For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people, When Moses had spoken every precept - The place to which the apostle alludes is Exodus 24:4-8, where the reader is requested to consult the notes.
And sprinkled both the book - The sprinkling of the book is not mentioned in the place to which the apostle refers, (see above), nor did it in fact take place. The words αυτο τε το βιβλιον, and the book itself, should be referred to λαβων, having taken, and not to ερῥαντισε, he sprinkled; the verse should therefore be read thus: For after every commandment of the law had been recited by Moses to all the people, he took the blood of the calves, and of the goats, with water and scarlet wool, and the book itself, and sprinkled all the people. The rite was performed thus: Having received the blood of the calves and goats into basins, and mingled it with water to prevent it from coagulating, he then took a bunch of hyssop, and having bound it together with thread made of scarlet wool, he dipped this in the basin, and sprinkled the blood and water upon the people who were nearest to him, and who might be considered on this occasion the representatives of all the rest; for it is impossible that he should have had blood enough to have sprinkled the whole of the congregation.
Some think that the blood was actually sprinkled upon the book itself, which contained the written covenant, to signify that the covenant itself was ratified by the blood.