(1) A contract may originate in the offer of a promise, and its acceptance by simple assent, but this applies only to contracts under seal, for, as will presently be seen, the law requires a consideration to support a promise not under seal, and mere assent is not enough. Thus, where one person promises another by writing under seal that he will do a certain thing, or pay a certain sum, and the promisee assents to the proposal, both are bound, and there is a contract.2

(2) As already shown, the presence of a public conveyance on the street is a constant offer by its proprietor to carry persons, and when a person steps into the conveyance he accepts the offer, and promises to pay the fare. This is an offer of an act for a promise.

(3) If a person who has lost property offers by advertisement a reward to any person who shall return it, he offers a promise for an act, and when a person returns the property he accepts and performs the act, and the promise becomes binding.

2 As to offers and contracts under seal, see post, pp. 62 et seq.

(4) If a person offers another to pay him a certain sum on a future day if the latter will promise to perform certain services for him before that day, or, vice versa, he offers a promise for a promise, and where the person to whom the offer is made accepts it by promising to perform the services or to pay, as the case may be, both parties are bound, the one to do the work and the other to make the payment. This is the offer of a promise for a promise.

A contract in which there is an offer of a promise for an act is sometimes called a "unilateral" contract, because there is a subsisting obligation on the part of only one party; and it is distinguished from a contract consisting of an offer of a promise for a promise, which is said to be "bilateral" because imposing an existing obligation on each party.3