The confusion comes from Whitman's using a (now archaic) word form. I don't know to what degree Whitman's specific choice "atomies" was standard in his time, but Whitman is generally considered a poet of the first rank, and poets are allowed to invent words and engineer novel usage. (Often, those two capabilities are marks of the greatest poets. Shakespeare was the most fertile because he was writing during the first period of what came to be modern English.)
- Atomies may refer to the atomic level of existence
I take this from context of this particular verse, Voice of the Rain, and because the idea is established at the outset of Leaves of Grass:
I celebrate myself, and sing myself,
And what I assume you shall assume,
For every atom belonging to me as good belongs to you.
Whitman: Song of Myself
This is supported by "And all that in them without me were seeds only..." in that seeds, dust, and atoms are small, basic units, similar to motes. You'll note that atom and mote are standard definitions of atomy.
This is further supported in that Whitman was famous for using lists in this poem in particular, thus using different words for similar concepts is not only consistent, but almost certainly intended in this passage. However,
- It's quite possible Whitman was intending a double meaning (again a mark of poetry) in the secondary usage of bones
Specifically, bones are often hidden in the "dust-layers of the globe". Whitman was a contemporary of Charles Darwin, and the paleontology was an exciting, rapidly developing area in science. [Note: The first edition of Leaves of Grass was published a few years before On the Origin of Species, but Voice of the Rain seems not to have appeared until the 1891 edition of Leaves.]
My personal feeling is that what Whitman's was really saying with atomies is "all of the sets of minutiae that comprise the world".
Atomy is related to anatomy, and this strengthens the anthropomorphic theme--that of the poet has giving voice to the rain. (See also "What the Thunder Said".) If the rain has a voice, surely the earth itself can be regarded as an organism, or an amalgam of organisms.
Leaves is, at times, quite sexual, and this passage is distinctly so. The rain is creating life in a process analogous to procreation: "I descend to lave the drouths, atomies, dust-layers of the globe,
And all that in them without me were seeds only, latent, unborn;
And forever, by day and night, I give back life to my own
origin..." In many ways, this section calls to mind the mating of Gaia and Ouranos (heaven and earth) but transforms the process into something nurturing as opposed to terrifying in that the progeny is sustaining, not destructive.