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beautiful specimens of micro-photographic art produced by 
one of our fellow-members, Mr. J. B. Dancer, F. R.A.S., 
during the last five years. So’ early as the year 1840 
Mr. Dancer began his investigations on the subject, and soon 
produced satisfactory results on silver plates. In May, 1853, 
when Dr. Joule, F. R.S., and some other friends erected a 
tablet to the memory of our late distinguished member, 
Mr. Wm. Sturgeon, the electrician, Mr. Dancer was so 
kind as to present me with a photograph of the tablet not 
larger than a pin’s head. His discovery was not allowed to 
rest, for hundreds of his beautiful specimens were sent all 
over the world. Within the last year or two, several parties 
have coolly claimed Mr. Dancer’s discovery, and when it is 
represented in a local print as something wonderful in 
M. Amadio having produced what Mr. Dancer did six years 
ago, it is only due to our fellow-member and townsman to set 
the public right as to who was the real discoverer of 
micro-photography.” 
A Paper was read by the Rev. T. P. Kiiikman, M.A., 
F.R.S., “On the j-nodal A-partitions of the r-gon.” The 
problem of the partitions of the r-gon which I have before 
investigated (Manchester Memoirs, 1858, and Philosophical 
Transactions, 1857), treats of the number of ways in which 
k diagonals can be drawn, none crossing another, each through 
two angles of the r-gon. The complete problem, which 
might be called the reticulations of the r-gon, considers in 
how many ways the area of the polygon can be divided into 
k smaller polygons, none covering another, whose sum shall 
be the entire r-gon, by lines passing through any of the 
r-angles, or through any of j points taken within the 
r-gon. The j internal points may be called the nodes of 
the partition, and it is evident that at least three of the drawn 
lines will meet in every node. When j=o, the problem is 
merely that case of these partitions which I have already 
completely considere<l. 
