Maseches Kiddushin, chapter 3, mishnah 6. The mishnah deals with a man who betroths a woman on condition that he will perform some act for her, whether by speaking on her behalf or by doing work for her, and also with a betrothal that depends on her father's consent.
The text of the mishnah:
"Al menas she'adaber alayich la'shilton ve'e'eseh imach kepo'el - diber aleha la'shilton ve'asah imah kepo'el, mekudeshes; ve'im lav, einah mekudeshes" - the case is a man who tells a woman that he has a connection with the government official, and she needs a favor from the authorities. On that basis he betroths her: I will speak with him on your behalf, or I will do work for you as a laborer. If he spoke on her behalf to the official and did work for her as a laborer, she is betrothed; if not, she is not betrothed.
The Gemara's explanation - the perutah effects the betrothal and the work is only a condition:
The Gemara explains that the betrothal takes effect only if, in addition to his speaking with the authorities or doing work for her, he also gives her a perutah. It emerges that the speaking and the work are not the substance of the betrothal but merely a condition, while the betrothal itself takes effect through the perutah.
The reason is this: our mishnah follows the view that when one hires a laborer, the wage is not incurred only at the completion of the work; rather, the obligation accrues progressively from beginning to end, throughout the entire process. Accordingly, as he does the work for her, the debt owed to him keeps accumulating, and by the time he completes his work the sum has already become a loan, something she owes him. It turns out that he is seeking to betroth her with money that she owes him, and one who betroths with a loan accomplishes nothing. For this reason we say that the betrothal takes effect through the perutah, and the speaking with the authorities or the work done for her is merely a condition.
"Al menas sheyirtzeh Abba":
The mishnah continues: one who betroths on condition that her father will consent - "Ratzah ha'av, mekudeshes; lo ratzah, einah mekudeshes" - if the father consented, she is betrothed; if he did not consent, she is not betrothed. The Gemara explains that he does not mean that the father must actively express consent, but rather that the father not object, and he sets a time frame for that objection: if the father does not object within thirty days. Therefore, once thirty days have passed and he has not objected, we know that she is betrothed, since the condition was that he not object within thirty days.
If the father died or the son died:
"Mes ha'av" - if the father died within those thirty days, she is betrothed, since there is no longer any concern that he will object to the betrothal.
"Mes ha'ben" - if the man who betrothed her died within the thirty days, "melamdin es ha'av lomar she'eino rotzeh" - we instruct the father to say that he does not consent. We teach the father to declare that he does not want the betrothal to take effect, and in this way the betrothal will not take effect at all, and the woman will not be bound to the yavam. For otherwise, in a case where the husband had no children, she would require chalitzah or yibum, and a problem could arise from that. To avoid this, we encourage the father to object, and through his objection she will not have been married.
In summary: in this mishnah we learned that a betrothal made conditional on speaking with the authorities or on doing work as a laborer takes effect through the perutah alone, while the act itself is nothing more than a condition, since a laborer's wage is incurred progressively as the work proceeds, and by its completion it is a loan, and one who betroths with a loan has not effected a betrothal. We also learned that "al menas sheyirtzeh Abba" means that the father not object within thirty days, and we examined the two cases: if the father died, she is betrothed, and if the son died, we instruct the father to object in order to remove the bond of yibum.