117 
Here a'’'+' stands for the product a(a+l)(a+2). . . to 
factors h, and for a{a — l)(a — 2) ... to 6 factors. 
I have to correct two oversights in the 16th and 22nd 
articles of my Paper, “ On the triedral partitions of the 
a;-ace” (Manchester Memoirs, 1858). In the 16th article, 
not only doubly irreversibles, but also the doubly reversibles, 
of article 15, are constructed, so that these ought to be sfib- 
tracted before dividing by two. In the 22nd article the triply 
reversibles of article 20, as well as triply irreversibles, are 
constructed ; it is therefore necessary to subtract the triply 
reversibles and then to divide by two, for the reason given in 
the 16 th article. 
The Paper, of which this is an abstract, will contain the 
corrected formulse. 
From the partitions of the r-gon having two triangles only 
for its marginal faces which are above considered, it is easy to 
obtain the expression of the partitions of the (r-|-a;)-gon, 
which have any two marginal faces, and have any number of 
angles unoccupied by diagonals. For this deduction formula? 
are given in this Paper. 
Dr. .Joule having taken the Chair, a Paper was read by 
the President, W. Fairbairn, F.R.S., &c., entitled “An 
experimental inquiry into the effect of severe pressure upon 
the properties of Gunpowder.” During the late war, the 
Author received from the Government authorities at Woolwich 
different samples of Waltham Abbey gunpowder, for the 
purpose of submitting them to severe compression, in order to 
ascertain the effect of close contact between the particles upon 
its explosive properties. At the Government works there is 
no machinery of sufficient strength to give a pressure of more 
than 5,000lbs. to 6,000lbs. per square inch, and as it was 
considered advisable to test the quality of the powder under 
the influence of greatly increased pressure, the Author was 
requested to compress it, in an apparatus of his own, calculated 
