The Earth is spherical and its centre is the centre of the Universe. The elevations and depressions caused by the action of water or violence of the winds do not affect its spheroidity. Its circumference is 5,059 yojana,* 2 kos, 1,154 daṇḍ. The ancient Greeks reckoned the circumference to be 8,000 farsakh* and its diameter 2,5455/11 farsakh. Modern geometers give 6,700 farsakh for the circumference and 2,1637/11 farsakh for the diameter. All concur in making one farsakh equal to 3 miles.

The Hindu philosophers have the following rule for determining the diameter and circumference To find the circumference. Multiply the given diameter which they call biyáṇs* by the multiplier 3,927 termed guṇit,* and divide the product by the divisor 1,250 called bhág;* and the quotient, labdhi* will be the circumference.* To find the diameter. Mul­tiply the given circumference by 1,250 the former divisor, and divide the product by 3,927, the former multiplier, and the quotient will be the diameter. The rule of Archimedes as given in Greek works, is accepted by the Hindus in the same manner, as an approximate calculation. The gist of the rule is that the relation of the diameter to the circumference is the ratio of 7: 22, or about thrice the diameter and one-seventh. Any given diameter is multiplied by 22, and divided by 7, the quotient being the circumference. Again the circumference multiplied by 7 and divided by 22 gives the diameter. The fraction, however, is really less than 1/7 and greater than 10/71.* It is evident that the Hindu rule was unknown to the Greeks or they would have vaunted it in their own praise. Glory be to Him who alone knoweth the relation of the diameter to the circumference.

Now the method of ascertaining the diameter of the (earth's) circum­ference was after this manner. On a level plain by means of instruments like the astrolabe, the armillary sphere or the quadrant of altitude, taking the elevation of the north pole of the Equinoctial, they proceed northwards, or southwards on the meridian line guided by the astrolabe, and raise the vertical indices above the plane of the circle so that they cover one another. And thus a distance is traversed which exceeds, or is less than the elevation above-mentioned by one degree. If the advance be to the north, it will increase; if to the south, the reverse. The distance from beginning to end is measured and the result forms a degree. Thus the circumference is found.

The ancients by this operation found the degree to be 22 farsakh and 2/9 or 66⅔ miles. When the plain of Sanjár near Mausil, was selected by the Caliph Al Mámún for this experiment, Khálid-b.-Abdu'l Malik Marwarúdi with a body of scientific men went towards the north, and Ali.-b.-Isá Uṣṭurlábi with another to the south. The former party found the degree longer than the latter; for when each had measured their respective dis­tances, it was found to be 188/9 farsakh or 56⅔ miles. The difference between the two was ⅔ of a mile.* Mámún as a test, asked the two parties the distance between Mecca and Baghdad. According to the above calcula­tion, multiplying 12° 40' by 56⅔ miles which is a degree, they made the dis­tance to be 720 kos.* By the order of the Caliph the most level and short­est route between the two cities was measured and the difference was found to be slight. It is strange that the accurate (Naṣíru'ddín) Ṭúsi in his Taḍkirah (u'l Náṣiríyah. Liber Memorialis de astronomia) should ascribe to the ancients what is related of the astronomers of Mámún's age regarding the measurement of a degree in the plain of Sanjár. Mulla Ḳuṭbu'ddín Shirázi* in his Tuḥfat (u'l Sháhíyah donum regium) and other works, expresses the opinion of the moderns in regard to the astronomers of that Caliph, in the manner I have related. There has been undoubtedly a slip of the pen in the Taḍkirah. The Hindu astronomers make the degree 14 yojanas, 436 ḍanḍ, 2 cubits and 4 digits, and explain it after the former manner.

Also on a level plain at sunrise they regulate the course of ghaṛís by means of the Siktajantra which is an instrument like an hour-glass, measured for 60 ghaṛís. With this they walk eastwards. After 84 yojanas and a fraction, there is a difference of one ghaṛí and the day advanced by that time.* This multiplied by 60 gives the circumference of the Earth.