When the Stirling numbers of the second kind were introduced by James Stirling in 1730, it was not combinatorially; rather, the numbers ${n \brace k}$ were defined via the polynomial identity
$$
x^n = \sum\_{k=1}^n {n \brace k} x(x-1)\ldots (x-(k-1)). ~~(\star)
$$
Most modern treatments of the Stirling numbers introduce ${n \brace k}$ combinatorially, as the number of ways of partitioning a set of size $n$ into $k$ non-empty blocks, and then (combinatorially) derive identities such as ($\star$).


While preparing for some upcoming talks on topics related to Stirling numbers, I realized that I have no idea who it was who first observed that the numbers ${n \brace k}$ defined by ($\star$) have a combinatorial interpretation. 


The earliest reference I can find is in W. Stevens, Significance of Grouping, Annals of Eugenics volume 8 (1937), pages 57--69 (available at <http://onlinelibrary.wiley.com/doi/10.1111/j.1469-1809.1937.tb02160.x/abstract>). This seems to predate any mention of ``Stirling numbers of the second kind'' on MathSciNet.


I imagine that this is a question that has been thoroughly researched --- does anyone know of a reference? 



Who first noticed that Stirling numbers of the second kind count partitions?
[Niels Nielsen,](http://en.wikipedia.org/wiki/Niels_Nielsen_(mathematician)) who coined the name "Stirling number of the second kind", gives the partition counting interpretation in his 1904 book [Handbuch der Theorie der Gammafunktion](https://archive.org/details/handbuchgamma00nielrich), page 70.


