What a grand and glorious doctrine is that of a Surety. I did not become him and he did not become me, yet he took all my sin unto himself and accounted to me the totality of his perfections. The wonder and grace of this is more than I can imagine. This is the glorious purpose that Christ fulfilled as Surety and Substitute on his cross. This is the theme of all true gospel preaching.

1. Imputation is also by way of Suretyship, and it is when the sins or debts of one person, are by law charged upon, or imputed to another in order to the salvation of the principal or personal transgressor. Here it is always understood that the payment of a Surety is as good and acceptable to the law as that of the principal
2. That the Surety cannot become paymaster in law, unless He take the debt or sin upon himself instead of the proper transgressor he being charged himself as transgressor, else the Law can make no demand upon him.
3. He must freely offer himself to be a Surety, for no person can be forced in any case to be the Surety for another.
4. When he hath engaged himself in suretyship, the law takes him person for person, the principal debt becomes his, and his righteousness and payment becomes the principles in a real legal commutation, here is no natural or moral change, but sponsorial and legal, made no logical change, for one relation is not changed into another, the surety into the principal, nor principal into the surety; but in the judgment of the Law the principal debt becomes the Surety's and the Surety's payment is the principals, whereupon the principal in respect of that sin or debt for which satisfaction is made, hath the discharge in full, and is as perfectly righteous as to that, as the Surety himself; he is not it may be so rich and honorable as his surety, but in respect of the debt satisfied, the law hath no more to say to him than to the Surety. - He that bears the sins of others must be a representative and public person, that must personate or bear the persons of them whose sins he bears, and must be either substituted by the court, or if by some other, he must be allowed to be capable and able to make payment, must be accepted and dealt with in the name and upon the account of the other, and becomes a debtor or transgressor in and for the person he doth represent in court, and becomes a delinquent in the eye of the law, the law imputing sin to him makes him sin, because he is supposed to own nothing on his own account; he that doth in market represent one or more, and stands not, nor acts for himself, but others, is a public person and representative. 

Isaac Chauncy {Neonomianism Unmasked 1692}