Bekhorot 40A

בשושן הבירה, אחת על קרן מזרחית צפונית ואחת על קרן מזרחית דרומית, שעל קרן מזרחית צפונית היתה יתירה על של משה חצי אצבע, ושעל קרן מזרחית דרומית היתה יתירה עליה חצי אצבע, נמצאת יתירה על של משה אצבע.

in the chamber of Shushan the capital, which was located above the eastern gate of the Temple Mount, one in the northeast corner and one in the southeast corner. The one that was in the northeast corner was longer than the cubit used by Moses in the building of the Tabernacle, which was 6 handbreadths, by half a fingerbreadth, and the one that was in the southeast corner was longer than the other one by another half a fingerbreadth. One therefore finds it longer than Moses’ cubit by a full fingerbreadth.

ולמה היו אחת גדולה ואחת קטנה? (כשהיו) [שהיו] אומנין נוטלין בקטנה, ומחזירין בגדולה, שלא יבואו לידי מעילה.

The Mishnah continues: And why did the rabbis say that there should be two measures of a cubit, one large and one small? It was so that the artisans who were working in the Temple would take payment according the amount of work they did, as measured by the small cubit, and return it to the Temple through their work, as measured by the large cubit, so they would not come to misuse consecrated property. If they would accept any payment that they did not deserve, they would be misusing consecrated property. It was with regard to the fingerbreadth mentioned in this Mishnah that the baraita cited above teaches that it is 1/4th of a handbreadth of any average person.

תרתי למה לי? חדא ⁠— דכספא וזהבא, וחדא ⁠— דבניינא.

The Talmud asks: Why do I need two large cubits? The Talmud answers: One, the shorter of the two, was used to measure silver and gold. Since silver and gold were valuable, the difference between the two measurements was set at only half a fingerbreadth, so that the artisans would not suffer too great a loss. And the other one, which was longer than Moses’ cubit by a full fingerbreadth, was used in the construction of wood and stone structures.