1) («+ 2)... (@+m-1), 
then will ; 
a » EF (@A) . (&) mitt =F («+ mA+m) u, 
a theorem which may be readily proved by induction from the fact that 
DA . (2) mtb = (2)m (a + MA) m+ U. 
Mr. W. R. Wilde read a description of two ancient Irish Boats, 
found in the county of Cavan, which he presented to the Museum on 
the part of Alexander Nesbitt and Robert Burrowes, Esqrs. 
The Ven. the Archdeacon of Ardfert read a paper ‘‘ On an original 
Portrait of the Old Countess of Desmond.” 
Mr. Wilde presented the following donations to the Museum :— 
A bronze dagger, found in the Dunshaughlin Crannoge, on the part 
of Mrs. Rothwell, of Kells. 
An iron bridle-bit, on the part’ of Mrs. Tyrrell, of Ballinderry, near 
Enfield. 
The thanks of the Academy were voted to the donors. 
