As for the qāḍiya cubit—also called the house-measuring cubit—it is shorter than the sawdāʾ cubit by one and two-thirds fingers. The first to establish it was the judge Ibn Abī Laylā, and it is the measure used by the people of Kalwādhā.
As for the Yūsufiyya, it is the cubit by which judges measure houses in the City of Peace. It is shorter than the sawdāʾ cubit by two-thirds of a finger, and the first to establish it was the judge Abū Yūsuf.
As for the sawdāʾ cubit, it is longer than the house cubit by one and two-thirds fingers. The first to establish it was al-Rashīd, who based it on the cubit of a black servant in his service. It is the measure commonly used for measuring textiles, commercial goods, buildings, and the level of the Nile in Egypt.
As for the lesser Hāshimiyya cubit, it is longer than the sawdāʾ cubit by two and two-thirds fingers. The first to introduce it was Bilāl ibn Abī Burda, who stated that it was the cubit of his grandfather, Mūsā al-Ashʿarī. It is shorter than the Ziyādiyya cubit by three-quarters of a tenth, and it is the measure used by the people of Basra and Kufa.
As for the greater Hāshimiyya cubit, it is the royal cubit. The first to transfer it to the Hāshimiyya standard was al-Manṣūr. It is longer than the sawdāʾ cubit by five fingers and two-thirds of a finger; measured in sawdāʾ cubits, it amounts to one cubit, one-eighth, and one-tenth. Measured against it by the lesser Hāshimiyya cubit, it falls short by three-quarters of a tenth. It was called the Ziyādiyya because Ziyād used it to survey the lands of al-Sawād. It is the measure used by the people of al-Ahwāz.
As for the ʿUmariyya cubit, it is the cubit of ʿUmar ibn al-Khaṭṭāb, may Allah be pleased with him, with which he surveyed the lands of al-Sawād. Mūsā ibn Ṭalḥa said, “I saw ʿUmar’s cubit, with which he surveyed the lands of al-Sawād: a cubit, a handspan, and an upright thumb.” Al-Ḥakam ibn ʿUtayba said, “ʿUmar, may Allah be pleased with him, took the longest and the shortest of them, combined three of them, took one-third of the result, and added to it a handspan and an upright thumb. He then capped both ends with lead and sent it to Ḥudhayfa and ʿUthmān ibn Ḥunayf, so that they could survey al-Sawād with it. The first to survey with it was ʿUmar ibn Hubayra.”
As for the Maʾmūniyya cubit, in terms of the sawdāʾ cubit it measures two cubits, two-thirds of a cubit, and three fingers. The first to establish it was al-Maʾmūn. It is the measure used for measuring verandas, dams, river dredging, and excavations. Our jurists used the Hāshimiyya cubit when calculating the distance of the farsakhs at which prayer may be shortened.
As for the dirham, it is necessary to know both its weight and its monetary standard. As for its weight, it was established in Islam that a dirham weighs six dāniqs, and that ten dirhams weigh seven mithqals. This was explicitly stated in the discussion of zakat in the narration of al-Maymūnī. He asked him about a man who possessed some coins weighing one black dirham and others weighing two dāniqs, such coins being issued in different places: “Are these, despite their deficiency, equal according to the standard weight?” He replied, “Combine them, then pay them according to the seven-mithqal standard.”