Adam Clarke on Exodus 24:7

The book of the covenant - The writing containing the laws mentioned in the three preceding chapters. As this writing contained the agreement made between God and them, it was called the book of the covenant; but as no covenant was considered to be ratified and binding till a sacrifice had been offered on the occasion, hence the necessity of the sacrifices mentioned here.

Half of the blood being sprinkled on the Altar, and half of it sprinkled on the People, showed that both God and They were mutually bound by this covenant. God was bound to the People to support, defend, and save them; the People were bound to God to fear, love, and serve him. On the ancient method of making covenants, see Clarke on Gen 6:18 (note); and see Clarke on Gen 15:18 (note). Thus the blood of the new covenant was necessary to propitiate the throne of justice on the one hand, and to reconcile men to God on the other. On the nature and various kinds of the Jewish offerings, see Clarke's note on Lev 7:1, etc.