When I first think of the term circumference, I remember those terribly boring winter days in high 
school geometry class, stoically calculating distances around the circles scrawled on the chalkboard.
   Then, some time during college (those years are all jumbled now), I read Aristotle, who talked about the 
two advantages of motion around the circumference of a circle, as he saw it: uninterrupted and continuous motion, 
and allowing the least possibility of change. I wonder if Emily Dickinson read much Aristotle?
   Of course, we know she did read R.W. Emerson, who believed that "the moral law lies at the center of 
nature and radiates to the circumference." 
   The "My Business is Circumference" letter gives us a clue about the context of Dickinson's use of the 
term. She's writing to T.W. Higginson, her writing mentor, in defense of her poesy, and though she appreciates 
the opportunity to be his "scholar," she feels the need to dub herself the "Representative of Verse." There are 
several ambiguities in the letter which would perhaps become clarified in those unpublished / unrecovered letters, 
and "My Business in Circumference" is ambiguous too, but we have the artifacts – her poems – to understand 
what seems to be an important proclamation for Emily.
   I look to "The Poets light?" as another vocation poem in which Dickinson explains the  relationship 
between the poet and the "wicks" (readers). The circumference, by definition, is the measure around the circle, 
not inside the circle. Dickinson stresses the fact that the poet's business (or concern), hers in particular, is to only 
revolve around the subject, and the reasons are: 1) studying a subject from a sufficient distance allows for a more 
objective and holistic view, 2) there's a certain respect a poet must give to the subject, just as the painter and 
photographer gives, so that one doesn't damage it (i.e. split the lark), and 3) using a circumferential perspective 
works to embrace a wider audience; not everyone has experienced an internal study of a given subject, but one can 
assume that most have experienced a passing observation, however fleeting, of the subject at hand. 
To radiate into the core of a subject is not only to reject the subject but also to reject one's own sensation 
of it. Poem #378 ("I saw no Way") speaks to this issue:

I touched the Universe –

And back it slid – and I alone –
A Speck upon a Ball –
Went out upon Circumference –
Beyond the Dip of Bell –

This poem tells me that when the speaker invaded (or radiated into) the Universe with a touch, 
she broke her rule that the poet must always maintain a circumferential study, to never make 
attempts to connect physically with the subject. When the speaker did this, the Universe pulled 
away and consequentially the speaker became isolated and feeling as insignificant as "A Speck 
upon a Ball" – which is where she should have been all along – upon the circumference of the 
earth and not penetrating/invading/radiating it. ( I wonder if there's also a sexual tint to 
circumference too: adoring and imagining from all points, but never making physical contact / 
penetration. )

In the Circumference poems, there are some other terms that keep resurfacing, namely: 
speck, particle, and Immortality. This last term, which curiously is the last word in #679, seems 
to me to be a very relevant issue in the business of circumference. Using circumference rather 
than radiation in the vocation of poetry allows atleast two things to happen: 1) a poem is going 
to have a greater immortality if it only addresses somewhat universal facts of the subject that 
people from Age to Age can embrace, and 2) going back to Aristotle, the continuous and 
unchanging motion around the subject gives an immortality to not only the poem addressing 
the subject but also the subject itself. 
In poem #802 ("Time feels so vast"), the circumference issue is a little foggier for me, 
because it seems to contradict immortality: 

Time feels so vast that were it not
For an Eternity—
I fear me this Circumference
Engross my Finity—

Why would Circumference be so grand that it overcomes the poet's mortality? I would think 
that the opposite of Circumference would cause that result: penetrating into the inner parts of 
the subject would be so daunting and unfulfilling because there would be no way to study 
everything inside that circumference. That inside stuff of the subject would "Engross my Finity" 
rather than the circumferential study, wouldn't it? Hmmm? maybe I need to read this one a 
few more times?
A final thought: Did Dickinson intend for her readers to read her poetry from the 
circumference? This may be a bunk question because we know that Dickinson was not aware 
of the audience she would later capture, but I think that answer would be NO. Her symbols 
make us radiate into various interpretations, and so we must dig a little (or penetrate) into the 
core of that symbol to gather a meaning for ourselves. If she wanted us to gain only a 
circumferential perspective of the poem's subject, then she would have spelled everything out 
for us exactly as she saw it (be more of a Whitman than a Dickinson).