It might help if you look at the possible meanings of both words - ‘balk’ and ‘account’.
‘Balk’ has a range of meanings, and they might seem quite different; however, as is often the case, the etymology of the word offers an interesting interconnecting link.
Here is the OED on the origin of ‘balk’:
Common Germanic, presenting several variant stems, with partial
differentiation of sense: Old English balca ridge, bank = Old Frisian
balca, Old Saxon balco, Middle Dutch balke, balc, Dutch balk, Old
High German balcho, balco, Middle High German balke, German balken
‘beam, trabs’, also Old English bolca ‘gangway of a ship’, and Old
Norse bjalki (Swedish biælke, bielke, Danish bjelke) ‘beam’,
corresponding respectively to a Germanic ablaut-series *balkon- ,
*bolkon- , *belkon- ; also Old Norse bálkr, bǫ́lkr, ‘beam, bar, partition, division’, Old Swedish balker, bolker, Swedish balk
‘beam, balk, partition, section of a law’ < Germanic *balku-z . Old
English balc ‘porca’ (see 3), is either an error for balca, or = Old
Norse bálkr. The relation of Old English bælc ‘covering (? flooring)’
is doubtful. The original sense was perhaps ‘bar’; compare Latin
suf-fla(g)men, < Aryan *bhalg-, bhlag- . The Old English balca (balc)
and Old Norse bálkr appear to be combined in the Middle English;
whether the latter distinguished balke and balk, the evidence does
not show. Balk is the analogous spelling: compare stalk, talk, walk,
etc.; but baulk is frequent, and in Billiards (sense 9) the
prevailing spelling.
Here is the OED on the usage of ‘balk’:
- Senses relating to ploughing: To make balks in ploughing; to plough
up in ridges. (This sense is now obsolete.)
- Senses relating to missing or avoiding, overlooking, refusing,
letting slip, and stopping short at an obstacle.
1783 Ainsworth's Thes. Linguæ Latinæ (new ed.) at Balk I will not
balk your house;
1848 L. Hunt Jar of Honey Pref. 4 No topic is
baulked if it come uppermost.
a1784 S. Johnson in Boswell Life Johnson (1831) I. 236 I
never ... balked an invitation out to dinner.
1826 H. Smith Gaieties & Gravities in C. Gibbon Casquet of Lit.
(1877) I. 326/2 My adviser insisted upon my not baulking my luck.
1862 Melbourne Leader 5 July His horse balked at a leap, and
threw him.
- Senses relating to checking or thwarting: to check, hinder,
thwart (a person or his action); to check (feelings, or a person in
his feelings); to frustrate, foil, render unsuccessful.
1821 Ld. Byron Two Foscari i. i, in Sardanapalus 195 They shall
not balk my entrance.
1746 Earl of Malmesbury Lett. I. 37 Lord Talbot was not much
baulked with this rebuke.
1873 H. Spencer Study Sociol. vii. 161 Time after time our hopes
are balked.
1848 C. Kingsley Saint's Trag. ii. v. 90 With which we try to
balk the curse of Eve.
Here is the OED on the usage of ‘account’:
- Senses relating to counting, enumerating, or calculating numerically
- Senses relating to accounting for money paid and received
- Senses relating to a statement of money held, etc., and related
senses, for instance, a statement as to the discharge of
responsibilities generally; an answering for conduct
- Senses relating to estimation, consideration
- Senses relating to narration, relation
The first three senses might be well understood; for the last two senses, here are some examples from the OED:
1920 J. Sargeaunt Trees, Shrubs, & Plants of Virgil 46 The kind
[of spelt] called ‘rutilum’ had ... a reddish grain, and was held in less
account.
1992 B. Unsworth Sacred Hunger xxvii. 264 Anyone that has not
these marks they look on as of no account.
1953 V. Nabokov Let. 2 May in Sel. Lett. (1989) 137 I wonder if
your account of your trip will make me Europe-sick, or at least
France-sick.
2009 P. Glennie & N. Thrift Shaping Day ii. 56 Our contention ... is
that Martin's omission of the clock from his account of church and
parish life provides a specific instance of the
‘taken-for-grantedness’ of timekeeping.
2004 HMV Choice Mar. 30/2 Viennese pianist Fellner's account of
the opening Prelude In C Major is, accordingly, songful and
mellifluous.
Perhaps, Whitman’s intended meaning could be interpreted through usage in senses related to thwarting, checking, foiling, frustrating for ‘balk’ and in senses related to consideration, narration, relation for ‘account’.
The love of the body of man or woman balks account, the body itself
balks account, That of the male is perfect, and that of the female is
perfect. The expression of the face balks account,
Is Whitman telling us that he feels that the nature of love of the body and the nature of the body itself frustrate all attempts to give them a full description? In the preceding part of the poem Whitman asks the questions:
Was it doubted that those who corrupt their own bodies conceal
themselves? And if those who defile the living are as bad as they who
defile the dead? And if the body does not do fully as much as the
soul? And if the body were not the soul, what is the soul?
Perhaps, in Whitman’s view, these questions ‘balk account’, or frustrate attempts to find answers to them.
It may be impossible to define the body, but it is possible to observe people and see manifestations of the nature of the human body in people's behaviour; Whitman describes people and their bodies in the remainder of the poem - for instance:
The bending forward and backward of rowers in row-boats, the
horse-man in his saddle, Girls, mothers, house-keepers, in all their performances,
It is important to remember that we can explore the meaning of words and their etymologies, and attempt to interpret the writer’s intentions, however, at some point, we enter into the territory where the reader must make his or her own decisions as to what the writer’s words mean for him or her.
A Framework for 'why this choice of phrasing'
Sometimes, examining how an author uses a particular word across his/her works might give a deeper insight into his possible intended meaning, as there may be unique patterns in his usage that might offer clues as to what significance any particular word may have held for him. Here are a few other examples of the use of ‘balk’ in Whitman works:
The shaved face, the unsteady eye, the impure complexion, if these
balk others they do not balk me
No danger shall balk Columbia’s lovers, If need be a thousand shall
sternly immolate themselves for one.
Nor will I allow you to balk me any more with what I was calling life,
For now it is convey’d to me that you are the purports essential
Other instances of use of balk, balks, balk’d in Whitman’s works can be found here: balks;
balk;
balk'd.
P.S. For the sake of completeness, here is the OED on the origin of ‘account’:
Anglo-Norman acunt, acunte, acount, acounte, account, accompt, Anglo-Norman and Old French acont, Anglo-Norman and Old French, Middle French aconte, Anglo-Norman and Middle French acompte, accompte financial statement or record, rendering of accounts (12th cent.), calculation, reckoning, claim, mention, reason, narrative, (in law) action of account, plea in an action (all 13th cent.), worth, importance (16th cent. or earlier), probably < a- a- prefix5 + conte, cunte count n.1
P.P.S. Probably that "couple of non-reliable sources" that claim "it means "cannot be described"" are not particularly "non-reliable":)
