अस्यावश्यकत्वे हेतुःWhy they are needed
Verse 5
शूद्राणां शूद्रभिन्नानामुपवीतं न विद्यते । तेषां नवैव संस्कारा द्विजातीनां दश स्मृताः ॥ ५ ॥
śūdrāṇāṁ śūdrabhinnānāmupavītaṁ na vidyatē | tēṣāṁ navaiva saṁskārā dvijātīnāṁ daśa smṛtāḥ || 5 ||
Translation
Śūdras and those other than śūdras have no sacred thread; for them there are only nine sacraments. For the twice-born, ten are laid down.
Word by word
- śūdrāṇāṁ
- of the śūdras
- śūdra
- from the śūdras
- bhinnānām
- (bhinnānām) of those other than; the mixed class
- upavītaṁ
- the sacred thread
- na
- not
- vidyatē
- exists
- tēṣāṁ
- for them
- nava
- nine
- ēva
- only
- saṁskārāḥ
- (saṁskārāḥ) sacraments
- dvijātīnāṁ
- for the twice-born
- daśa
- ten
- smṛtāḥ
- are laid down
Meaning
The difference between the classes in this matter. The sacred thread (upavīta), given at the investiture, belongs to the three twice-born classes, brāhmaṇa, kṣatriya and vaiśya, who therefore have all ten sacraments. The śūdras, and "those other than śūdras", whom the commentary explains as the mixed class (varṇa-saṅkara, the fifth class of the Kali age named in chapter 8), have no thread and so nine sacraments. As verse 184 will add, their sacraments are performed without Vedic mantras. This is the text's own ordering of the classes.

Commentary
Hariharānanda Bhāratī’s Sanskrit commentary, translated
"Śūdrabhinnānām": of those of mixed class (varṇasaṅkara). "Teṣām": of the śūdras and of those other than śūdras (the mixed). "Dvijātīnām": of brāhmaṇas, kṣatriyas and vaiśyas.