Medhātithi’s commentary (manubhāṣya):
She who has no brother,—such a girl one should not marry,—‘for fear of her having, the character of the appointed daughter;’ i.e., by reason of her being an ‘appointed daughter;’ i.e., by reason of there being the doubt that the girl’s father might have performed those rites that would have made her an ‘appointed daughter.’
“Why should such a doubt arise at all?”
Such a doubt would arise if the girl’s father is not known, having died or having gone away to a foreign country. Under such circumstances, the girl is given away in marriage either by her mother or by other members of her father’s family. Since it is laid down that when the girl has reached the marriageable age, if her father happen to be absent, she shall be given away in marriage by the said relations.’ The exact rule on this point we shall quote later on. If the father is known, however, there is no fear of the girl being an ‘appointed daughter as he will himself declare whether or not she has been ‘appointed.’
‘Or’ in the text should be taken in the sense of ‘if;’ the sense being that ‘if the father is not known, the girl should not be married.’
Others have taken the two clauses as formulating two independent prohibitions: (a) ‘If the father is not known’—i.e., if it is not known from whom she is born; this being a prohibition of marrying the girl of unknown parentage;—and (b) the next prohibition is to be construed as ‘one should not marry the girl who has no brother, for fear of her being an appointed daughter.’ They further point out that the latter phrase, ‘for fear of her being an appointed daughter,’ cannot be construed with the clause, ‘if her father is not known.’
In the whole of this section on Marriage, wherever the prohibition is not based upon grounds that are not perceptible—e.g., ‘one should marry a maiden who is not his father’s sapiṇḍa,’ etc., (when the grounds of interdiction are trascendental, not perceptible, as in the case of the prohibition of marriage with a diseased girl, etc.),—if the prohibition is disobeyed, the ‘marriage’ itself remains unaccomplished. Hence, if one happens to marry a girl belonging to the same gotra as himself, the marriage, even though performed, would be as good as not performed; and this for the simple reason that the character of ‘marriage’ is determined by scriptural injunction,—just like the character of the ‘Fire-laying’ rite; and, hence, a transgression of the injunction means the non-accomplishment of -the Rite. In the case of Fire-laying, it is found that if there is omission of any subsidiary detail, the Āhavanīya’ and other ‘Fires’ are not accomplished; similarly, a girl that belongs to the same ‘gotra’ as a man can never become the ‘wife’ of that man. Hence it has been ordained that such a girl, even though she may have gone through the sacramental rites, shall be given up. Further, in connection with such marriages, Vaśiṣṭha and other revered writers have prescribed specie lexpiratory rites. Even though, in reality, what each a marriage involves is only a discrepancy in the Rite caused by the transgression of one of the interdictions relating to a subsidiary detail,—and it does not involve any sin on the part of the man,—yet the Expiratory Rite has to be performed, in view of its being directly enjoined by the scriptures. Or, we may take it thus that what is prohibited is ‘intercourse’ with a girl of the same ‘gotra,’ and the Expiatory Rite relates to the series of acts perpetrated by the man (in the form of the marriage-ceremonies.)
As regards the prohibition of marriage with girls belonging to families that may have dropped the sacred rites and so forth,—it is based upon perceptible grounds; and, hence, when such girls are married, the ‘marriage’ is duly accomplished, the girl actually becomes the man’s ‘wife,’ and she shall not be given up. It is in view of this fact that in verse 6, we have the laudatory epithet ‘even though they be great,’ which draws a line of distinction between the two sets of prohibitions. Such also is the custom among all cultured people: they do occasionally marry girls ‘with tawny hair,’ etc., but never one that belongs to the same gotra.—(11)
Having posted the above, I would like to add the following:
According to Rig Veda, Manu lived much earlier to Sage Viswamitra, who composed Mandala III. So he was as old as the Rig Veda, which period cannot be established with certainty.
Edit 22-12-19
Rig Veda III.31.1 speaks about a sonless person, who takes care of his grandson, a son of his daughter. As Manu existed before Sage Viswamitra, who composed this mantra, this rule 3.11 from Manu Smriti must be an interpolation.
WISE, teaching, following the thought of Order, the sonless gained a
grandson from his daughter. Fain, as a sire, to see his child
prolific, he sped to meet her with an eager spirit.
