In his lecture to Vāli, which Manu-smṛti verses is Rāma talking about?

Question

From here, Rāma, in his lecture to Vāli, defending his actions, mentions the following two verses from Manu-smṛti. Which exact verses (ch. and verse no.) from Manu is Rāma referring to?

'When kings impose proper punishment on the humans who have sinned, they become sinless and enter heaven as with the pious souls with good deeds.' So says one verse of Manu. [4-18-31]

'Either by punishment or by clemency a thief will be absolved from sin, but the king who does not impose proper punishment will derive the blot of that sin.' So says the other verse of Manu. [4-18-32]

Answer 1

Rāma is referring to these two verses from the Manu-smṛti:

राजभिः कृतदण्डास् तु कृत्वा पापानि मानवाः ।
नि-र्मलाः स्वर्गम् आयान्ति सन्तः सुकृतिनो यथा ॥ ८-३१८

8.318. But men who have committed crimes and have been punished by the king, go to heaven, being pure like those who performed meritorious deeds.

 

शासनाद् वा विमोक्षाद् वा स्तेनः स्तेयाद् विमुच्यते ।
अशासित्वा तु तं राजा स्तेनस्य-अन्पोति किल्बिषम् ।। ८-३१६

8.316. Whether he be punished or pardoned, the thief is freed from the (guilt of) theft; but the king, if he punishes not, takes upon himself the guilt of the thief.