Is line 3 of Household in its correct place?

It is in its correct place (當位): a yang line in an odd position or a yin line in an even one, which the tradition reads as a line at ease where it stands.

Hexagram 37, line 3

九三Line 3 of Household

Nine in the third place · 家人 jiā rén

sternnesslaughter and chatterlosing measure

爻辭 The line text

家人嗃嗃，悔厲吉；婦子嘻嘻，終吝。

The third line, undivided, shows its subject (treating) the members of the household with stern severity. There will be occasion for repentance, there will be peril, (but) there will (also) be good fortune. If the wife and children were to be smirking and chattering, in the end there would be occasion for regret.

Its symbolism

家人嗃嗃，未失也；婦子嘻嘻，失家節也。

When 'the members of the household are treated with stern severity,' there has been no (great) failure (in the regulation of the family). When 'wife and children are smirking and chattering,' the (proper) economy of the family has been lost.

In plain words

The members of the household are treated with harsh severity: regret and danger, but good fortune. The wife and children giggle and chatter: in the end, regret. Line three is yang in a yang place at the top of Li, fire, and it corresponds to nothing — line six is yang too — so its hardness has no softening partner. The text weighs two failures and prefers the first. The small Image explains: severity 'has not lost' the family's order (未失), whereas laxity 'has lost the household's measure' (失家節). Too strict a house is uncomfortable; a house without any measure comes apart.

If this line is changing

If you must err, err on the side of firmness and then soften; a household or a team that has lost all sense of measure is harder to recover than one that was too strict.

Where the line stands

A solid line, yang — written 九 (nine), the number of an old yang line that moves when cast.
It is in its correct place (當位): a yang line in an odd position or a yin line in an even one, which the tradition reads as a line at ease where it stands.
It belongs to the lower trigram 離 Li (the Clinging) (fire).
It has no correspondence (無應) with line 6: both lines are yang, so this line must find its support in its neighbours or in itself.

之卦 When this line moves

家人 Household becomes ䷩ 42 益 Augmenting

Wind and thunder strengthening each other: increase. Favourable to undertake something and to cross the great river; those above give to those below, and everyone rejoices.

What it becomes42 · 益 Augmentingyì

The six lines of 家人 Household

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Love and relationships Work and career A yes-or-no decision

Questions about this line

What does Nine in the third place of hexagram 37, Household, mean?: The members of the household are treated with harsh severity: regret and danger, but good fortune. The wife and children giggle and chatter: in the end, regret. Line three is yang in a yang place at the top of Li, fire, and it corresponds to nothing — line six is yang too — so its hardness has no softening partner. The text weighs two failures and prefers the first. The small Image explains: severity 'has not lost' the family's order (未失), whereas laxity 'has lost the household's measure' (失家節). Too strict a house is uncomfortable; a house without any measure comes apart.
What does hexagram 37 become when line 3 changes?: Household becomes hexagram 42, 益 Augmenting: Wind and thunder strengthening each other: increase. Favourable to undertake something and to cross the great river; those above give to those below, and everyone rejoices.
Is line 3 of Household in its correct place?: It is in its correct place (當位): a yang line in an odd position or a yin line in an even one, which the tradition reads as a line at ease where it stands.

Cast a reading Hexagram 37 in full Changing lines explained

Chinese text: the received Zhouyi (Wuyingdian lineage). English: James Legge, The Yî King, Sacred Books of the East XVI, 1882 (public domain).